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Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
Derivatives Pricing (WCM 2010)
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Derivatives Pricing (WCM 2010)

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  • Title Page – Style 1
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    • 1. Derivatives PricingEducational Seminar 5Tuesday, February 2, 2010
    • 2. DisclaimerThis presentation was prepared exclusively for the benefit and use of the members of Western Capital Markets (“WCM”) forthe purpose of teaching and discussing financial and investment matters. This presentation is proprietary to WCM .The information and any analyses contained in this presentation are taken from, or based upon, information obtained fromthe WCM Executive Team or from publicly available sources. Any information taken from external literature is appropriatelyreferenced. The completeness and accuracy of this presentation cannot be assured by WCM.To the extent projections and financial analyses are set forth herein, they may be based on estimated financial performanceprepared by WCM and are intended only to suggest reasonable ranges of results. Any calculations or value rangesindicated herein are preliminary and should not be construed as opinions of WCM or their individual members as to value,fair market value, or target prices at which a transaction would be considered fair from a financial point of view and must notbe relied upon or disclosed as constituting such a document or opinion.WCM does not take liability for any inaccurate information, and is not liable for any investment advice. Before acting on anyinformation, from WCM or external sources, you should contact a Certified Financial Advisor. 2
    • 3. AgendaI. Intro to Derivatives ConceptsII. OptionsIII. Forwards & Futures ContractsIV. Questions WCM WCM’s “Fearless Leader” 3
    • 4. WCM’s NEW “Fearless Leaders” Kenny Ari4
    • 5. Intro to Derivatives ConceptsSECTION I
    • 6. What is a Derivative? Derivative: A contract between two counterparties whose value is derived from an underlying asset  Underlying Asset: An asset that must be delivered if the contract is exercised  If Derivative = Options  Underlying Asset = Stocks  If Derivative = Forwards/Futures  Underlying Asset = {Currencies, Oil, Natural Gas, Other Commodities}  Derivatives are contracts on a specific asset, spanning a specific time period, between two parties. This can be arranged on an exchange, where market participants post bid and ask prices on a standardized list of contracts, or OTC (over the counter) where clients deal with a market maker individually. Derivatives are a “zero-sum game” (the gains from entering a contract for one party are equal in magnitude to the loss for the other party involved in the contract) Derivatives can be used to manage risk (i.e. “lock-in” prices and prevent losses due to market volatility)  Example: If I need natural gas to power my manufacturing plant (especially in the winter), but I want to be able to budget for these costs in the summer and not have to pay really high prices once it becomes winter, I can enter a contract to “lock-in” a price for natural gas in the coming winter Derivatives, especially when used improperly, can be risky (there are elements of leverage and speculation)  Leverage occurs because an expensive asset can be controlled with relatively little money. Though this magnifies the return in bull markets, it magnifies losses in bear markets  Speculators bet on future prices (why would we lock in a price of $10 for natural gas in a year when we think it will actually only cost $5 in a year? To lock in at a certain price is implicitly taking a position on where you think the price of the underlying security will be in the future.) Some staggering losses resulted from improper use of derivatives (i.e. Orange County - highly leveraged, wrong bet) 6
    • 7. Examples of Where/Why Derivatives are Used – Part I Hedging Automotive manufacturer  Manufactures cars in the US  Costs of inputs (labour, parts, etc.) are in USD  Sells in Europe  Sales are received in Euros €  Can the relative exchange rate between countries affect profits?  Yes. So, GM could “lock-in” an exchange rate using derivatives to prevent from swings in the exchange rate over time. Insurance Ketchup producer foresees a spike in tomato prices over the next year  What action can Heinz take?  How about buy extra tomatoes now?  Perhaps. But won’t the tomatoes go rotten in a year’s time?  Answer: “Lock-in” prices through forward contract with tomato farmer  Heinz is likely willing to accept consequences of poor prediction (even if prices don’t rise, at least they had a form of “insurance” through the forward contract to ensure they were prepared for the opposite to happen!) 7
