You are given that some stock has satisfies the following: S(0) = 105 r = dividend rate= 0.03, A one year at the money European put costs 21.688. What is the implied volatility of this stock?

Problem 5.5. Please give me exact answer.

Homework 5 Due Friday, October 14th at noon Name 5.1. Suppose that the price of a nondividend paying stock is 25, and the price of a put option on this stock is 3.29. You also know that = 0.32 and = 0.13. Estimate the new value of the put if the stock's value changes to 23. 5.2. Suppose that we have the same framework as the problem #5.1. In addition, the theta value is = 0.26, and the price change occurs over the course of two weeks. Estimate the value of the put after two weeks. 5.3. Let S, c, and p be a stock; a stock, a European call on the stock, and a European put on the stock. The prices of each are 42, 4.15, and 1.70, respectively. Two investors, A and B, invest in portfolios containing quantities of the call and the put on the stock. Investor A purchases 2 calls and 1 put. The elasticity of A's portfolio is 3.36. Investor B purchases 4 calls and writes 6 puts. B = 4.8. (a) What is the elasticity of the call? (b) What is the dividend rate of S? 5.4. You wish to purchase some options on a stock that satisfies the following: S(0) = 20 r = 0.04 = 0.25 For a six month European call on S with strike 20, C = 0.56779 (a) What is the price of a strike 20 asset or nothing call? (b) What is the price of a strike 20 cash or nothing call? (c) What is the price of a gap option that pays S(0.5) and zero otherwise? 1 of 3 15 at time 0.5 when S(0.5) > 20 Homework 5 5.5. You are given that some stock has satisfies the following: S(0) = 105 r= = 0.03 A one year at the money European put costs 21.688. What is the implied volatility of this stock? Book Problems: Chapter 12, problem 14: Consider a bull spread where you buy a 40-strike put and sell a 45-strike call. Suppose = .3, r = .08, = 0, and T = .5 a. Suppose S = 40. What are delta and gamma? b. Suppose S = 45. What are delta and gamma? c. Are any of your answers to (a) and (b) dierent? If so, why? Chapter 12, problem 20: Let S = 100, K = 90, = .3, r = .08, = .05, and T = 1. a. What is the Black-Scholes call price? b. Now price a put where S = 90, K = 100, = .3, r = .05, = .08, and T = 1. c. What is the link between your answers to (a) and (b)? Why? Chapter 13, problem 1: Suppose you sell a 45-strike call with 91 days to expiration. What is delta? If the option is on 100 shares, what investment is required for a delta-hedged portfolio? What is your overnight profit if the stock tomorrow is $39? What if the stock price is $40.50? Chapter 13, problem 2: Suppose you sell a 40-strike put with 91 days to expiration. What is delta? If the option is on 100 shares, what investment is requires for a delta-hedged portfolio? What is your overnight profit if the stock price tomorrow is $39? What if it is $40.50? Chapter 14, problem 2: Suppose you observe the prices {5,4,5,6,5} What are the arithmetic and geometric averages? Now you observe {3,4,5,6,7}. What are the two averages? What happens to the dierence between the two measures of the average as the standard deviation of the observations increases? 2 of 3 Homework 5 Chapter 14, problem 3: Suppose that S = 100, K = 100, r = .08, = .3, = 0, and T = 1. Construct a standard two-period binomial stock price tree using the method in Chapter 10 (use the forward tree). a. Consider stock price averages computed by averaging the 6-month and 1-year prices. What are the possible arithmetic and geometric averages after 1 year? b. Construct a binomial tree for the average. How many nodes does it have after 1 year? c. What is the price of an Asian arithmetic average price call? d. What is the price of an Asian geometric average price call? 3 of 3