Chap 9
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1. The document discusses key properties and relationships involving stock options, including how the price of calls and puts are affected by variables like the stock price, strike price, time to expiration, volatility, and interest rates. 2. It explores the difference between American and European options and conditions where an arbitrage opportunity may exist. 3. The document examines the potential to exercise American options early and reasons why calls on non-dividend paying stocks usually are not exercised early.
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Recommended
Chap 10
This document discusses various trading strategies involving options. It identifies the main types of strategies as those that take a position in an option and the underlying asset, those that take a position in multiple options of the same type (a spread), and those that use a combination of calls and puts. It then provides examples and diagrams of specific strategies, including bull spreads, bear spreads, butterfly spreads, calendar spreads, straddles, strips, straps, and strangles.
7 2 Graphing Simple Quadratic Functions
The document discusses graphing simple quadratic functions by hand without a calculator or table of values. It provides examples of graphing quadratic equations like y = x^2, y = 1/2x^2 + 2, and y = 5x^2 - 8, explaining how to identify the vertex and determine if the graph has roots by setting it equal to 0. It then gives a real world example of graphing the function d=-16t^2 +30 that models the height of a stick dropped from a flying eagle over time, noting that the domain is non-negative to only measure time positively and the range does not exceed 30 feet since that was the starting height.
Slides to RSA Presentation
1. In 1977, Whitfield Diffie and Martin Hellman proposed the idea of public-key cryptography, where one key is used for encryption and another for decryption.
2. In 1978, Ronald Rivest, Adi Shamir and Leonard Adelman published the RSA algorithm, which became the de facto standard for public-key cryptography for 30 years. It uses a "trap-door" based on the difficulty of factoring large numbers.
3. The RSA algorithm works by using two large prime numbers to generate a public key for encryption and a private key for decryption. Encryption and decryption are done by exponentiation and taking the remainder modulo the product of the prime numbers.
診断報告書を秒速で作るためのExcelショートカット講座
診断士試験に合格し、実務補習を控えている方を中心に、時間をロスせずにExcel作業を進めるためのノウハウ（ショートカットキー）を紹介しています。 作業を高速化し、実務補習の中で「頭を使う時間」を最大化しましょう。
Shortcut gimp for gimper
This document contains a list of keyboard shortcuts for the GIMP image editor software in Linux. It includes shortcuts for tools, files, dialogs, views, editing functions, layers, selections, and plugins. Some examples are the R key for the Rectangular Select tool, Ctrl+S for saving an image, and Ctrl+Z for undo.
coloring method
3-Coloring is NP-complete. The document shows that 3-SAT reduces to 3-Coloring in polynomial time, proving 3-Coloring is NP-hard. The reduction works by creating a graph where each variable gets two nodes and each clause gets an OR-gadget. If the graph is 3-colorable, it encodes a satisfying assignment, and vice versa.
Chap 1
1) Derivatives are financial instruments whose value is dependent on an underlying asset such as stocks, bonds, currencies or commodities. Common derivatives include futures, forwards, swaps and options.
2) Derivatives are traded both over-the-counter between institutions and on organized exchanges. The total notional value of the over-the-counter market is many times larger than the exchange market.
3) Derivatives are used for hedging risks, speculation, arbitrage and adjusting portfolio exposures without selling existing positions. Traders include hedgers who offset price risks, speculators who take views on markets, and arbitrageurs who exploit pricing inefficiencies.
Ch18 4e t rev cmc
1) O documento discute a abertura dos mercados de bens e mercados financeiros em três dimensões: abertura dos mercados de bens, mercados financeiros e mercados de fatores.
2) Apresenta gráficos sobre as exportações e importações dos EUA e do Brasil como proporção do PIB ao longo do tempo.
3) Discutem conceitos como taxas de câmbio nominais e a escolha dos consumidores entre bens nacionais e estrangeiros com a abertura dos mercados.
Recommended
Chap 10
This document discusses various trading strategies involving options. It identifies the main types of strategies as those that take a position in an option and the underlying asset, those that take a position in multiple options of the same type (a spread), and those that use a combination of calls and puts. It then provides examples and diagrams of specific strategies, including bull spreads, bear spreads, butterfly spreads, calendar spreads, straddles, strips, straps, and strangles.
