11 12 11 Review Session Final Exam

11 12 11 Review Session Final Exam - Review Session before...

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Unformatted text preview: Review Session before Final Finance for non MBAs December 11th, 2011 TA: Pablo Villanueva (using previous TAs notes) pvillanueva@stanford.edu 2 Agenda for Today 1. Practice Questions Binomial Options Pricing. Capital Structure. Currency Hedging. Put-Call Parity. Q1: Binomial options pricing Consolidated Manufacturing Inc. (ConMan) issues stock options to its CEO, Rip Yuoff. The stock options the ConMan grants to Rip are at-the-money when the options are originally issued. But these options are then re-priced whenever the stock goes down, which means that the strike price of the option is set to the new, lower stock price. It is also the case that Rip immediately hedges his risk from these options as soon as they are granted by trading ConMans stock. Suppose ConMan is currently trading for $50 per share, and pays no dividends. Its share price will go up or down by 20% each year, as shown in the tree below: Question 1a The risk-free rate is 10% per year (EAR). a) Use the binomial model to compute the value of a 2-year at-the- money call option that will be re-priced whenever the stock drops. Question 1a: Solution Step 1: Find final payoffs. In up-up state, strike is 50, payoff C uu = 22. In up-down state, strike is 50, payoff C ud = 0. In down-up state, strike is 40, payoff is C du = 8. In down-down state, strike is 40, payoff is C dd = 0. Step 2: Find possible option prices in 1 year. At each point, can replicate option for one period using mixture of shares and B $1 bonds. Eqn (21.5): Question 1a: Solution (contd) Price of portfolio = price of option = B + S . In up state (S = 60), plug C u = 22, C d = 0, S u = 72, S d = 48, and r = 10% into (21.5) to get: = 0.92 and B = -40 option worth 0.92 x 60 40 =$ 15 in up state. In down state (S = 40), use C u = 8, C d = 0, S u = 48, S d = 32, and r = 10% to get: = 0.5 and B = -14.6 option worth 0.5 x 60 40 =$ 5.45 in down state. Question 1a: Solution (contd) We now have (call prices in red): Question 1a: Solution (contd) Step 3: Find option price today. Using possible option prices in year 1 C u = 15 and C d = 5.45, we get = 0.48 and B = -12.4 option worth 0.48 x 50 12.4=$ 11.465 today. Question 1b: Early Exercise? b) Will Rip every exercise these options early? Explain. Question 1b: Solution No he will not. The option is always worth more (C = 11.465, C u = 15, C d = 5.45) than its current intrinsic value (ex = 0, ex u = 10, ex d = 0). If he needs to draw down his savings he can sell the replicating portfolio, which yields more money at the same opportunity cost as early exercise....
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This note was uploaded on 01/08/2012 for the course MS&E 245G taught by Professor Perez-gonzalas during the Fall '11 term at Stanford.

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11 12 11 Review Session Final Exam - Review Session before...

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