This document provides an introduction to risk management and financial derivatives. It discusses the concepts of risk, risk management strategies, and three fundamental types of financial derivatives: forward contracts, futures, and options. The key topics covered are:
1) Risk management uses financial derivatives to hedge against price changes in underlying assets.
2) Forward contracts, futures, and options are described as different types of agreements to buy or sell underlying assets at a future time.
3) Option pricing models are needed to determine the value of options, which depend on the price of the underlying asset. Finding these models is the main subject of the book.
This document defines options terminology and provides explanations of key concepts related to options contracts, including:
- An option contract gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a specified date.
- Key parties are the option buyer/holder and option writer/seller. The writer receives a premium from the buyer in exchange for undertaking the obligation.
- Important terms include the exercise/strike price, premium, expiration/exercise dates, and classifications of options as in, out, or at-the-money.
- The value of an option has two components - intrinsic value and time value - which are influenced by factors like the underlying
This document provides an overview of options and their valuation. It defines key terms like calls, puts, exercise price, underlying asset, and premium. It describes the differences between European and American options and possibilities at expiration like in-the-money, out-of-the-money, and at-the-money. The document outlines the payoffs of call and put options at expiration. It also discusses options trading in India, index options, and combinations of options and shares. Finally, it introduces models for option valuation, including the binomial tree approach and the Black-Scholes model.
This document summarizes key concepts related to derivatives and risk management. It discusses forwards, futures, swaps, and options contracts. It explains how forwards, futures, and swaps work to transfer risk, while options provide choice. The cost-of-carry model for pricing forwards is described. Forward rate agreements are introduced as interest rate derivatives. Forward exchange rates are projected using interest rate parity.
Derivatives are financial instruments whose value is dependent on an underlying asset such as a commodity, currency, stock, bond, or market index. Common derivative products include forwards, futures, options, and swaps. Forwards involve a customized over-the-counter agreement to buy or sell an asset in the future at an agreed upon price, while futures trade on an exchange with standardized contracts. Options provide the right but not the obligation to buy or sell the underlying asset at a predetermined strike price by a specified date. The value of derivatives is influenced by factors like the price and volatility of the underlying asset.
This document provides an introduction to options, including the different types (calls and puts), how they work, key terminology, and factors that influence pricing. An option gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before expiration. The buyer pays a premium to the seller for this right. Key terms discussed include strike price, expiration date, and long/short positions. Factors like time to expiration, volatility, and interest rates impact an option's price. The Black-Scholes model is commonly used to price options based on these variables.
Financial derivatives are financial instruments linked to an underlying asset or indicator. Derivatives allow parties to trade financial risks independently from owning the underlying asset. There are several types of derivatives, including futures, forwards, options, and swaps. Futures are standardized forward contracts traded on an exchange. Options give the holder the right but not obligation to buy or sell the underlying asset. Swaps involve exchanging cash flows between two parties over time based on a notional principal amount. Derivatives are used by hedgers, speculators, and arbitrageurs to manage risk, seek profit, and exploit pricing discrepancies.
The document discusses various types of derivatives instruments used to manage financial risk, including forwards, futures, options, and swaps. It provides examples of how these derivatives are used to hedge risks related to commodities, interest rates, currencies, equities, indexes, and other underlying assets. The key types of derivatives discussed are over-the-counter contracts and exchange-traded contracts, along with examples of each like forwards, futures, and options.
This document defines options terminology and provides explanations of key concepts related to options contracts, including:
- An option contract gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a specified date.
- Key parties are the option buyer/holder and option writer/seller. The writer receives a premium from the buyer in exchange for undertaking the obligation.
- Important terms include the exercise/strike price, premium, expiration/exercise dates, and classifications of options as in, out, or at-the-money.
- The value of an option has two components - intrinsic value and time value - which are influenced by factors like the underlying
This document provides an overview of options and their valuation. It defines key terms like calls, puts, exercise price, underlying asset, and premium. It describes the differences between European and American options and possibilities at expiration like in-the-money, out-of-the-money, and at-the-money. The document outlines the payoffs of call and put options at expiration. It also discusses options trading in India, index options, and combinations of options and shares. Finally, it introduces models for option valuation, including the binomial tree approach and the Black-Scholes model.
This document summarizes key concepts related to derivatives and risk management. It discusses forwards, futures, swaps, and options contracts. It explains how forwards, futures, and swaps work to transfer risk, while options provide choice. The cost-of-carry model for pricing forwards is described. Forward rate agreements are introduced as interest rate derivatives. Forward exchange rates are projected using interest rate parity.
Derivatives are financial instruments whose value is dependent on an underlying asset such as a commodity, currency, stock, bond, or market index. Common derivative products include forwards, futures, options, and swaps. Forwards involve a customized over-the-counter agreement to buy or sell an asset in the future at an agreed upon price, while futures trade on an exchange with standardized contracts. Options provide the right but not the obligation to buy or sell the underlying asset at a predetermined strike price by a specified date. The value of derivatives is influenced by factors like the price and volatility of the underlying asset.
This document provides an introduction to options, including the different types (calls and puts), how they work, key terminology, and factors that influence pricing. An option gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before expiration. The buyer pays a premium to the seller for this right. Key terms discussed include strike price, expiration date, and long/short positions. Factors like time to expiration, volatility, and interest rates impact an option's price. The Black-Scholes model is commonly used to price options based on these variables.
Financial derivatives are financial instruments linked to an underlying asset or indicator. Derivatives allow parties to trade financial risks independently from owning the underlying asset. There are several types of derivatives, including futures, forwards, options, and swaps. Futures are standardized forward contracts traded on an exchange. Options give the holder the right but not obligation to buy or sell the underlying asset. Swaps involve exchanging cash flows between two parties over time based on a notional principal amount. Derivatives are used by hedgers, speculators, and arbitrageurs to manage risk, seek profit, and exploit pricing discrepancies.
The document discusses various types of derivatives instruments used to manage financial risk, including forwards, futures, options, and swaps. It provides examples of how these derivatives are used to hedge risks related to commodities, interest rates, currencies, equities, indexes, and other underlying assets. The key types of derivatives discussed are over-the-counter contracts and exchange-traded contracts, along with examples of each like forwards, futures, and options.
Derivatives derive their value from underlying assets such as stocks, commodities, currencies, and bonds. The main types of derivatives are forwards, futures, and options. Forwards involve an obligation for both parties to fulfill the contract terms at a future date. Futures are standardized contracts traded on an exchange with high liquidity. Options confer the right but not obligation to buy or sell the underlying asset at a strike price by an expiry date. Key participants in derivatives markets include speculators, hedgers, and arbitrageurs. Common derivatives strategies involve futures arbitrage, hedging, and using options spreads. Greeks like delta and gamma help analyze how option prices change with movements in the underlying asset.