7 2 Graphing Simple Quadratic Functions
The document discusses graphing simple quadratic functions by hand without a calculator or table of values. It provides examples of graphing quadratic equations like y = x^2, y = 1/2x^2 + 2, and y = 5x^2 - 8, explaining how to identify the vertex and determine if the graph has roots by setting it equal to 0. It then gives a real world example of graphing the function d=-16t^2 +30 that models the height of a stick dropped from a flying eagle over time, noting that the domain is non-negative to only measure time positively and the range does not exceed 30 feet since that was the starting height.
Slides to RSA Presentation
1. In 1977, Whitfield Diffie and Martin Hellman proposed the idea of public-key cryptography, where one key is used for encryption and another for decryption.
2. In 1978, Ronald Rivest, Adi Shamir and Leonard Adelman published the RSA algorithm, which became the de facto standard for public-key cryptography for 30 years. It uses a "trap-door" based on the difficulty of factoring large numbers.
3. The RSA algorithm works by using two large prime numbers to generate a public key for encryption and a private key for decryption. Encryption and decryption are done by exponentiation and taking the remainder modulo the product of the prime numbers.
診断報告書を秒速で作るためのExcelショートカット講座
診断士試験に合格し、実務補習を控えている方を中心に、時間をロスせずにExcel作業を進めるためのノウハウ（ショートカットキー）を紹介しています。 作業を高速化し、実務補習の中で「頭を使う時間」を最大化しましょう。
Shortcut gimp for gimper
This document contains a list of keyboard shortcuts for the GIMP image editor software in Linux. It includes shortcuts for tools, files, dialogs, views, editing functions, layers, selections, and plugins. Some examples are the R key for the Rectangular Select tool, Ctrl+S for saving an image, and Ctrl+Z for undo.
coloring method
3-Coloring is NP-complete. The document shows that 3-SAT reduces to 3-Coloring in polynomial time, proving 3-Coloring is NP-hard. The reduction works by creating a graph where each variable gets two nodes and each clause gets an OR-gadget. If the graph is 3-colorable, it encodes a satisfying assignment, and vice versa.
Chap 1
1) Derivatives are financial instruments whose value is dependent on an underlying asset such as stocks, bonds, currencies or commodities. Common derivatives include futures, forwards, swaps and options.
2) Derivatives are traded both over-the-counter between institutions and on organized exchanges. The total notional value of the over-the-counter market is many times larger than the exchange market.
3) Derivatives are used for hedging risks, speculation, arbitrage and adjusting portfolio exposures without selling existing positions. Traders include hedgers who offset price risks, speculators who take views on markets, and arbitrageurs who exploit pricing inefficiencies.
Ch18 4e t rev cmc
1) O documento discute a abertura dos mercados de bens e mercados financeiros em três dimensões: abertura dos mercados de bens, mercados financeiros e mercados de fatores.
2) Apresenta gráficos sobre as exportações e importações dos EUA e do Brasil como proporção do PIB ao longo do tempo.
3) Discutem conceitos como taxas de câmbio nominais e a escolha dos consumidores entre bens nacionais e estrangeiros com a abertura dos mercados.
Chap 7
An interest rate swap is an agreement to exchange interest rate cash flows, typically involving one party paying a fixed rate in exchange for a floating rate from the other party. A currency swap involves exchanging principal amounts in different currencies and paying interest on those principal amounts. Swaps allow parties to transform fixed rate assets and liabilities into floating rate, or vice versa, based on their comparative advantage in borrowing costs in fixed vs floating markets. Swaps can be valued as a portfolio of forward contracts or by comparing the values of fixed and floating rate bonds.
Chap 8
A call option gives the holder the right to buy the underlying asset, while a put option gives the holder the right to sell. European options can only be exercised at expiration, while American options can be exercised at any time before expiration. The document then discusses long and short positions in call and put options and provides examples of profit diagrams for different option positions. It also reviews the key terms, underlying assets, and specifications of exchange-traded options. The document concludes by discussing dividends and stock splits, market makers, margins, warrants, executive stock options, and convertible bonds.
Chap 5
1. The document discusses the determination of forward and futures prices for different types of assets, including consumption assets like oil and investment assets like gold. It presents the key formulas for relating the forward or futures price to the expected future spot price based on factors like interest rates, storage costs, and yield.
2. Short selling is discussed as selling securities you do not own by borrowing them from another client and later replacing them.
