Lecture7_BinomialOptionPricing

29 1571 payoff so the investors choice is between a

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Unformatted text preview: binomial tress to price American options (3) Meanwhile, the current stock price is 34.29 Meanwhile, (see J27). So, if the investor can make positive payoff by exercising the option at this node, the payoff is 50 – 34.29 = 15.71 payoff So, the investor’s choice is between (a) So, exercise the put now = 15.71 and (b) wait for the next step = 15.54. Obviously, the investor will choose (a) Obviously, So, in each node, we just need to ask the Excel So, to compute the maximum of (a) the positive payoff by exercising the option now and (b) the expected payoff of waiting 15-24 Using binomial tress to price American options (4) As a result, we get that the following: As - Call option with strike = 50, it’s price = 3.47 Call - Put option with strike = 50, it’s price = 2.37 Put Binomial 9-step Call Put European 3.47 2.25 American 3.47 2.37 The above matrix highlights the fact that the price The of American option is always higher than or equal to European option (the option to exercise anytime is valuable) is 15-25 Real example: IBM option (1) Now, let’s use binomial trees to price IBM options Now, and compare it with the current market price and The current stock price = 182.39 on Oct. 8, 2011 15-26 Real example: IBM option (2) Now, let’s check the option price of IBM matures Now, on Oct. 21, 2011 (10 trading days to go) on 15-27 Real example: IBM option (3) Now, how to set up the parameters? We use the Now, previous 10 days to estimate the following previous 1. Drift term (risk-free rate = stock return in a riskneutral world) = 0.00502 (r) in daily frequency in 2. Volatility term = 0.01513 (σ) in daily frequency 3. Dividend rate sets to be 0 4. δt = 1 in daily frequency 4. 5. T = 10 days to be traded by Oct. 21, 2011 6. Step number = 10 See “IBMoptoin” tab 15-28 Real example: IBM option (4) Our calculation implies the price of $25.47, which Our is higher than the market price $18.95 is So, if we believe in our calculation, the market So, price is “cheaper” than our estimation. What should we do? we We can either (a) buy the option at the price We $18.95 and wait the price to go to $25.47 or (b) establish a replicate portfolio by buying the stock, buying a put option at exercise price 165, and borrowing money from the bank 15-29 Exercise 1 Now, compute the price of American put and call Now, based on all the same set-up, but change the step number to 15 steps, see the “Exercise 1” tab number As shown in the “Exercise 1 - ans” tab: - Call price = 3.44 Call - Put price = 2.35 Put Call Binomial 9 steps Binomial 15 steps Euro Call 3.47 3.44 Amer Call 3.47 3.44 Put Binomial 9 steps Binomial 15 steps Euro Put 2.25 2.22 Amer Put 2.37 2.35 15-30 How American option prices react to input changes: stock price...
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