    • 8. Examples of Where/Why Derivatives are Used – Part II Speculation You believe that RIM will win the patent infringement lawsuit with other cell-phone manufacturer  Thus, RIM shares will appreciate if they win based a higher certainty of profits in the future  Purchase call options  Relatively low cost of investment  “Betting the Farm” (e.g. willing to lose entire investment) Incentives Cisco Systems allows employees to participate in a stock option plan  Employees with stock options have an incentive to work hard because if the price of the stock appreciates, their call options will allow them to buy the stocks at a low price and sell at a higher price in the market (therefore making them a profit!)  Stock options  Hard work  Higher stock price  Everyone’s happy!  Options are often used as an incentive in young, growing companies (e.g. tech) 8
    • 9. How Are Derivatives Traded? Derivatives can be traded on an exchange or OTC (“Over The Counter”)  Exchanges  Examples: CME (Chicago Mercantile Exchange ) & NYMEX (New York Mercantile Exchange)  Derivatives traded on exchanges are standardized contracts for the assets. This has benefits:  Trades are public and contract positions can easily be “closed” (offsetting by taking opposite positions)  Regulation and a third-party clearing house ensures a ‘safe’ market - virtually no default risk since the clearing house is the counterparty to each trade. There are “margin” requirements (requirements for a certain amount of liquid cash set aside in a margin account used as security in case the options tank in value and need to have losses paid out). Losses from one party are transferred to the winning party  However, standardization may mean imperfect derivatives since contract terms may not meet client needs  OTC  Some clients require specialized contracts  OTC is a private engagement where the: amount, timing of delivery, and quality of asset (for some commodities such as “Grade A beef”) are specified  Less regulation than on exchange, therefore default risk is higher (no clearing house)  These contract is usually settled at expiry.  However, the specificity prevents offsetting positions and often difficult to arrange (might be hard to find someone who wants to sell 100 tonnes of Grade A beef in 5 months at a price of $100/tonne!)  These contracts are settled at expiry, and there is no need to post margin or have payouts pegged to 9 fluctuations in asset price.  Often, if a contract is done with a bank, ‘margin’ will be deducted from the credit available to the client
    • 10. OptionsSECTION II
    • 11. What is a Stock Option? Options are a contract that entitle the holder the right (but not obligation) to buy or sell an asset at a specific time and at a specific price (the strike price)  A premium is paid for this opportunity  Options are traded in batches of 100 units  2 parties involved in an option trade  Buyer aka “Holder”  Seller aka “Writer” Several types of these options:  An American option may be exercised at any time before the expiry date  A European option may be exercised only at the expiry date of the option  Others – Bermudan, Asian, etc. 11
    • 12. Call vs. Put Options Call Option Two basic kinds (market positions) of stock options:  Call option: the holder has the right to buy a stock at an agreed-upon price at any time up to an agreed-upon date  Option is valuable when it is “in the money” (i.e. the market price of the underlying asset is above than the strike price). When the strike is higher than market price, the option is “out-of-the-money” and is only useful if the contract has still some time before expiry.  The buyer of a call is said to be long in a call and the writer is said to be short in a call  Strike Price = $300, Stock Spot Price (Dec 5) = $280, Expiry = Jan 31 2009, Interest rate = 1%  Call Option on Dec 5 = $25, Realized Payoff = $40, Profit = $15 12
    • 13. Call vs. Put OptionsPut Option  Put option: the holder has the right to sell a stock at an agreed-upon price at any time up to an agreed-upon date  The buyer of a put option has the right to sell an asset. This will be valuable when the price of the asset falls below the strike price. An “in the money” scenario when the market price of the underlying security is below the strike price. “Out of the money” scenario occurs when the market price is above the strike price.  Strike Price = $15, Stock Spot Price (Dec 10) = $17, Expiry = Jan 31 2009, Interest rate = 0%  Put Option on Dec 10 = $1.5, Realized Payoff = $9, Profit = $7.513