Derivatives derive their value from underlying assets. There are various types including forwards, futures, options, and swaps. Forward contracts are bilateral agreements to buy or sell an asset in the future at predetermined terms. Futures are standardized forward contracts that are traded on an exchange. Options provide the right but not obligation to buy or sell an asset by a specified date. Swaps involve exchanging cash flows of underlying assets like interest rates or currencies. Derivatives allow participants to hedge or speculate on price movements of the underlying assets.
This document provides an introduction and overview of financial derivatives. It discusses the key types of derivatives like forwards, futures, and options. It defines derivatives as financial instruments whose value is based on an underlying asset. Forwards are customized over-the-counter contracts while futures are exchange-traded with standardized terms. Options provide the right but not obligation to buy or sell the underlying asset. The document also covers hedging strategies using derivatives and the factors that affect option pricing.
The document discusses key concepts related to options pricing including: the minimum and maximum value of a call option; factors that affect call prices such as exercise price, time to maturity, interest rates, and stock volatility; the difference between American and European style options; and the potential early exercise of American call options on dividend and non-dividend paying stocks.
This document provides an introduction to option contracts, including definitions, key features, advantages and disadvantages, and types of options. It discusses call and put options, as well as European and American options. Key terminology for options like long, short, strike price, in-the-money, out-of-the-money, and at-the-money are also explained. The document is intended to provide a basic understanding of stock options and how they can be used.
This document defines and explains options contracts. It discusses that an options contract is an agreement that gives the buyer the right, but not the obligation, to buy or sell an asset at a future date at an agreed upon price. It outlines key features of options contracts including the underlying instrument, contract size, premium, strike price, and expiration date. It also defines put and call options and discusses concepts like moneyness, intrinsic and time value, and examples of calculating these values. Finally, it covers advantages like making money and hedging risk, and disadvantages like options being a wasting asset and complexity.
Risk Management Using Derivatives in Financial Planning Journal by Gaurav K B...Corporate Professionals
Derivatives can be used effectively for risk management purposes such as hedging currency, commodity price, interest rate, and credit risks. Key points:
1) Derivatives like forwards, futures, options and swaps allow companies to hedge existing exposures to financial risks.
2) The right risk management techniques need to be used, as derivatives can reduce risks but improper use may increase risks.
3) Different derivative products are suited to different risk exposures. For example, currency risks are best hedged with forwards or options, while interest rate risks can be managed using interest rate swaps.
Derivatives futures,options-presentation-hareeshHareesh M
This document defines and explains various types of derivatives contracts including futures, options, forwards, and swaps. It describes how futures and options are traded on exchanges versus over-the-counter markets. Key terms like underlying assets, strike price, and expiration date are defined for different derivative products. Economic benefits of using derivatives for hedging and speculation are also summarized.
Futures and swaps allow parties to manage risks associated with price fluctuations in underlying assets. A futures contract is a standardized agreement to buy or sell an asset at a predetermined price at a specified future date. Key elements of futures contracts include the underlying asset, settlement/delivery date, and futures price. Futures are traded on organized exchanges and involve clearinghouses that guarantee contracts. Futures can be used for hedging, speculation, or arbitrage. Swaps allow parties to exchange cash flows of one party's financial instrument for those of the other party.
This document provides an introduction to derivatives. It defines derivatives as financial instruments whose value is derived from an underlying asset. The three main types of derivatives discussed are forwards, futures, and options. Forwards are customized bilateral contracts to buy or sell an asset in the future at a predetermined price. Futures are standardized exchange-traded versions of forwards that have no counterparty risk. Daily mark-to-market settlements determine profits and losses on futures positions. Options provide the right but not the obligation to buy or sell an asset at a future date.
Option pricing is determined by 5 key factors: the asset's cash price, strike price, volatility, time to expiration, and interest rates. The Black-Scholes model uses these factors to price European options, assuming the asset pays no dividends, markets are efficient, and other restricting assumptions. It models the asset's price as following geometric Brownian motion to derive a theoretical option price formula involving the standard normal distribution.
This document provides an overview and introduction to currency futures, options, and swaps. It defines these derivative instruments and discusses how they work. Specifically, it explains how currency futures contracts are traded and marked to market daily on an exchange. It also outlines the basics of currency options, including the types of options and how they are priced. Finally, it defines currency and interest rate swaps as agreements to exchange cash flows, and discusses why companies enter into swaps.
The document discusses derivatives, which are financial instruments derived from underlying assets like stocks, bonds, currencies, and commodities. Derivatives include options, futures, forwards, and swaps. They allow investors to hedge risk or speculate. Derivatives gain value based on fluctuations in the underlying asset and are used for both risk management and investment purposes. Common derivative types and how they work are also explained.
Derivatives are financial instruments whose value is dependent on an underlying asset. The three main types of derivatives are forwards, futures, and options. Forwards and futures are contracts to buy or sell an asset at a future date at a predetermined price, while options provide the right but not obligation to buy or sell an asset at a strike price. Derivatives allow traders to hedge risk, reduce transaction costs, manage portfolios, and enhance liquidity in markets.
This document discusses factors that affect option pricing and different types of options. The key factors that affect option pricing are the underlying asset price, expected volatility, strike price, time until expiration, interest rates, and dividends. The value of a call option increases when the underlying asset price increases, while the value of a put option decreases. European options can only be exercised at expiration, Bermudan options can be exercised at predefined intervals, and American options can be exercised at any time.
This document provides an introduction and overview of derivatives, including their history, types, and uses. It discusses futures, forwards, and options contracts. Futures are exchange-traded standardized contracts that require daily margin payments and settlement. Forwards are over-the-counter customized contracts that involve credit risk. Options provide the right but not obligation to buy or sell an underlying asset at a specified price on or before expiration. The document defines call and put options and explores factors that influence option pricing.
Derivatives can be used to manage financial risk. Common derivatives include options, forward contracts, futures contracts, and swaps. Derivatives allow firms to hedge risks like foreign exchange risk, interest rate risk, and commodity price risk. For example, an oil company can use put options to hedge against falling oil prices. Forward contracts lock in future exchange rates. Futures contracts are similar to forwards but are traded on exchanges. Swaps allow exchange of cash flows to modify risk exposure. Derivatives are widely used by large companies to reduce cash flow volatility and financial distress costs through hedging.
The document is a project report submitted by Deepali Dalvi on futures and options contracts. It includes an introduction to derivatives, the history of derivatives and futures markets, an overview of futures and options terminology, and descriptions of different types of derivative contracts such as forwards, futures, calls, puts and options trading strategies. The report also discusses the purpose of futures markets, arbitrage opportunities, clearing mechanisms, differences between futures and forwards, stock index futures, and the NSE's derivatives market. It aims to provide a comprehensive overview of the key concepts relating to futures and options.
This is a partial preview of the document found here:
https://flevy.com/browse/business-document/financial-derivatives-103
Description:
Along with the basics of various financial derivatives required for risk management, it also covers various hedging strategies, comparisons, option valuation and brief on forward rate agreements.
