Essentials of Investments (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
10th Edition
ISBN: 9780077835422
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 16, Problem 6PS
Reconsider the determination of the hedge ratio in the two-state model (Section
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Reconsider the determination of the hedge ratio in the two-state model, where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for the following exercise prices: (a) 120, (b) 110, (c) 100, (d) 90? (e) What do you conclude about the hedge ratio as the option becomes progressively more in the money?
Reconsider the determination of the hedge ratio in the two-state model where we showed that one-third share of stock would hedge one option. The possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $100 (down state).
What would be the call option hedge ratio for each of the following exercise prices: $135, $122, $111, $100, given the possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $100 (down state)?
Exercise Price
Hedge Ratio
$135
?
$122
?
$111
?
$100
?
Reconsider the determination of the hedge ratio in the two-state model where we showed that one-third share of stock would hedge one option. The possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $115 (down state).
Required:
What would be the call option hedge ratio for each of the following exercise prices: $135, $127, $120, $115, given the possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $115 (down state)?
What do you conclude about the hedge ratio as the option becomes progressively more in the money?
Chapter 16 Solutions
Essentials of Investments (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Ch. 16 - Prob. 1PSCh. 16 - A put option on a stock with a current price of 33...Ch. 16 - Prob. 3PSCh. 16 - Prob. 4PSCh. 16 - In each of the following questions, you are asked...Ch. 16 - Reconsider the determination of the hedge ratio in...Ch. 16 - Show that Black-Scholes call option hedge ratios...Ch. 16 - We will derive a two-State put option value in...Ch. 16 - a. Calculate the value of a call option on the...Ch. 16 - Prob. 10PS
Ch. 16 - Prob. 11PSCh. 16 - Prob. 12PSCh. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - Prob. 16PSCh. 16 - 17. Find the Black-Scholes value of a put option...Ch. 16 - Prob. 18PSCh. 16 - What would be the Excel formula in Spreadsheet...Ch. 16 - Prob. 20PSCh. 16 - Prob. 21PSCh. 16 - Prob. 22PSCh. 16 - Prob. 23PSCh. 16 - Prob. 24PSCh. 16 - Prob. 25PSCh. 16 - Prob. 26PSCh. 16 - Prob. 27PSCh. 16 - Prob. 28PSCh. 16 - Prob. 29PSCh. 16 - Prob. 30PSCh. 16 - Prob. 31PSCh. 16 - Prob. 32PSCh. 16 - Prob. 33PSCh. 16 - Prob. 34PSCh. 16 - Prob. 35PSCh. 16 - Prob. 36PSCh. 16 - Prob. 38CCh. 16 - Prob. 39CCh. 16 - Prob. 40CCh. 16 - Prob. 41CCh. 16 - Prob. 42CCh. 16 - Prob. 43CCh. 16 - Prob. 44CCh. 16 - Prob. 1CPCh. 16 - Prob. 2CP
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- We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of the put?b. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio?c. What is the present value of the portfolio?d. Given that the stock currently is selling at 100, solve for the value of the put.arrow_forwardWe will derive a two-state put option value in this problem. Data: S0 = $180; X = $190; 1 + r = 1.10. The two possibilities for ST are $210 and $110.a. The range of S is $100 while that of P is $80 across the two states. What is the hedge ratio of the put? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) (The answer for this one is -.80) :)b. Form a portfolio of four shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.) c. What is the present value of the portfolio? (Round your answer to 2 decimal places.) d. Given that the stock currently is selling at $180, calculate the put value. (Do not round intermediate calculations and round your answer to 2 decimal places.)arrow_forwardWe 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.)arrow_forward
- 1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.77. and put option value is 1.99 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. explainc. What would be the extent of your profit in (a) depend on? explainarrow_forwardSuppose that JPMorgan Chase sells call options on $2.40 million worth of a stock portfolio with beta = 1.50. The option delta is 0.55. It wishes to hedge its resultant exposure to a market advance by buying a market-index portfolio. Suppose it use market index puts to hedge its exposure. The index at current prices represents $2,000 worth of stock and the contract multiplier is 400. Required: How many dollars’ worth of the market-index portfolio should it purchase? What is the delta of a put option? Complete the following:arrow_forwardSuppose that JPMorgan Chase sells call options on $2.40 million worth of a stock portfolio with beta = 1.50. The option delta is 0.55. It wishes to hedge its resultant exposure to a market advance by buying a market-index portfolio. Suppose it use market index puts to hedge its exposure. The index at current prices represents $2,000 worth of stock and the contract multiplier is 400. Required: How many dollars’ worth of the market-index portfolio should it purchase? What is the delta of a put option? Complete the following: Do number 1 and 3arrow_forward
- 1. What is the fair value for a two-year American put option with a strike price of $85 over a stock which is trading at $86.15 which has a volatility of 37% when the risk free rate is 1.75% using the two step binomial tree? a) What is the delta of this option? b) What is the probability of a down movement in this stock? c) What is the probability of an up movement in this stock? d) What is the proportional move up for this stock e) What is the proportional move down for this stock f) What would be the value of the call option with the same strike price?arrow_forward1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.7739. and put option value is 1.8101 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?arrow_forwardIf while valuing a put option using a binomial tree you find a hedge ratio=3/5 is necessary, what does this mean should be in our portfolio to have a riskless gain in either state of the world? A. It means that you should buy 3 stocks and buy 5 calls B. It means you should buy 3 stocks and buy 5 puts C. It means that you should buy 3 stocks and short 5 calls D. It means you should buy 3 stocks and short 5 putsarrow_forward
- You're considering purchasing Proctor and Gamble Stock. Suppose the risk-free interest rate is 5.0% and the stock market's expected return is 13.50%. Also, suppose that if the stock market's value rises by 1%, stock in Proctor and Gamble typically rises by 1%. a. What is the percentage of Proctor and Gamble's risk premium? c. What is the correct discount rate to use according to the Capital Asset Pricing Model (CAPM) when analyzing the present value of future cash flows from this stock?arrow_forwardIf while valuing a put option using a binomial tree you find a hedge ratio=3/5 is necessary, what does this mean should be in our portfolio to have a riskless gain in either state of the world? It means that you should buy 3 stocks and buy 5 calls It means you should buy 3 stocks and buy 5 puts It means that you should buy 3 stocks and short 5 calls It means you should buy 3 stocks and short 5 putsarrow_forwardConsider a two-state outcome for the following problem: Winterhold Publishing House Current Stock Price $25.00 Exercise Price $27.00 Risk-free Rate 0.05 Share Price, High $30.00 Share Price, Low $20.00 Required: Using the data above, please find the hedge ratio. You currently own several shares of this company. The purchase puts according to the Hedge ratio to construct a non-random portfolio. Show the payoff for both outcomes, then solve for present value and the price of the put.arrow_forward
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