3. Examples are provided of using the formulas to check for arbitrage opportunities between spot and forward gold prices under different interest rate scenarios.
Chap 2
- Futures contracts are exchange-traded agreements to buy or sell an asset at a predetermined price on a specified future date. They are standardized and settled daily through margin accounts.
- Margins are deposits that minimize the risk of default by requiring maintenance of a minimum account balance. Daily price fluctuations result in gains or losses being deposited to or withdrawn from the margin account.
- A long position in gold futures is established with an initial margin deposit. The daily settlement process results in funds being added to or withdrawn from the margin account depending on price movements of the gold futures contract.
Chap 5
1. The document discusses the determination of forward and futures prices for different types of assets, including consumption assets like oil and investment assets like gold. It presents the key formulas for relating the forward or futures price to the expected future spot price based on factors like interest rates, storage costs, and yield.
2. Short selling is discussed as selling securities you do not own by borrowing them from another client and later replacing them.
3. Examples are provided for arbitrage opportunities between spot and forward gold prices under different interest rate scenarios.
Chap 3
There are two main types of hedges using futures contracts: long hedges and short hedges. Long hedges lock in future purchase prices while short hedges lock in future sale prices. Companies should focus on hedging to minimize risks from market variables like interest rates and exchange rates. However, hedging also introduces basis risk and may not be optimal if competitors do not hedge. The optimal hedge ratio balances reducing risk from changes in the spot price with basis risk from changes in the futures price. Hedging equity portfolios or individual stocks helps manage systematic risk and allows investors to reduce or increase their market exposure.
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Este documento discute os mercados financeiros e a determinação da taxa de juros de equilíbrio. Ele explica que a taxa de juros é determinada pelo equilíbrio entre a demanda e a oferta de moeda do Banco Central, que depende da renda, taxa de juros e oferta monetária. Os bancos desempenham um papel importante ao receber depósitos e manter reservas, afetando assim a demanda por moeda do Banco Central.
Chap 9
1. The document discusses key properties and relationships involving stock options, including how the price of calls and puts are affected by variables like the stock price, strike price, time to expiration, volatility, and interest rates.
2. It explores the difference between American and European options and conditions where an arbitrage opportunity may exist.
3. The document examines the potential to exercise American options early and reasons why calls on non-dividend paying stocks generally should not be exercised early.
Chap 4
The document discusses interest rates and bond pricing. It defines different types of rates like Treasury rates and LIBOR. It also covers concepts like continuously compounded rates, zero rates, bond yields, and the bootstrap method for constructing a zero curve from market data. Forward rates represent the future implied rates along the current yield curve. Forward rate agreements allow parties to exchange interest payments at a fixed rate versus the future market rate. Bond duration and convexity measure sensitivity to yield changes.
Derivatives
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.
Chap 6
The document discusses various topics related to interest rate futures, including:
1) Day count conventions used in different money market instruments and bonds in the US.
2) How treasury bond prices are quoted and how futures contracts work for treasury bonds.
3) Eurodollar futures contracts which are based on 3-month LIBOR rates and how they are settled.
4) How forward rates can be determined from Eurodollar futures and extending the LIBOR zero curve.
5) Duration matching and calculating hedge ratios to hedge interest rate risk.
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Malaysian government securities
MGS futures contracts allow investors to take positions on Malaysian government bond (MGS) prices without physically holding the bonds. Institutional investors can use MGS futures as a temporary substitute when the physical bond market is illiquid. Speculators provide liquidity to the market by taking long or short positions based on their views of how interest rates and bond prices may move in the future. Hedgers use MGS futures to offset risks to their bond portfolios from potential interest rate changes. The document provides examples of how an institutional investor, speculator, and hedger might use MGS futures contracts.
Chapter 5 pricing
This document discusses the determination of forward and futures prices. It introduces the concepts of investment assets versus consumption assets and explains how short selling works. It then provides the basic formulas for relating the forward or futures price to the spot price based on interest rates. The formulas are adapted for assets that pay income or have storage costs. Arbitrage opportunities that can arise when the theoretical relationship between spot and forward/futures prices does not hold are also discussed.