Moisés Meza Díaz es un maestro en El Cabezón, Jalisco, una comunidad rural de aproximadamente 2,000 habitantes. Imparte clases de ciencias sociales y humanidades a estudiantes de secundaria y bachillerato entre las edades de 12 y 18 años. Uno de los principales problemas sociales que enfrenta la comunidad son los embarazos adolescentes y que los estudiantes abandonen la escuela para trabajar y apoyar la economía familiar. El maestro busca estrategias para evitar la deserción escolar y apoyar a los estud
I had to make a Newsletter for Actively Listening to your child to Parents that would have children in my classroom. Tell me what you think! How'd I do? Did I catch your attention & keep you interested?
Derivatives derive their value from underlying assets such as stocks, commodities, currencies, and bonds. The main types of derivatives are forwards, futures, and options. Forwards involve an obligation for both parties to fulfill the contract terms at a future date. Futures are standardized contracts traded on an exchange with high liquidity. Options confer the right but not obligation to buy or sell the underlying asset at a strike price by an expiry date. Key participants in derivatives markets include speculators, hedgers, and arbitrageurs. Common derivatives strategies involve futures arbitrage, hedging, and using options spreads. Greeks like delta and gamma help analyze how option prices change with movements in the underlying asset.
Derivatives derive their value from underlying assets. There are various types including forwards, futures, options, and swaps. Forward contracts are bilateral agreements to buy or sell an asset in the future at predetermined terms. Futures are standardized forward contracts that are traded on an exchange. Options provide the right but not obligation to buy or sell an asset by a specified date. Swaps involve exchanging cash flows of underlying assets like interest rates or currencies. Derivatives allow participants to hedge or speculate on price movements of the underlying assets.
This document provides an introduction and overview of financial derivatives. It discusses the key types of derivatives like forwards, futures, and options. It defines derivatives as financial instruments whose value is based on an underlying asset. Forwards are customized over-the-counter contracts while futures are exchange-traded with standardized terms. Options provide the right but not obligation to buy or sell the underlying asset. The document also covers hedging strategies using derivatives and the factors that affect option pricing.
The document discusses key concepts related to options pricing including: the minimum and maximum value of a call option; factors that affect call prices such as exercise price, time to maturity, interest rates, and stock volatility; the difference between American and European style options; and the potential early exercise of American call options on dividend and non-dividend paying stocks.
This document provides an introduction to option contracts, including definitions, key features, advantages and disadvantages, and types of options. It discusses call and put options, as well as European and American options. Key terminology for options like long, short, strike price, in-the-money, out-of-the-money, and at-the-money are also explained. The document is intended to provide a basic understanding of stock options and how they can be used.
This document defines and explains options contracts. It discusses that an options contract is an agreement that gives the buyer the right, but not the obligation, to buy or sell an asset at a future date at an agreed upon price. It outlines key features of options contracts including the underlying instrument, contract size, premium, strike price, and expiration date. It also defines put and call options and discusses concepts like moneyness, intrinsic and time value, and examples of calculating these values. Finally, it covers advantages like making money and hedging risk, and disadvantages like options being a wasting asset and complexity.
Risk Management Using Derivatives in Financial Planning Journal by Gaurav K B...Corporate Professionals
Derivatives can be used effectively for risk management purposes such as hedging currency, commodity price, interest rate, and credit risks. Key points:
1) Derivatives like forwards, futures, options and swaps allow companies to hedge existing exposures to financial risks.
2) The right risk management techniques need to be used, as derivatives can reduce risks but improper use may increase risks.
3) Different derivative products are suited to different risk exposures. For example, currency risks are best hedged with forwards or options, while interest rate risks can be managed using interest rate swaps.
Derivatives futures,options-presentation-hareeshHareesh M
This document defines and explains various types of derivatives contracts including futures, options, forwards, and swaps. It describes how futures and options are traded on exchanges versus over-the-counter markets. Key terms like underlying assets, strike price, and expiration date are defined for different derivative products. Economic benefits of using derivatives for hedging and speculation are also summarized.
Futures and swaps allow parties to manage risks associated with price fluctuations in underlying assets. A futures contract is a standardized agreement to buy or sell an asset at a predetermined price at a specified future date. Key elements of futures contracts include the underlying asset, settlement/delivery date, and futures price. Futures are traded on organized exchanges and involve clearinghouses that guarantee contracts. Futures can be used for hedging, speculation, or arbitrage. Swaps allow parties to exchange cash flows of one party's financial instrument for those of the other party.
This document provides an introduction to derivatives. It defines derivatives as financial instruments whose value is derived from an underlying asset. The three main types of derivatives discussed are forwards, futures, and options. Forwards are customized bilateral contracts to buy or sell an asset in the future at a predetermined price. Futures are standardized exchange-traded versions of forwards that have no counterparty risk. Daily mark-to-market settlements determine profits and losses on futures positions. Options provide the right but not the obligation to buy or sell an asset at a future date.
Option pricing is determined by 5 key factors: the asset's cash price, strike price, volatility, time to expiration, and interest rates. The Black-Scholes model uses these factors to price European options, assuming the asset pays no dividends, markets are efficient, and other restricting assumptions. It models the asset's price as following geometric Brownian motion to derive a theoretical option price formula involving the standard normal distribution.
This document provides an overview and introduction to currency futures, options, and swaps. It defines these derivative instruments and discusses how they work. Specifically, it explains how currency futures contracts are traded and marked to market daily on an exchange. It also outlines the basics of currency options, including the types of options and how they are priced. Finally, it defines currency and interest rate swaps as agreements to exchange cash flows, and discusses why companies enter into swaps.
The document discusses derivatives, which are financial instruments derived from underlying assets like stocks, bonds, currencies, and commodities. Derivatives include options, futures, forwards, and swaps. They allow investors to hedge risk or speculate. Derivatives gain value based on fluctuations in the underlying asset and are used for both risk management and investment purposes. Common derivative types and how they work are also explained.
Derivatives are financial instruments whose value is dependent on an underlying asset. The three main types of derivatives are forwards, futures, and options. Forwards and futures are contracts to buy or sell an asset at a future date at a predetermined price, while options provide the right but not obligation to buy or sell an asset at a strike price. Derivatives allow traders to hedge risk, reduce transaction costs, manage portfolios, and enhance liquidity in markets.
This document discusses factors that affect option pricing and different types of options. The key factors that affect option pricing are the underlying asset price, expected volatility, strike price, time until expiration, interest rates, and dividends. The value of a call option increases when the underlying asset price increases, while the value of a put option decreases. European options can only be exercised at expiration, Bermudan options can be exercised at predefined intervals, and American options can be exercised at any time.
This document provides an introduction and overview of derivatives, including their history, types, and uses. It discusses futures, forwards, and options contracts. Futures are exchange-traded standardized contracts that require daily margin payments and settlement. Forwards are over-the-counter customized contracts that involve credit risk. Options provide the right but not obligation to buy or sell an underlying asset at a specified price on or before expiration. The document defines call and put options and explores factors that influence option pricing.