    • 14. Pricing Options An option is essentially priced on two main factors (intrinsic and time values)  Premium = Time Value + Intrinsic Value  Intrinsic Value  Degree of “in-the-money”  Call Option  Intrinsic Value = Market Price - Exercise Price  Put Option  Intrinsic Value = Exercise Price - Market Price  Time Value  Difficult to value  Various models have been developed to attempt to price this  Black-Scholes Formula  Binomial Pricing  The time value depends on many factors including:  Volatility: an asset with a higher SD or higher Beta (in the case of equities) will command a higher premium because there is a greater likelihood that it’s price will fluctuate (and make the option in the money)  Interest rates: this represents the cost of holding the asset. With higher rates, it is more expensive to finance holding the security so the option premium is higher (for a call) 14
    • 15. Black-Scholes Option Pricing ModelMyron Scholes and Fischer Black  Received Nobel Prizes for their work  Scholes is Canadian (COOL!) and is a McMaster Graduate (NOT COOL!)Formula is based on a Partial Differential Equation (Diffusion):  C = S * N * d1 - Ke^(-rt)Nd2  P = C - S + Ke^(-rt)  d1 = [ln(S/K) + (r + s^2/2)*t]/[s*t^0.5]  d2 = d1 - s*t^0.5The 5 “black box” inputs into the equation  S – Stock Price  What is the current market price of the stock?  t – time until option expires  How much time is left until the option expires?  K – Option Strike Price  What is the exercise or strike price of the option?  r – risk free rate  What is the “risk-free” interest rate (yield of appropriate US govt. treasury)  s – volatility of returns  How much has the stock fluctuated in the past? 15
    • 16. Problems with Black-Scholes Option Pricing Model The Black-Scholes equations made Myron Scholes and Fischer Black rich at Long-Term Capital Management (LTCM), however, as more people caught on to their pricing methods and “holes” in the formula were discovered, LTCM went bankrupt The Black-Scholes options pricing model employs less-than-perfect assumptions:  No transaction costs  Stock pays no dividend  Securities perfectly divisible  Stock moves in Geometric Brownian motion  Efficient Market Hypothesis Collectively, these assumptions enable perfect “Delta Hedging”  Delta hedging is when someone continuously buys and sells stocks to remain fully hedged, but profits on the greater volatility in the market ∂V ∆= ∂S 16
    • 17. Futures & Forwards ContractsSECTION III
    • 18. Introduction to Forward Contract Pricing Consumption vs. Investment Assets:  “Investment assets” are held by significant # of people purely for investment purposes (Examples: gold, silver)  “Consumption assets” are assets held primarily for consumption (Examples: copper, oil) “Short Selling”:  Short selling involves selling securities you do not own  Your broker borrows the securities from another client and sells them in the market in the usual way  At some stage you must buy the securities back so they can be replaced in the account of the client  You must pay dividends and other benefits the owner of the securities receives Calculating Forward prices:  If the spot price of gold is S & the futures price is for a contract deliverable in T years is F, then F = S (1+r )T, where r is the 1-year risk-free rate of interest (but this does not account for continuous compounding…)  SCENARIO 1 - When interest rates are measured with “continuous compounding”, then:  F0 = S0erT  This equation relates the forward price and the spot price for any investment asset that provides no income and has no storage costs  SCENARIO 2 - When an investment asset provides a known dollar income , then:  F0 = (S0 – I )erT, where I is the present value of the income during life of forward contract  SCENARIO 3 - When an investment asset provides a known yield , then:  F0 = S0 e(r–q )T, where q is the average yield during the life of the contract (with continuous compounding) 18
    • 19. Forward Contracts vs. Futures Contracts Forward and futures prices are usually assumed to be the same. When interest rates are uncertain they are, in theory, slightly different: A strong positive correlation between interest rates and the asset price implies the futures price is slightly higher than the forward price A strong negative correlation implies the reverse Forward Contracts Futures Contracts Private contract between two parties Traded on an exchange Not standardized Standardized Usually one specified delivery date Range of delivery dates Settled at end of contract Settled daily Delivery or final settlement usual Usually closed out prior to maturity Some credit risk Virtually no credit risk Index Arbitrage:  When F0 > S0e(r-q)T an arbitrageur buys the stocks underlying the index and sells futures  When F0 < S0e(r-q)T an arbitrageur buys futures and shorts or sells the stocks underlying the index  Index arbitrage involves simultaneous trades in futures and many different stocks  Very often a computer is used to generate the trades  Occasionally (e.g., on Black Monday) simultaneous trades are not possible and the theoretical no-arbitrage relationship between F0 and S0 does not hold 19
    • 20. QuestionsSECTION IV

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