PSTAT 170 INTRODUCTION TO MATHEMATICAL FINANCE QUIZ 3
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PSTAT 170 INTRODUCTION TO MATHEMATICAL FINANCE
QUIZ 3
AUGUST 22, 2022
Problem 1 (10 pt). Let S0 = $88.57. r = 5%, and δ = 0.02. Construct a two-period binomial tree for a European call option with a one year maturity and a strike price K = $95. The stock dynamics are given by u = 1.25 and d = 0.9. At each node provide the premium, Δ, and B .
Problem 2 (15 pt). The closing price of Applied Materials shares was $108.27 on August 18, 2022. The following call options maturing on September 30, 2022, are available:
Call |
Strike |
12.97 C 5.85 |
98 108 110 |
Use the convexity of the option price with respect to the strike price to find the maximum value of C so that arbitrage is not possible.
Problem 3 (15 pt). Consider a financial market modeled by a 3-period binomial tree. Suppose a stock price at time 0 is S0 = $53, and u = 1.15, d = 0.8. The continuous compound interest rate is r = 4%. Note that one period is one year and the dividend yield is 0.
(a) Calculate the price at t = 0 of an European put option with expiration date T = 3 and strike K = 50.
(b) Calculate the price at t = 0 of an American put option with expiration date T = 3 and strike K = 50.
(c) What is the optimal exercise policy of the American put option? (i.e. Decide whether you should exercise at t = 0, 1, 2 for different stock prices.)
2022-09-06