Derivatives can be used to manage financial risk. Common derivatives include options, forward contracts, futures contracts, and swaps. Derivatives allow firms to hedge risks like foreign exchange risk, interest rate risk, and commodity price risk. For example, an oil company can use put options to hedge against falling oil prices. Forward contracts lock in future exchange rates. Futures contracts are similar to forwards but are traded on exchanges. Swaps allow exchange of cash flows to modify risk exposure. Derivatives are widely used by large companies to reduce cash flow volatility and financial distress costs through hedging.
The document is a project report submitted by Deepali Dalvi on futures and options contracts. It includes an introduction to derivatives, the history of derivatives and futures markets, an overview of futures and options terminology, and descriptions of different types of derivative contracts such as forwards, futures, calls, puts and options trading strategies. The report also discusses the purpose of futures markets, arbitrage opportunities, clearing mechanisms, differences between futures and forwards, stock index futures, and the NSE's derivatives market. It aims to provide a comprehensive overview of the key concepts relating to futures and options.
This is a partial preview of the document found here:
https://flevy.com/browse/business-document/financial-derivatives-103
Description:
Along with the basics of various financial derivatives required for risk management, it also covers various hedging strategies, comparisons, option valuation and brief on forward rate agreements.
Moisés Meza Díaz es un maestro en El Cabezón, Jalisco, una comunidad rural de aproximadamente 2,000 habitantes. Imparte clases de ciencias sociales y humanidades a estudiantes de secundaria y bachillerato entre las edades de 12 y 18 años. Uno de los principales problemas sociales que enfrenta la comunidad son los embarazos adolescentes y que los estudiantes abandonen la escuela para trabajar y apoyar la economía familiar. El maestro busca estrategias para evitar la deserción escolar y apoyar a los estud
I had to make a Newsletter for Actively Listening to your child to Parents that would have children in my classroom. Tell me what you think! How'd I do? Did I catch your attention & keep you interested?
Big Foxx is a branding and technology company that provides services such as branding, website and mobile app development, online marketing, video production, and other services. They have worked with over 65 clients across 11 sectors including food and hospitality, manufacturing, apparel, and IT. Some of their case studies include developing branding, websites, and marketing campaigns for food chains, restaurants, jewelry brands, and film festivals. They aim to build trust and positioning for brands while leveraging technology to make processes fast and smart.
The study aimed to examine the relationships between parenting styles, academic motivation, and GPA in college students. 67 college students completed questionnaires on their parents' parenting styles and their own academic motivation. Results found no significant relationships between authoritative parenting style and academic motivation or GPA. There were also no relationships found between academic motivation and GPA. However, permissive parenting was negatively correlated with academic motivation, and authoritarian parenting was negatively correlated with GPA. This did not support the hypothesis that authoritative parenting would relate to higher motivation and performance. The findings indicate that permissive and authoritarian parenting may be less optimal for student success compared to authoritative parenting.
The document discusses the impact of marital conflict on children, including when destructive conflict tactics like physical aggression, insults, or hostility are used in front of children. While parents may try to shield children, research finds children are usually present for domestic disputes. Witnessing certain types of conflict can negatively impact children's development. The document advocates for constructive conflict resolution like calm discussion and compromise when children are present. As youth professionals, we must be aware that conflict children witness at home can short and long-term effects, so promoting healthy relationships is important.
Derivatives are financial instruments whose prices are derived from underlying assets such as stocks, interest rates, or commodities. There are several types of derivatives including options, futures, forwards, and swaps. Options give the holder the right but not the obligation to buy or sell the underlying asset. Futures and forwards are agreements to buy or sell an asset at a future date for a predetermined price. Swaps involve exchanging periodic payments between two parties based on interest rates, currencies, or other financial metrics. Derivatives can be used for hedging risk, speculation, and arbitrage opportunities.
The document provides an introduction to financial derivatives, including forwards, futures, options, and swaps. It defines each type of derivative and provides examples. Key points covered include:
- Derivatives derive their price from an underlying asset such as a commodity, currency, bond, or stock.
- Forwards and swaps are over-the-counter (OTC) contracts while futures and options trade on exchanges.
- Common uses of derivatives include hedging risk, speculation, and arbitrage.
- Margin requirements and daily settlement help manage counterparty risk in derivatives markets.
Derivatives are financial contracts whose value is dependent on an underlying asset. There are several types of derivatives including forwards, futures, options, and swaps. Derivatives allow participants to hedge risks, speculate, or engage in arbitrage. Derivatives can be exchange-traded or over-the-counter. Common derivatives include commodity derivatives, financial derivatives, and complex derivatives involving interest rates. Forwards, futures, options, and swaps each have unique features regarding trading, settlement, and valuation. Overall, derivatives help investors and businesses manage risks in global financial markets.
This document provides an overview of derivatives, including definitions, key features, and types. It defines a derivative as a contract whose price is derived from an underlying asset. There are three main types of derivative market participants: hedgers who face risk, speculators who bet on price movements, and arbitrageurs who trade to profit from pricing discrepancies. The document discusses forward contracts, futures contracts, and options, explaining their features, advantages/disadvantages, and how their prices are determined. It also covers some options terminology and factors that affect options pricing.
This document summarizes key concepts in financial derivatives and option pricing. It discusses:
1) Financial markets where buyers and sellers trade financial instruments and assets. Common financial assets include bonds, currencies, commodities and stocks.
2) Financial derivatives, which derive their value from underlying assets, include options, forwards/futures, and swaps. Plain vanilla options include calls, which confer the right to buy an asset, and puts, which confer the right to sell.
3) European options can only be exercised at expiration, while American options can be exercised anytime until expiration. Exotic options have non-standard payoff structures.
4) No-arbitrage pricing implies that the fair price of
Options Pricing The Black-Scholes ModelMore or .docxhallettfaustina
*
Options Pricing: The Black-Scholes ModelMore or less, the Black-Scholes (B-S) Model is really just a fancy extension of the Binomial Model.
(Fancy enough, however, to win a Nobel Prize…).
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How B-S extends the Binomial Model1. Instead of assuming two possible states for future exchange rates, and thus returns (i.e., “up” and “down”), B-S assumes a continuous distribution of returns, R, so that returns can take on a whole range of values.
Binomial B-S
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How B-S extends the Binomial ModelIn fact, exchange rate returns are approximately normally distributed, so this is a “reasonable” assumption:
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How B-S extends the Binomial Model2. Instead of just one time period, B-S assumes multiple time periods and that the time between periods is instantaneous (i.e., continuous).
(See lecture)
Also, the time between periods t=0, t=1, t=2, etc. shrinks to zero, so that spot rate is changing at every instant.
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How B-S extends the Binomial ModelThis is more realistic, since actual currency trades take place on a second-to-second, nearly continuous basis.
