Option Contracts
Chapter 24
Innovative Financial InstrumentsDr. 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
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)
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
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
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.
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.
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.
Improving Forecast Accuracy
Subdivide interval into subintervals, and form a stock price tree
Work backward on each pair of possible outcomes from the future
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The Binomial Option Pricing Model
Two-State Option Pricing Model– up movement or down movement– forecast stock price changes from one subperiod to
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The Black-Scholes Valuation Model
For a European call option on a non-dividend paying stock, Black and Scholes developed the following:
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
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Estimating Volatility
Mean and standard deviation of a series of price relatives:
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.
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
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
Option Trading Strategies
Protective put options Covered call options Straddles, strips, and
straps
Strangle Chooser options Spreads Range forwards
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
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
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
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
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.
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.
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
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
The InternetInvestments Online
www.cboe.com/productswww.cboe.com//institutional/flex.htmlwww.finance.wat.ch/cbt/optionswww.optionmax.com