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Option Contracts

Chapter 24. Option Contracts. Innovative Financial Instruments. Dr. A. DeMaskey. Derivatives. Forwards fix the price or rate of an underlying asset Options allow holders to decide at a later date whether such fixing is in their best interest. Option Market Convention.

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Option Contracts

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  1. Chapter 24 Option Contracts Innovative Financial Instruments Dr. A. DeMaskey

  2. Derivatives • Forwards • fix the price or rate of an underlying asset • Options • allow holders to decide at a later date whether such fixing is in their best interest

  3. Option Market Convention • Private transactions (OTC) • asset illiquid • credit risk is one-sided • created in response to needs • associations of broker-dealers • Chicago Board Options Exchange (CBOE) • Options Clearing Corporation (OCC)

  4. Price Quotations for Exchange-Traded Options • Equity options • CBOE, AMEX, PHLX, PSE • typical contract for 100 shares • require secondary transaction if exercised • time premium affects pricing

  5. Price Quotations for Exchange-Traded Options • Stock index options • only settle in cash • Foreign currency options • allow sale or purchase of a set amount of non-USD currency at a fixed exchange rate • quotes in USD • Options on futures contracts (futures options) • right, but not the obligation, to enter into a futures contract at a later date at a predetermined price

  6. The Fundamentals of Option Valuation • Risk reduction tools when used as a hedge • Theoretical value of option depends on combining it with its underlying security to create a synthetic riskfree portfolio. • Theoretically, it is always possible to use the option as a perfect hedge against fluctuations in the value of the underlying asset.

  7. Put-Call Parity versus Option Valuation • The portfolio implied by the put-call parity transaction does not require special calibration. • Put-call parity paradigm does not require a forecast of the future price level of the underlying asset.

  8. Basic Approach • Create a riskless hedge portfolio by combining options with the underlying security. • Hold one share of stock long and some number of call options so that the position is riskless. • Number of call options (h) needed is established by ensuring portfolio has same value at expiration regardless of forecasted stock values. • Solve for hedge ratio, h, which has both direction and magnitude. • Assume no arbitrage opportunities exit, so that the value of the hedge portfolio should grow at the riskfree rate.

  9. Improving Forecast Accuracy • Subdivide interval into subintervals, and form a stock price tree • Work backward on each pair of possible outcomes from the future

  10. The Binomial Option Pricing Model • Two-State Option Pricing Model • up movement or down movement • forecast stock price changes from one subperiod to the next • up change (u) • down change(d) • number of subperiods where:

  11. The Binomial Option Pricing Model

  12. The Black-Scholes Valuation Model • For a European call option on a non-dividend paying stock, Black and Scholes developed the following:

  13. The Black-Scholes Valuation Model • Value is a function of five variables: • Current security price • Exercise price • Time to expiration • Riskfree rate • Security price volatility • C = f(S, X, T, RFR, s)

  14. Estimating Volatility • Mean and standard deviation of a series of price relatives:

  15. Problems With Black-Scholes Valuation • Stock prices do not change continuously. • Arbitrageable differences between option values and prices (due to brokerage fees, bid-ask spreads, and inflexible position sizes). • Riskfree rate and volatility levels do not remain constant until the expiration date.

  16. Option Valuation: Extensions and Advanced Topics • Valuing European-style put options • Valuing options on dividend bearing securities • Valuing American-style options • Stock index options • Foreign currency options • Futures options

  17. Exotic Options • Asian options • Terminal payoff determined by the average price of the underlying security during the life of the contract. • Payoff = max [0, Average(S) - X] • Lookback options • Terminal payoff based on the maximum price of the underlying security achieved during the life of the contract. • Payoff = max [0, max(S) - X] • Digital options • Terminal payoff is fixed. • Payoff = $Q if ST > 0 or $0 if ST < 0

  18. Protective put options Covered call options Straddles, strips, and straps Strangle Chooser options Spreads Range forwards Option Trading Strategies

  19. Protective Put Options • Purchase at-the-money put to hedge against a fall in the price of a stock already held (Long Stock) + (Long Put) = (Long Call) + (Long T-Bill) • Insures position in equity • Preserves potential for capital gains if stock price rises, but limits loss if stock price falls

  20. Covered Call Option • Sale of a call option while owning the stock (Long Stock) + (Short Call) = (Long T-Bill) + (Short Put) • Generates income from premiums • Risks: • Stock may be called away if price rises • Price of stock my decline by more then premium received

  21. Straddles, Strips, and Straps • Straddle • Simultaneous purchase (or sale) of a call and a put with the same underlying asset, exercise price, and expiration date • Buyer expects price to move a lot up or down • Seller expects price to remain fairly stable • Long Strap • Purchase of two calls and one put with the same exercise price • Buyer expects price increase is more likely • Long Strip • Purchase of two puts and one call with the same exercise price • Buyer expects price decrease is more likely

  22. Strangle • Simultaneous purchase or sale of a call and a put on the same underlying security with the same expiration date, but whose exercise prices are both out-of-the money. • Reduces initial cost • Price will have to move more for a profit • Modest risk-reward structure

  23. Chooser Options • Investor selects exercise price and expiration date, but decides after the purchase whether the option is a put or a call. • This is an option with an embedded option that is more expensive.

  24. Spreads • Purchase of one contract and the sale of another, in which the options are alike in all respects except for one distinguishing characteristic. • Money Spread • Sell an out-of-the money call and buy an in-the-money call on the same stock with the same expiration date. • Calendar Spread • Purchase and sale of two calls (or two puts) with the same exercise price but different expiration dates.

  25. Spreads • Bull Spread • Buy an in-the-money call and sell an out-of-the money call • Profitable when stock prices rise • Bear Spread • Buy and out-of-the-money call and sell an in-the-money call • Profitable when stock prices fall • Butterfly Spread • Combining a bull money spread and a bear money spread • Buy one in-the-money call, sell two at-the-money calls, and buy one out-of-the-money call

  26. Range Forward • Combination of two option positions • Buy an out-of-the money put and sell an out-of-the money call of the same size • Purchase of put is financed by sale of call • Sell upside potential with call • Obtain downside risk protection with put • Cost of hedging is reduced • Known as cylinder

  27. www.cboe.com/products www.cboe.com//institutional/flex.html www.finance.wat.ch/cbt/options www.optionmax.com The InternetInvestments Online

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