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How B-S extends the Binomial ModelIt turns out that these two extensions are enough to make the math very hard. Thus, deriving the B-S model is no easy task.
The most important thing to recognize is that despite the above complications, the basic underlying approach of the B-S model remains the same…
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How B-S extends the Binomial Model3. Create a replicating portfolio and price the option using a no-arbitrage argument.Calculate NS and NB: Now, since these are constantly changing over time, this process is called “dynamic hedging”.Replicating portfolio:It turns out that it is possible to use a combination of foreign currency and USD, and now in addition, options themselves, to form a riskless portfolio (i.e., return is known for sure).No-arbitrage: Riskless portfolios must have the same price as risk-free securities, otherwise arbitrage is possible. Use this fact to figure out c.
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The Black-Scholes Options Pricing FormulaPutting the above all together, we get the Black-Scholes formula for pricing a European call option on foreign currency:
where
and S, X, T as before
r = domestic risk-free rate, r* = foreign risk-free rate
s = volatility of the foreign currency (sd of returns).
*
The Black-Scholes Options Pricing Formula
Also, N(x) = Prob that a random variable will be less than x under the standard normal distribution (i.e., cumulative distribution function).Calculate in EXCEL using “=NORMSDIST(x)”.
represents discounting when interest rates are continuously compounded, so basically it corresponds to:
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The document provides an overview of derivatives, including:
- Derivatives derive their value from an underlying asset such as stocks, bonds, commodities, currencies, or interest rates.
- The main types of derivatives are forwards, futures, options, and swaps. Forwards and futures are traded on exchanges while swaps and most options are over-the-counter.
- Derivatives can be used for hedging risk or speculation. They allow investors to gain exposure to assets with greater leverage compared to investing directly in the underlying assets.
Derivatives derive their value from underlying assets such as stocks, commodities, currencies, and bonds. The main types of derivatives are forwards, futures, and options. Forwards involve an obligation for both parties to fulfill the contract terms at a future date. Futures are standardized contracts traded on an exchange with high liquidity. Options confer the right but not obligation to buy or sell the underlying asset at a strike price by an expiry date. Key participants in derivatives markets include speculators, hedgers, and arbitrageurs. Common derivatives strategies involve futures arbitrage, hedging, directional spreads, and volatility spreads.
The document discusses derivative markets, including forwards, futures, and options. Forwards are customized contracts to buy or sell an asset at a future date, while futures are standardized contracts traded on exchanges. Options provide the right but not obligation to buy or sell an asset, with call options giving the right to buy and put options the right to sell.
The document provides an overview of derivatives, including their definition, categories, and key types. It discusses forwards, futures, options, and how they are priced. Forwards involve a contractual obligation to buy or sell an asset at a fixed price on a future date. Futures are exchange-traded forwards that are standardized and involve a clearinghouse. Options give the holder the right, but not obligation, to buy or sell an asset at a preset price. Derivatives are priced based on the no-arbitrage principle to eliminate riskless profit opportunities.
This document provides an overview of currency futures, options, and interest rate swaps. It begins with introductions to derivatives, currency forwards and futures contracts, and currency options. The key differences between futures and forwards are explained. Examples are provided of how currency futures contracts work via daily marking to market and the role of a clearing house. The document also covers the basics of currency options, including put and call options and factors that affect option pricing. Finally, the document uses an example to illustrate how an interest rate swap agreement between a bank and company could save both parties money versus borrowing directly.
Derivatives are financial instruments whose value is derived from an underlying asset. There are several types of derivatives:
1) Forward contracts are customized agreements between two parties to buy or sell an asset at a future date for a fixed price, exposing the parties to counterparty risk.
2) Futures contracts are similar to forwards but are exchange-traded, with standardized terms, eliminating counterparty risk.
3) Options contracts give the holder the right, but not the obligation, to buy or sell the underlying asset at a specified price on or before the expiration date.
4) Warrants and convertibles give holders the right to buy or convert into the underlying asset within a given time period.
Derivatives are financial instruments whose value is derived from an underlying asset. There are several types of derivatives:
1) Forward contracts are customized agreements between two parties to buy or sell an asset at a future date for a fixed price, exposing the parties to counterparty risk.
2) Futures contracts are similar to forwards but are exchange-traded, with standardized terms, eliminating counterparty risk.
3) Options contracts give the holder the right, but not the obligation, to buy or sell the underlying asset at a specified price on or before the expiration date.
4) Warrants and convertibles give holders the right to buy or convert into the underlying asset within a given time period.
Answer -1). Swap - A swap is a derivative in which two counter p.pdfaparnaagenciestvm
Answer :-
1). Swap :- A swap is a derivative in which two counter parties exchange cash flows of one
party\'s financial instrument for those of the other party\'s financial instrument. The benefits in
question depend on the type of financial instruments involved. For example, in the case of a
swap involving two bonds, the benefits in question can be the periodic interest (coupon)
payments associated with such bonds.
The swap agreement defines the dates when the cash flows are to be paid and the way they
areaccrued and calculated. Usually at the time when the contract is initiated, at least one of these
series of cash flows is determined by an uncertain variable such as a floating interest rate, foreign
exchange rate, equity price, or commodity price.
The cash flows are calculated over a notional principal amount. Consequently, swaps can be in
cash or collateral. They can be used to hedge certain risks such as interest rate risk, or to
speculate on changes in the expected direction of underlying prices. Swaps are private
agreements between two parties to exchange cash flows in the future according to a pre-arranged
formula. They can be regarded as portfolios of forward contracts. The two commonly used swaps
are interest rate swaps and currency swaps.
A). Interest rate swaps: -However, this may lead to a company borrowing fixed when it wants
floating or borrowing floating when it wants fixed. This is where a swap comes in. A swap has
the effect of transforming a fixed rate loan into a floating rate loan or vice versa.
B). Currency swaps: - A currency swap involves exchanging principal and fixed rate interest
payments on a loan in one currency for principal and fixed rate interest payments on an equal
loan in another currency.
2). Options :- An option is a contract which gives the buyer (the owner or holder of the option)
the right, but not the obligation, to buy or sell an underlying asset or instrument at a specific
strike price on a specified date, depending on the form of the option.The strike price may be set
by reference to the spot price (market price) of the underlying security or commodity on the day
an option is taken out, or it may be fixed at a discount in a premium. The seller has the
corresponding obligation to fulfill the transaction—to sell or buy—if the buyer (owner)
\"exercises\" the option.
Options are of two types – Calls and Puts. Calls give the buyer the right but not the obligation to
buy a given quantity of the underlying asset, at a given price on or before a given future date.
Puts give the buyer the right, but not the obligation to sell a given quantity of the underlying
asset at a given price on or before a given date.
In basic terms, the value of an option is commonly decomposed into two parts :-
a). The first part is the intrinsic value, which is defined as the difference between the market
value of the underlying and the strike price of the given option.
b). The second part is the time value, which depends on a set.