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Conheça este e mais materiais em:
blog.ideiaconsultoria.com.br
www.ideiaconsultoria.com.br
Chapter 13
The document discusses the Black-Scholes-Merton model for valuing stock options. It describes the random walk assumption used in the model and how it implies stock prices will follow a lognormal distribution. The Black-Scholes formula for option prices is presented, which values options based on the stock price, strike price, risk-free rate, time to expiration, and volatility. The concept of implied volatility is introduced, which is the volatility input to the Black-Scholes formula that produces the market price. Adjustments to the model for dividends are also covered.
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An interest rate swap is an agreement to exchange cash flows at specified future times according to certain rules. In a typical "plain vanilla" interest rate swap, one party pays a fixed interest rate on a notional principal while the other party pays a floating rate, usually based on LIBOR. Currency swaps involve exchanging principal amounts in different currencies in addition to periodic interest payments. Swaps allow parties to transform fixed rate obligations/investments into floating rate or to gain exposure to another currency. Swaps can be valued by comparing the cash flows of a fixed rate bond to a floating rate bond or as a portfolio of forward rate agreements.
Call and put Options
This document provides an overview of call and put options, including:
- Call options give the buyer the right to purchase an underlying asset at a specified strike price. Put options give the buyer the right to sell an underlying asset at a specified strike price.
- Options have an expiration date and are used for speculation or hedging. Speculators try to profit from price changes, while hedgers use options to reduce risk.
- The value of an option depends on the value of the underlying asset and volatility. At expiration, call options are worth the maximum of the asset price minus strike price and zero. Put options are worth the maximum of strike price minus asset price and zero.
- Buy
Cost accounting solutions chapter 2 (1)
cost accounting by polimeni & fabozzi... solutions of chapter 2
http://www.coursehero.com/tutor-profile/mm226/
Chapter no 2 CGS
The document provides information and examples related to cost accounting, including:
1) Exercises calculating cost of goods manufactured, cost of goods sold, prime cost, conversion cost, and total variable cost.
2) Journal entries for the manufacturing cost accounting cycle.
3) Cost of goods manufactured and cost of goods sold statements for multiple companies.
Chapter 10
The document discusses key concepts related to stock options, including:
1) It defines the notation used to describe option pricing models and lists how underlying variables like stock price, strike price, volatility, and time to expiration affect call and put prices.
2) It explains that American options are generally worth at least as much as equivalent European options due to the ability to exercise early.
3) The document derives put-call parity and no-arbitrage bounds for call and put prices under various assumptions about dividends. It also discusses the potential for arbitrage opportunities when observed prices violate these bounds.
4) Factors affecting early exercise of American options are explored, noting that calls on non-div
My pricing of american options
This document discusses pricing models for American option contracts. It begins by outlining the standard model, which values American options based on the moment that guarantees maximum option value. However, the author proposes an alternative view, where the optimal exercise time is when the underlying asset reaches its maximum value on [0,T]. Exercising at this maximum value ensures a payoff equal to the selling price, avoiding arbitrage. The document formalizes this idea using concepts like risk-neutral probabilities and derivations of put-call parity relationships to define fair option prices.
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An interest rate swap is an agreement to exchange interest rate cash flows, typically involving one party paying a fixed rate in exchange for a floating rate from the other party. A currency swap involves exchanging principal amounts in different currencies and paying interest on those principal amounts. Swaps allow parties to transform fixed rate assets and liabilities into floating rate, or vice versa, based on their comparative advantage in borrowing costs in fixed vs floating markets. Swaps can be valued as a portfolio of forward contracts or by comparing the values of fixed and floating rate bonds.
Chap 8
A call option gives the holder the right to buy the underlying asset, while a put option gives the holder the right to sell. European options can only be exercised at expiration, while American options can be exercised at any time before expiration. The document then discusses long and short positions in call and put options and provides examples of profit diagrams for different option positions. It also reviews the key terms, underlying assets, and specifications of exchange-traded options. The document concludes by discussing dividends and stock splits, market makers, margins, warrants, executive stock options, and convertible bonds.
Chap 5
1. The document discusses the determination of forward and futures prices for different types of assets, including consumption assets like oil and investment assets like gold. It presents the key formulas for relating the forward or futures price to the expected future spot price based on factors like interest rates, storage costs, and yield.
2. Short selling is discussed as selling securities you do not own by borrowing them from another client and later replacing them.
3. Examples are provided of using the formulas to check for arbitrage opportunities between spot and forward gold prices under different interest rate scenarios.
