5 300 150 0 o stock price 500 payoff 05 500 150

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Unformatted text preview: th an exercise price of $400. For simplicity, assume that the stock can either fall to $300 or rise to $500. - Consider the payoff to the option given the two possible outcomes: o Stock price = $300 Payoff = $0 o Stock price = $500 Payoff = $500 – $400 = $100 - Compare this to the alternative: Buy 0.5 stock & borrow $150 o Stock price = $300 Payoff = 0.5 · $300-$150 = $0 o Stock price = $500 Payoff = 0.5 · $500-$150 = $100 - As the payoff to the option equals the payoff to the alternative of buying 0.5 stock and borrowing $150 (i.e. the option equivalent), the price must be identical. Thus, the value of the option is equal to the value of 0.5 stocks minus the present value of the $150 bank loan. - If the 3-month interest rate is 1%, the value of the call option on the Google stock is: o Value of call = Value of 0.5 shares – PV(Loan) = 0.5 · $400–$150/1.01= 51.5 The option equivalent approach uses a hedge ratio or option delta to construct a replicating portfolio, which can be priced. The option delta is defined as the spread in option value...
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