This document provides an overview of derivatives and forward markets. It defines derivatives as products whose value is derived from underlying variables like assets, indices, or rates. Common derivative products discussed include forwards, futures, options, and swaps. Forwards involve private contracts to buy or sell an asset at a future date, while futures are standardized exchange-traded forwards. Options provide the right but not obligation to buy or sell an asset. Swaps involve exchanging cash flows of underlying items like interest rates or currencies. The document also discusses key participants in derivatives markets like hedgers who manage risk, speculators who take positions based on price views, brokers who facilitate trades, and market makers who provide liquidity.
This document provides an introduction and table of contents to a project report on exotic options and their products and applications. It discusses forward contracts and vanilla options such as calls and puts in chapter 2. Chapter 3 covers exotic options including lookback options, compound options, binary options, barrier options, and mountain range options like Atlas and Himalayan options. The document aims to explain how these derivatives work and their benefits and drawbacks for investors seeking to hedge risks, speculate, or arbitrage pricing inefficiencies.
This document provides an overview of financial derivatives. It defines derivatives as instruments whose value is derived from an underlying asset. The four main types of derivatives are forwards, futures, options, and swaps. Derivatives allow parties to transfer risks related to price fluctuations and are used for hedging and speculative purposes. While derivatives pose risks, they also serve important economic functions like facilitating price discovery and transferring risk. Derivative markets in India operate through designated exchanges and are regulated by SEBI.
This document provides an overview of key concepts from Chapter 1 of an introductory derivatives textbook. It discusses what derivatives are, their common uses for hedging and speculation, and perspectives of different market participants. It also covers financial engineering, the role of financial markets, risk sharing, and how derivatives are used in practice. The chapter introduces forwards and options, including their payoffs and profit/loss profiles for long and short positions. It discusses uses of derivatives for hedging from the perspective of producers and buyers.
This document provides an overview of Chapter 1 of an ACTEX FM DVD on derivatives. It introduces key concepts around derivatives including their uses for risk management, speculation, and reduced transaction costs. It discusses perspectives of end users, market makers, and economic observers. It also covers financial engineering, the role of financial markets, risk sharing, and how derivatives are used in practice.
13 Jun 24 ILC Retirement Income Summit - slides.pptxILC- UK
ILC's Retirement Income Summit was hosted by M&G and supported by Canada Life. The event brought together key policymakers, influencers and experts to help identify policy priorities for the next Government and ensure more of us have access to a decent income in retirement.
Contributors included:
Jo Blanden, Professor in Economics, University of Surrey
Clive Bolton, CEO, Life Insurance M&G Plc
Jim Boyd, CEO, Equity Release Council
Molly Broome, Economist, Resolution Foundation
Nida Broughton, Co-Director of Economic Policy, Behavioural Insights Team
Jonathan Cribb, Associate Director and Head of Retirement, Savings, and Ageing, Institute for Fiscal Studies
Joanna Elson CBE, Chief Executive Officer, Independent Age
Tom Evans, Managing Director of Retirement, Canada Life
Steve Groves, Chair, Key Retirement Group
Tish Hanifan, Founder and Joint Chair of the Society of Later life Advisers
Sue Lewis, ILC Trustee
Siobhan Lough, Senior Consultant, Hymans Robertson
Mick McAteer, Co-Director, The Financial Inclusion Centre
Stuart McDonald MBE, Head of Longevity and Democratic Insights, LCP
Anusha Mittal, Managing Director, Individual Life and Pensions, M&G Life
Shelley Morris, Senior Project Manager, Living Pension, Living Wage Foundation
Sarah O'Grady, Journalist
Will Sherlock, Head of External Relations, M&G Plc
Daniela Silcock, Head of Policy Research, Pensions Policy Institute
David Sinclair, Chief Executive, ILC
Jordi Skilbeck, Senior Policy Advisor, Pensions and Lifetime Savings Association
Rt Hon Sir Stephen Timms, former Chair, Work & Pensions Committee
Nigel Waterson, ILC Trustee
Jackie Wells, Strategy and Policy Consultant, ILC Strategic Advisory Board
South Dakota State University degree offer diploma Transcriptynfqplhm
办理美国SDSU毕业证书制作南达科他州立大学假文凭定制Q微168899991做SDSU留信网教留服认证海牙认证改SDSU成绩单GPA做SDSU假学位证假文凭高仿毕业证GRE代考如何申请南达科他州立大学South Dakota State University degree offer diploma Transcript
Budgeting as a Control Tool in Government Accounting in Nigeria
Being a Paper Presented at the Nigerian Maritime Administration and Safety Agency (NIMASA) Budget Office Staff at Sojourner Hotel, GRA, Ikeja Lagos on Saturday 8th June, 2024.
Discover the Future of Dogecoin with Our Comprehensive Guidance36 Crypto
Learn in-depth about Dogecoin's trajectory and stay informed with 36crypto's essential and up-to-date information about the crypto space.
Our presentation delves into Dogecoin's potential future, exploring whether it's destined to skyrocket to the moon or face a downward spiral. In addition, it highlights invaluable insights. Don't miss out on this opportunity to enhance your crypto understanding!
https://36crypto.com/the-future-of-dogecoin-how-high-can-this-cryptocurrency-reach/
Monthly Market Risk Update: June 2024 [SlideShare]Commonwealth
Markets rallied in May, with all three major U.S. equity indices up for the month, said Sam Millette, director of fixed income, in his latest Market Risk Update.
For more market updates, subscribe to The Independent Market Observer at https://blog.commonwealth.com/independent-market-observer.
Madhya Pradesh, the "Heart of India," boasts a rich tapestry of culture and heritage, from ancient dynasties to modern developments. Explore its land records, historical landmarks, and vibrant traditions. From agricultural expanses to urban growth, Madhya Pradesh offers a unique blend of the ancient and modern.
What Lessons Can New Investors Learn from Newman Leech’s Success?Newman Leech
Newman Leech's success in the real estate industry is based on key lessons and principles, offering practical advice for new investors and serving as a blueprint for building a successful career.
An accounting information system (AIS) refers to tools and systems designed for the collection and display of accounting information so accountants and executives can make informed decisions.
How Poonawalla Fincorp and IndusInd Bank’s Co-Branded RuPay Credit Card Cater...beulahfernandes8
The eLITE RuPay Platinum Credit Card, a strategic collaboration between Poonawalla Fincorp and IndusInd Bank, represents a significant advancement in India's digital financial landscape. Spearheaded by Abhay Bhutada, MD of Poonawalla Fincorp, the card leverages deep customer insights to offer tailored features such as no joining fees, movie ticket offers, and rewards on UPI transactions. IndusInd Bank's solid banking infrastructure and digital integration expertise ensure seamless service delivery in today's fast-paced digital economy. With a focus on meeting the growing demand for digital financial services, the card aims to cater to tech-savvy consumers and differentiate itself through unique features and superior customer service, ultimately poised to make a substantial impact in India's digital financial services space.