Chap 2
- Futures contracts are exchange-traded agreements to buy or sell an asset at a predetermined price on a specified future date. They are standardized and settled daily through margin accounts.
- Margins are deposits that minimize the risk of default by requiring maintenance of a minimum account balance. Daily price fluctuations result in gains or losses being deposited to or withdrawn from the margin account.
- A long position in gold futures is established with an initial margin deposit. The daily settlement process results in funds being added to or withdrawn from the margin account depending on price movements of the gold futures contract.
Chap 5
1. The document discusses the determination of forward and futures prices for different types of assets, including consumption assets like oil and investment assets like gold. It presents the key formulas for relating the forward or futures price to the expected future spot price based on factors like interest rates, storage costs, and yield.
2. Short selling is discussed as selling securities you do not own by borrowing them from another client and later replacing them.
3. Examples are provided for arbitrage opportunities between spot and forward gold prices under different interest rate scenarios.
Chap 3
There are two main types of hedges using futures contracts: long hedges and short hedges. Long hedges lock in future purchase prices while short hedges lock in future sale prices. Companies should focus on hedging to minimize risks from market variables like interest rates and exchange rates. However, hedging also introduces basis risk and may not be optimal if competitors do not hedge. The optimal hedge ratio balances reducing risk from changes in the spot price with basis risk from changes in the futures price. Hedging equity portfolios or individual stocks helps manage systematic risk and allows investors to reduce or increase their market exposure.
Ch04 4e t
Este documento discute os mercados financeiros e a determinação da taxa de juros de equilíbrio. Ele explica que a taxa de juros é determinada pelo equilíbrio entre a demanda e a oferta de moeda do Banco Central, que depende da renda, taxa de juros e oferta monetária. Os bancos desempenham um papel importante ao receber depósitos e manter reservas, afetando assim a demanda por moeda do Banco Central.
Chap 9
1. The document discusses key properties and relationships involving stock options, including how the price of calls and puts are affected by variables like the stock price, strike price, time to expiration, volatility, and interest rates.
2. It explores the difference between American and European options and conditions where an arbitrage opportunity may exist.
3. The document examines the potential to exercise American options early and reasons why calls on non-dividend paying stocks generally should not be exercised early.
Chap 4
The document discusses interest rates and bond pricing. It defines different types of rates like Treasury rates and LIBOR. It also covers concepts like continuously compounded rates, zero rates, bond yields, and the bootstrap method for constructing a zero curve from market data. Forward rates represent the future implied rates along the current yield curve. Forward rate agreements allow parties to exchange interest payments at a fixed rate versus the future market rate. Bond duration and convexity measure sensitivity to yield changes.
Derivatives
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.
Chap 6
The document discusses various topics related to interest rate futures, including:
1) Day count conventions used in different money market instruments and bonds in the US.
2) How treasury bond prices are quoted and how futures contracts work for treasury bonds.
3) Eurodollar futures contracts which are based on 3-month LIBOR rates and how they are settled.
4) How forward rates can be determined from Eurodollar futures and extending the LIBOR zero curve.
5) Duration matching and calculating hedge ratios to hedge interest rate risk.
Como investir-na-bolsa-de-valores
O documento fornece instruções sobre como investir em ações na Bolsa de Valores, descrevendo o que é a Bolsa, por que foi criada para facilitar o financiamento de empresas e negociação de ativos, e os passos para começar a investir, incluindo escolher uma corretora e usar o home broker.
Malaysian government securities
MGS futures contracts allow investors to take positions on Malaysian government bond (MGS) prices without physically holding the bonds. Institutional investors can use MGS futures as a temporary substitute when the physical bond market is illiquid. Speculators provide liquidity to the market by taking long or short positions based on their views of how interest rates and bond prices may move in the future. Hedgers use MGS futures to offset risks to their bond portfolios from potential interest rate changes. The document provides examples of how an institutional investor, speculator, and hedger might use MGS futures contracts.
Chapter 5 pricing
This document discusses the determination of forward and futures prices. It introduces the concepts of investment assets versus consumption assets and explains how short selling works. It then provides the basic formulas for relating the forward or futures price to the spot price based on interest rates. The formulas are adapted for assets that pay income or have storage costs. Arbitrage opportunities that can arise when the theoretical relationship between spot and forward/futures prices does not hold are also discussed.
