FIN 4504 Final Exam Study Guide 1 Elements to of an option The option contract o A contract giving the holder the right but not the obligation to buy or sell 100 shares of stock at a preset price called the exercise or strike price o Expirations of 1 2 3 6 9 months and sometimes 1 year are normal contract periods Contracts expire on the Saturday following the third Friday of the expiration month o Contracts may be sold prior to maturity o A hedge against price changes o Types of options Listed Options OTC Options Index Options Options on Futures Foreign Currency Options Interest Rate Options Exotic Options 2 Option issuer maker responsibilities interests OCC Option Clearing Corporation is jointly owned by option exchanges OCC backs performance of both counterparties o To limit OCC s risk option seller or writer must post margin Margin varies with option price and whether the option position is covered or exposed o A call option writer seller who already owns the stock against which the option is written can just let the broker hold that stock as margin When an option is exercised an option seller is randomly selected o If a call is exercised the selected call writer must deliver 100 shares of stock in exchange for receiving the strike price o If a put is exercised the selected put writer must purchase 100 shares of stock at the strike price 3 Influences to value valuation of options a Intrinsic value Stock price minus exercise price or the cash flow that could be attained by immediate exercise of an in the money call option S0 K for a call i Intrinsic value is set to 0 for out of the money or at the money options ii Time value Difference between the premium price or the actual call price and the intrinsic value 1 Time value has no relation to time value of money iii As long as the option holder can choose not to exercise the payoff cant be worse than zero iv Most of an options time value is typically a volatility value If exercising is assured the volatility value becomes minimal b Determinants if option values i Six values that should affect the value of a call option the stock price the exercise price the volatility of the stock price the time to expiration the interest rate and the dividend rate ii The call option should increase in value with the stock price and decrease in value with the exercise price because the payoff to an exercised ST X iii Call option value also increase with the volatility of the underlying stock price Determinants of call option values If this variable increases The value of a call option Stock Price S Exercise price K Volatility Time to expiration T Interest rate rf Dividend payouts Increases Decreases Increases Increases Increases Decreases o Binomial option pricing c Two state option pricing i This problem requires a substantial amount of math not given on his bullets so I am not adding it as I think it wont be tested on if you do however want to look over it its pages 526 529 of the book If you don t have the book you can email me and I ll scan it for you This is an example from the book if you want an idea ii EX Suppose the stock now sells at 100 and the price will either increase by a factor of u 1 2 to 120 u stands for up or fall by a factor of d 9 to 90 d is down by year end 1 A call option on the stock might specify an exercise price of 110 and a time to expiration of one year Interest rate is 10 At year end the payoff to the holder of the call option will be either zero if stock falls or 10 if the stock price goes to 120 iii Binomial model An option valuation model predicated on the assumption that stock prices can move to only two values over any short period o Black Scholes option valuation d While the binomial model described is extremely flexible it requires a computer to be useful in actual trading An option pricing formula would be far easier to use If you make two assumptions that both risk free interest rate and stock price volatility are constant over the life of the option you can use the Black Scholes Formula same as above lengthy formula that I don t think he will put on the test I will provide the conceptual side of it e Black Scholes Formula A formula to value an option that uses the stock price the risk free interest rate the time to expiration and the standard deviation of the stock return C 0 S0 e T N d1 X e rT N d2 where ln s0 X r 2 2 T d1 T and d2 d1 T f Some important assumptions underlying the formula i The stock will pay a constant continuous dividend yield until the option expiration date ii Both interest rate r and variance rate 2 of the stock are constant iii Stock prices are continuous meaning that sudden extreme jumps such as those in the aftermath of an announcement of a takeover attempt are ruled out g Some market participants give it a twist rather than calculating a Black Scholes formula option value for a given stock standard deviation they ask instead What standard deviation would be necessary for the option price that I actually observe to be consistent with the Black Scholes formula This is called Implied volatility h Put call parity relationship i So far we have focused on the pricing of call options In many important cases put prices can be derived simply from the prices of calls ii Suppose you buy a call option and write a put option each with the same exercise price X and the same expiration date T At expiration the payoff on your investment will equal the payoff to the call minus the payoff that must be made on the put The payoff for each option will depend on whether the ultimate stock price ST exceeds the exercise price at expiration If the parity relationship is ever violated an arbitrage opportunity arises iii iv This is the payoff pattern Payoff of call held Payoff of put written Total ST X 0 X ST ST X ST X ST X 0 ST X v The net cash outlay necessary to establish the open position is C P The call is purchased for C while written put generates income of P Likewise the levered equity position requires a net cash outlay of S0 Xe rT the cost of the stock less the proceeds from borrowing The put call parity relationship equation is C P S0 Xe rT o Using the Black Scholes formula i Hedge ratios and the black Scholes formula i A tool that enables us to summarize the overall exposure of portfolios of option with various exercise prices and times to expiration is the hedge ratio ii Hedge ratio or delta the …