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

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

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

4. Price Quotations for Exchange-Traded Options u 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 u Stock index options – only settle in cash u Foreign currency options – allow sale or purchase of a set amount of non-USD currency at a fixed exchange rate – quotes in USD u 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 u 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 u The portfolio implied by the put-call parity transaction does not require special calibration. u Put-call parity paradigm does not require a forecast of the future price level of the underlying asset.

8. Basic Approach u 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. u Solve for hedge ratio, h, which has both direction and magnitude. u Assume no arbitrage opportunities exit, so that the value of the hedge portfolio should grow at the riskfree rate.

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

10. The Binomial Option Pricing Model u 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 u For a European call option on a non- dividend paying stock, Black and Scholes developed the following:

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

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

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

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

17. Exotic Options u 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] u 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] u Digital options – Terminal payoff is fixed. – Payoff = $Q if S T > 0 or $0 if S T < 0

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

19. Protective Put Options u 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 u 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 u 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 u Long Strap – Purchase of two calls and one put with the same exercise price – Buyer expects price increase is more likely u Long Strip – Purchase of two puts and one call with the same exercise price – Buyer expects price decrease is more likely

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

24. Spreads u Purchase of one contract and the sale of another, in which the options are alike in all respects except for one distinguishing characteristic. u 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. u Calendar Spread – Purchase and sale of two calls (or two puts) with the same exercise price but different expiration dates.

25. Spreads u Bull Spread – Buy an in-the-money call and sell an out-of-the money call – Profitable when stock prices rise u Bear Spread – Buy and out-of-the-money call and sell an in-the-money call – Profitable when stock prices fall u 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 u 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

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