Palestra capital de giro
A Gestão do Capital de Giro é o sangue que circula para a operação da empresa. Mais de 40% das empresas tem problemas na falta de capital para suportar suas operações. Saiba nesta apresentação o que é, como calcular, as etapas desta proposta e uma simulação dos resultados na sua empresa.
Conheça este e mais materiais em:
blog.ideiaconsultoria.com.br
www.ideiaconsultoria.com.br
Chapter 13
The document discusses the Black-Scholes-Merton model for valuing stock options. It describes the random walk assumption used in the model and how it implies stock prices will follow a lognormal distribution. The Black-Scholes formula for option prices is presented, which values options based on the stock price, strike price, risk-free rate, time to expiration, and volatility. The concept of implied volatility is introduced, which is the volatility input to the Black-Scholes formula that produces the market price. Adjustments to the model for dividends are also covered.
Ch07 hullofod8thedition
An interest rate swap is an agreement to exchange cash flows at specified future times according to certain rules. In a typical "plain vanilla" interest rate swap, one party pays a fixed interest rate on a notional principal while the other party pays a floating rate, usually based on LIBOR. Currency swaps involve exchanging principal amounts in different currencies in addition to periodic interest payments. Swaps allow parties to transform fixed rate obligations/investments into floating rate or to gain exposure to another currency. Swaps can be valued by comparing the cash flows of a fixed rate bond to a floating rate bond or as a portfolio of forward rate agreements.
Call and put Options
This document provides an overview of call and put options, including:
- Call options give the buyer the right to purchase an underlying asset at a specified strike price. Put options give the buyer the right to sell an underlying asset at a specified strike price.
- Options have an expiration date and are used for speculation or hedging. Speculators try to profit from price changes, while hedgers use options to reduce risk.
- The value of an option depends on the value of the underlying asset and volatility. At expiration, call options are worth the maximum of the asset price minus strike price and zero. Put options are worth the maximum of strike price minus asset price and zero.
- Buy
Cost accounting solutions chapter 2 (1)
cost accounting by polimeni & fabozzi... solutions of chapter 2
http://www.coursehero.com/tutor-profile/mm226/
Chapter no 2 CGS
The document provides information and examples related to cost accounting, including:
1) Exercises calculating cost of goods manufactured, cost of goods sold, prime cost, conversion cost, and total variable cost.
2) Journal entries for the manufacturing cost accounting cycle.
3) Cost of goods manufactured and cost of goods sold statements for multiple companies.
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3) The document derives put-call parity and no-arbitrage bounds for call and put prices under various assumptions about dividends. It also discusses the potential for arbitrage opportunities when observed prices violate these bounds.
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This document outlines arbitrage bounds and pricing restrictions for call and put options. It states that a call option cannot sell for more than the underlying asset price, and a put cannot sell for more than the strike price. It also provides the lower bound restrictions for calls and puts on non-dividend paying stocks. The document discusses that early exercise of American options is never optimal and outlines put-call parity for European options.
put call parity
The document discusses properties of stock options, specifically put-call parity. It defines put-call parity as the relationship between the value of a European call option and put option with the same exercise price and date. Put-call parity can be used to identify arbitrage opportunities when it does not hold. The document also examines how put-call parity applies to American options and options on dividend paying stocks. Early exercise of American put options may be optimal unlike American call options.
Portfolio management
The document describes three problems related to constructing optimal self-financing portfolios consisting of stocks and options. Problem 1 involves a portfolio with one stock and one option, Problem 2 involves one stock and two options, and Problem 3 prices an up-and-out option using a finite difference method. For each problem, the document outlines the portfolio composition, parameters, and numerical approach taken to determine optimal quantities of options to minimize portfolio variance.
American option
This document discusses pricing models for American options. It specifies that American options can be exercised at any time prior to maturity, unlike European options which can only be exercised at maturity. The value of an American option is defined as the expected value of the European option price using the random exercise time. American options can be decomposed into their European counterpart plus an early exercise premium. Determining the optimal early exercise time is formulated as finding the stopping time that maximizes the expected discounted payoff over the lifetime of the contract. References for further reading on pricing American options are also provided.
Pricing American Options - Duality approach in Monte Carlo
The document discusses pricing American options using the duality approach in Monte Carlo simulations. It formulates the American option pricing problem as an optimal stopping problem, where the value is the expected discounted payoff under the optimal exercise rule. It approximates the continuation value function using least squares regression, simulating the regression coefficients with Monte Carlo asset price paths. The approach recursively calculates values moving backward from the expiration to price the option using the estimated continuation values.
