CONNECT WITH LEARNSMART FOR BODIE: ESSE
CONNECT WITH LEARNSMART FOR BODIE: ESSE
11th Edition
ISBN: 2819440196239
Author: Bodie
Publisher: MCG
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Chapter 16, Problem 6PS

Reconsider the determination of the hedge ratio in the two-state model (Section 16 . 2 ), where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for each of the following exercise prices: a $ 12 0   b $ 11 0   c $ 1 00   d $ 9 0 ? What do you conclude about the hedge ratio as the option becomes progressively more in the money? LO 16 5

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2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.
We will derive a two-state call option value in this problem. Data: S0 = $190; X = $200; 1 + r = 1.10. The two possibilities for ST are $220 and $120. The portfolio consists of 1 share of stock and 5 calls short.  Required: a. The range of S is $100 while that of C is $20 across the two states. What is the hedge ratio of the call? (Round your answer to 2 decimal places.) b. Calculate the value of a call option on the stock with an exercise price of $200. (Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective per-period rate.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Data: S0 = 102; X = 115; 1 + r = 1.1. The two possibilities for ST are 146 and 84. Required: The range of S is 62 while that of P is 31 across the two states. What is the hedge ratio of the put? Form a portfolio of one share of stock and two puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio? Given that the stock currently is selling at 102, calculate the put value.
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