The Rise and Fall of Ponzi Schemes in America.pptxDiana Rose
Ponzi schemes, a notorious form of financial fraud, have plagued America’s investment landscape for decades. Named after Charles Ponzi, who orchestrated one of the most infamous schemes in the early 20th century, these fraudulent operations promise high returns with little or no risk, only to collapse and leave investors with significant losses. This article explores the nature of Ponzi schemes, notable cases in American history, their impact on victims, and measures to prevent falling prey to such scams.
Understanding Ponzi Schemes
A Ponzi scheme is an investment scam where returns are paid to earlier investors using the capital from newer investors, rather than from legitimate profit earned. The scheme relies on a constant influx of new investments to continue paying the promised returns. Eventually, when the flow of new money slows down or stops, the scheme collapses, leaving the majority of investors with substantial financial losses.
Historical Context: Charles Ponzi and His Legacy
Charles Ponzi is the namesake of this deceptive practice. In the 1920s, Ponzi promised investors in Boston a 50% return within 45 days or 100% return in 90 days through arbitrage of international reply coupons. Initially, he paid returns as promised, not from profits, but from the investments of new participants. When his scheme unraveled, it resulted in losses exceeding $20 million (equivalent to about $270 million today).
Notable American Ponzi Schemes
1. Bernie Madoff: Perhaps the most notorious Ponzi scheme in recent history, Bernie Madoff’s fraud involved $65 billion. Madoff, a well-respected figure in the financial industry, promised steady, high returns through a secretive investment strategy. His scheme lasted for decades before collapsing in 2008, devastating thousands of investors, including individuals, charities, and institutional clients.
2. Allen Stanford: Through his company, Stanford Financial Group, Allen Stanford orchestrated a $7 billion Ponzi scheme, luring investors with fraudulent certificates of deposit issued by his offshore bank. Stanford promised high returns and lavish lifestyle benefits to his investors, which ultimately led to a 110-year prison sentence for the financier in 2012.
3. Tom Petters: In a scheme that lasted more than a decade, Tom Petters ran a $3.65 billion Ponzi scheme, using his company, Petters Group Worldwide. He claimed to buy and sell consumer electronics, but in reality, he used new investments to pay off old debts and fund his extravagant lifestyle. Petters was convicted in 2009 and sentenced to 50 years in prison.
4. Eric Dalius and Saivian: Eric Dalius, a prominent figure behind Saivian, a cashback program promising high returns, is under scrutiny for allegedly orchestrating a Ponzi scheme. Saivian enticed investors with promises of up to 20% cash back on everyday purchases. However, investigations suggest that the returns were paid using new investments rather than legitimate profits. The collapse of Saivian l
The Rise and Fall of Ponzi Schemes in America.pptx
Risk mgmt and derinatives
1. Chapter 1
Risk Management and Financial
Derivatives
We begin with a brief and straightforward introduction to the basic con-
cepts, properties and pricing principles of financial derivatives, and a clear
statement of the main subject of the book-the valuation problem of
option pricing.
1.1 Risk a n d Risk Management
Risk-uncertainty of the outcome.
Risk can bring unexpected gains. It can also cause unforeseen losses,
even catastrophes.
Risks are common and inherent in the financial markets and commod-
ity markets: asset risk (stocks...), interest rate risk, foreign exchange risk,
credit risk, commodity risk and so on.
There are two totally different attitudes toward risks:
1. Risk aversion: quantify an identified risk and control it, i.e., to
devise a plan to manage the exposed risk and convert it into a desired form.
Basically, two kinds of plans are available: a. Replace the uncertainty with
a certainty to avoid the risk of adverse outcomes even if this requires giving
up the potential gaining opportunity. b. B e willing to pay a certain price
for the potential gaining opportunity, while avoiding the risk of adverse
outcomes.
2. Risk seeking: willing to take the risk with one's money, in hope
of reaping risk profits from investments in risky assets out of their frequent
price changes. Acting in hope of reaping risk profits from the market price
changes is called speculation.
Financial derivatives are a kind of risk management instrument. A
derivative's value depends on the price changes in some more fundamental
2. 2 Mathematical Modeling and Methods of Option Pricing
underlying assets.
Many forms of financial derivatives instruments exist in the financial
markets. Among them, the three most fundamental financial derivatives
instruments are: forward contracts, futures, and options. If the un-
derlying assets are stocks, bonds, foreign exchange rates and commodi-
ties etc., then the corresponding risk management instruments are: stock
futures (options), bond futures (options), currency futures (options) and
commodity futures (options) etc.
In risk management of the underlying assets using financial derivatives,
the basic strategy is hedging, i.e., the trader holds two positions of equal
amounts but opposite directions, one in the underlying markets, and the
other in the derivatives markets, simultaneously. This risk management
strategy is based on the following reasoning: it is believed that under nor-
mal circumstances, prices of underlying assets and their derivatives change
roughly in the same direction with basically the same magnitude; hence
losses in the underlying assets (derivatives) markets can be offset by gains
in the derivatives (underlying assets) markets; therefore losses can be pre-
vented or reduced by combining the risks due to the price changes.
The subject of this book is pricing of financial derivatives and risk man-
agement by hedging.
1.2 Forward Contracts a n d Futures
Forward contract -an agreement to buy or sell at a specified future
time a certain amount of an underlying asset a t a specified price.
A forward contract is an agreement to replace a risk with a certainty.
The buyer in the contract is said to hold a long position, and the
seller is said to hold a short position. The specified price in the contract
is called the delivery price and the specified time is called maturity.
Let K-delivery price, and T-maturity, then a forward contract's
payoff V at maturity is:
T
V = ST- K , (long position)
T
V = K - ST,(short position)
T
where ST denotes the price of the underlying asset at maturity t = T.
3. Risk Management and Financial Derivatives
long position .
short position
Forward Contracts are generally traded OTC (over-the-counter).
Future----same as a forward contract, an agreement to buy or sell at a
specified future time a certain amount of an underlying asset at a specified
price. Futures have evolved from standardization of forward contracts.
Futures differ from forward contracts in the following respects:
a. Futures are generally traded on an exchange.
b. A future contract contains standardized articles.
c. The delivery price on a future contract is generally determined on an
exchange, and depends on the market demands.
1.3 Options
Options- an agreement that the holder can buy from, or sell to, the
seller of the option at a specified future time a certain amount of an un-
derlying asset a t a specified price. But the holder is under no obligation to
exercise the contract.
The holder of an option has the right, but not the obligation, to carry
out the agreement according to the terms specified in the agreement. In an
options contract, the specified price is called the exercise price or strike
price, the specified date is called the expiration date, and the action to
perform the buying or selling of the asset according to the option contract
is called exercise.
According to buying or selling an asset, options have the following types:
call option is a contract to buy at a specified future time a certain
amount of an underlying asset at a specified price.
4. 4 Mathematical Modeling and Methods of Option Pricing
put option is a contract to sell at a specified future time a certain
amount of an underlying asset at a specified price.