Options pricing using Lattice models
This document describes pricing options using lattice models, specifically binomial trees. It provides details on:
1) Using a binomial tree to price a European call option by replicating the option payoff at each node.
2) Matching the moments of the binomial and Black-Scholes models to derive the Cox-Ross-Rubinstein (CRR) binomial tree.
3) Implementing the CRR model in C++ to price European call and put options via backward induction on the tree.
Options pricing and hedging
A new derivation of the Black Scholes Equation (BSE) based on integral form stochastic calculus is presented. Construction of the BSE solution is based on infinitesimal perfect hedging. The perfect hedging on a finite time interval is a separate problem that does not change option pricing. The cost of hedging does not present an adjustment of the BS pricing. We discuss a more profound alternative approach to option pricing. It defines option price as a settlement between counterparties and in contrast to BS approach presents the market risk of the option premium.
Alternative option pricing and cva
There are several significant drawbacks in derivative price modeling which relate to global regulations of the derivatives market. Here we present a unified approach which in stochastic market interprets option price as a random variable. Therefore spot price does not complete characteristic of the price in stochastic environment. Complete derivatives price includes the spot price as well as thevalue of market risk implied by the use of the spot price. This interpretation is similar to the notion of therandom variable in Probability Theory in which an estimate of the random variable completely defined by its cumulative distribution function
Vidyasagar rocond09
The document provides an introduction to quantitative finance concepts including option pricing models. It begins with an outline and terminology. It then covers the Black-Scholes option pricing model, which uses stochastic calculus to derive a partial differential equation for pricing European options. The document also discusses replicating strategies in discrete and continuous time models, as well as extensions like American options and the Greeks.
Cambridge
1) The document discusses pricing models for derivatives such as options and interest rate swaps. It introduces concepts such as local volatility, which models implied volatility as a function of strike price and time to maturity.
2) Black-Scholes pricing is based on the assumption of a perfect hedging strategy, but the document notes this is formally incorrect as the hedging portfolio defined does not satisfy the required equations.
3) Local volatility presents the option price as a function of strike and time to maturity, with the diffusion coefficient estimated from option price data, whereas Black-Scholes models the price as a function of the underlying and time, with volatility as an input.
Bo pricing
- The document describes binomial option pricing models for valuing European call and put options on stocks that can move up or down over one or multiple time periods.
- It provides a replicating portfolio approach to derive the option pricing formulas in one and two period binomial models.
- Estimates for the up and down movements (Ru and Rd) in a multi-period model can be derived from the mean and standard deviation of the underlying stock's returns over the time period.
- For example, with a 4 month option, 14% annual stock returns, 23% volatility, the up movement would be 12.36% and down movement -6.
BB_11_Futures & Options_Hull_Chap_12.pptx
The document provides an overview of option valuation using the binomial model. It describes a multi-period binomial model where the underlying stock price can move up or down by a factor u or d at each period. The value of a call option is calculated as the expected discounted payoff over the periods. Key steps include: (1) Setting parameters u, d, p to match the stock's expected return, variance over each period, and a simplifying condition; (2) Using risk-neutral valuation to price options assuming stock returns the risk-free rate; (3) Applying the one-period model recursively to value options over multiple periods.
Similar to Chap 9 (20)
Pricing American Options - Duality approach in Monte Carlo
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BONKMILLON Unleashes Its Bonkers Potential on Solana.pdf
Introducing BONKMILLON - The Most Bonkers Meme Coin Yet
Let's be real for a second – the world of meme coins can feel like a bit of a circus at times. Every other day, there's a new token promising to take you "to the moon" or offering some groundbreaking utility that'll change the game forever. But how many of them actually deliver on that hype?
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BONKMILLON Unleashes Its Bonkers Potential on Solana.pdf
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Chap 9
- 1. Properties of Stock Options Chapter 9
- 3. Effect of Variables on Option Pricing (Table 9.1, page 206) c p C P + + – + + + + + + + + – + – – – – + – + – + Variable S 0 K T r D ? ?
- 15. The Impact of Dividends on Lower Bounds to Option Prices (Equations 9.5 and 9.6, pages 21 8 -2 19 )