According to terms on exercise in the contract, options have the follow-
ing types:
European options can be exercised only on the expiration date.
American options can be exercised on or prior to the expiration date.
Define K - strike price and T- expiration date, then an option's
payoff (value) V at expiration date is:
T
VT = (ST- K)+, ( call option)
VT = (K -ST)+, ( put option)
where ST denotes the price of the underlying asset at the expiration date
K K
call option put option
Option is a contingent claim. Take a call option as example. If ST,the
underlying asset's price at expiration date, is higher than the strike price
K , then the holder of the option can exercise the rights to buy the asset
at the strike price K(to gain profits). Otherwise, the option is a worthless
paper. Thus, to price an option is essentially to set a price to this kind
of contingent claims. The significance of this fact goes well beyond the
scope of derivatives pricing, and applies to many other industries such as
investment and insurance etc.
The price paid for a contingent claim is called the premium. The
needs of clients vary. Correspondingly, there exist a variety of options-the
financial products developed by financial institutions. Every type of options
requires pricing. Option pricing is the main subject discussed in this book.
Taking into account the premium p, the total gain PT of the option holder
at its expiration date is
5. Risk Management and Financial Derivatives 5
[ Total gain ] = [ Gain of the option at expiration ] - [ Premium 1,
(call option)
(put option)
1.4 Option Pricing
As a derived security, the price of an option varies with the price of its
underlying asset. Since the underlying asset is a risky asset, its price is a
random variable. Therefore the price of any option derived from it is also
random. However, once the price of the underlying asset is set, the price
of its derived security (option) is also determined. i.e., if the price of an
underlying asset at time t is St, the price of the option is Vt, then there
exists a function V(S, t ) such that
whereV(S, t)is a deterministic function of two variables. Our task is to deter-
mine this function by establishing a model of partial differential equations.
VT, an option's value at expiration date, is already set, which is the
option's payoff:
V =
T { (K
(ST - K)+,
- ST)+.
(call option)
(put option)
6. 6 Mathematical Modeling and Methods of Option Pricing
The problem of option pricing is to find V = V(S, t ) ,(0 < S < m,0 5
t <
T ) ,such that
V(S,T) = (S - K)+, (call option)
(K - S)+. (put option)
In particular, if a stock's price a t the option's initial date t = 0 is So,we
want to know how much to pay for the premium p, i.e.
The problem of option pricing is hence a backward problem.
1.5 Types of Traders
There are three types of derivatives traders in the security exchange mar-
kets:
1. Hedger
Hedging: to invest on both sides to avoid loss. Most producers and
trading companies enter the derivatives markets to shift or reduce the price
risks in the underlying asset markets to secure anticipated profits.
Example A US company will pay 1 million British Pound to a British
supplier in 90 days. Now it faces a currency risk due to the uncertain
USD/Pound exchange rates. If the Pound goes up, it will cost the company
more for the payment, thus will hurt the company's profits. Suppose the
exchange rate is currently 1.6 USD/Pound, and the Pound may go up, the
company may consider the following hedging plans:
Plan 1 Purchase a forward contract to buy 1 million Pound with 1,
650,000 Yuan 90 days later, and thus lock the cost of the payment in USD.
Plan 2 Purchase a call option to buy 1 million Pound with 1, 600,
000 USD 90 days later. The company pays a premium of 64, 000 USD
(assuming a 4% fee) for the option.
The following table shows the results of the above risk-avoiding plans.
current rate 90 days later no hedging forward contract call option
(USD/Pound) rate(USD/Pound) (USD) hedge(USD) hed~e(USD)
7. Risk Management and Financial Derivatives 7
One can see from this example: if the company adopts no hedging plan,
its payment will increase if the Pound rate goes up, and thus will hurt its
total profits. If the company signs a forward contract to lock the cost of
the 90 days later payment, it has avoided a loss if the Pound goes up, but
it has also given up the opportunity of gaining if the Pound goes down. If
the company purchases a call option, it can prevent loss if the Pound goes
up, and it can still gain if the Pound goes down, but it must pay a premium
for the option.
2. Speculator
Speculation: an action characterized by willing to risk with one's
money by frequently buying and selling derivatives (futures, options) for
the prospect of gaining from the frequent price changes.
A speculator assumes the price risk, hoping to gain risky profits by
holding certain positions (long or short).
Speculators are indispensable for the existence of hedging business, and
they came into markets as a necessary result of the growth of the hedg-
ing business. It is speculators who take over the price risks shifted from
the hedgers, and thus become the major bearers of the risks in the deriva-
tives markets. Speculation is an indispensable lubricant in the derivatives
markets. Indeed, frequent speculative transactions make hedging strategies
workable.
Comparing to investing in an underlying asset, investments in its options
are characterized by high profits a n d high risk, since an investment in
options markets provides a much higher level of leverage than an investment
in the spot markets. Such an investor invests only a small amount of money
(to pay the premium) but can speculate on assets valued dozens of times
higher than that of the invested money.
Example Suppose the price of a certain stock is 66.6 USD on April
30, and the stock may go up in August. The investor may consider the
following investing strategies:
A. The investor spends 666, 000 USD in cash to buy 10, 000 shares on
April 30.
B. The investor pays a premium of 39,000 USD to purchase a call option
to buy 10, 000 shares at the strike price 68.0 USD per share on August 22.
Now examine the investor's profits and r e t u r n s in two scenarios (ig-
noring the interests).
Situation I The stock goes up to 73.0 USD on August 22.
Strategy A. The investor sells the stocks on August 22 to get 730,000
8. 8 Mathematical Modeling and Methods of Option Pricing
USD in cash.
730 Ooo - 666 Oo0
return = 100% = 9.6%;
666 000
Strategy B. The investor exercises the option to receive a payoff:
payoff = 730 000 - 680 000 = 50 OOOUSD
50 000 - 39 000
return = x 100% = 28.2%.
39 000
Situation I1 The stock goes down to 66,O USD on August 22.
Strategy A. The investor suffers a loss:
loss = 666 000 - 660 000 = 6000USD,
Strategy B. The investor receives a payoff:
payoff = (660 000 - 680 000)+ = 0.
The investor loses the entire invested 39, 000 USD, hence a loss of 100%.
3. Arbitrageur
Arbitrage: based on observations of the same kind of risky assets,
taking advantage of the price differences between markets, the arbitrageur
trades simultaneously at different markets to gain riskless instant profits.
Arbitrage is not the same as speculation: speculation is to seek profits
promised by predictions of the future prices, and is thus risky. Arbitrage
is to snatch profits originated in the reality of the price differences between
markets, and is therefore riskless.
An opportunity for arbitrage cannot last long. Since once an opportu-
nity for arbitrage arises, the market prices will soon reach a new balance
due to actions of the arbitrageurs and the opportunity will thus disappear.
Therefore, all discussions in this book are founded on the basis that arbi-
trage opportunity does not exist.