Corporate Finance (4th Edition) (Pearson Series in Finance) - Standalone book
4th Edition
ISBN: 9780134083278
Author: Jonathan Berk, Peter DeMarzo
Publisher: PEARSON
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Chapter 20, Problem 27P
Suppose the S&P 500 is at 900, and a one-year European call option with a strike price of $400 has a negative time value. If the interest rate is 5%, what can you conclude about the dividend yield of the S&P 500? (Assume all dividends are paid at the end of the year.)
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Modigliani-Miller Theorem I.
7. Options
A. How does the price of a call option respond to the following changes, other things
equal? Does the price go up or down? Explain briefly the intuition for your
answer.
(i). Exercise price rises.
(ii). Volatility of stock price rises.
3
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45.
a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage?
b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
Chapter 20 Solutions
Corporate Finance (4th Edition) (Pearson Series in Finance) - Standalone book
Ch. 20.1 - What is the difference between an American option...Ch. 20.1 - Does the holder of an option have to exercise it?Ch. 20.1 - Prob. 3CCCh. 20.2 - What is a straddle?Ch. 20.2 - Explain how you can use put options to create...Ch. 20.3 - Explain put-call parity.Ch. 20.3 - If a put option trades at a higher price from the...Ch. 20.4 - What is the intrinsic value of an option?Ch. 20.4 - Can a European option with a later exercise date...Ch. 20.4 - How does the volatility of a stock affect the...
Ch. 20.5 - Is it ever optimal to exercise an American call on...Ch. 20.5 - When might it be optimal to exercise an American...Ch. 20.5 - Prob. 3CCCh. 20.6 - Explain how equity can be viewed as a call option...Ch. 20.6 - Explain how debt can be viewed as an option...Ch. 20 - Explain the meanings of the following financial...Ch. 20 - What is the difference between a European option...Ch. 20 - Below is an option quote on IBM from the CBOE Web...Ch. 20 - Prob. 4PCh. 20 - Prob. 5PCh. 20 - You own a call option on Intuit stock with a...Ch. 20 - Assume that you have shorted the call option in...Ch. 20 - You own a put option on Ford stock with a strike...Ch. 20 - Assume that you have shorted the put option in...Ch. 20 - What position has more downside exposure: a short...Ch. 20 - Consider the October 2015 IBM call and put options...Ch. 20 - You are long both a call and a put on the same...Ch. 20 - You are long two calls on the same share of stock...Ch. 20 - A forward contract is a contract to purchase an...Ch. 20 - You own a share of Costco stock. You are worried...Ch. 20 - Dynamic Energy Systems stock is currently trading...Ch. 20 - You happen to be checking the newspaper and notice...Ch. 20 - In mid-February 2016, European-style options on...Ch. 20 - Suppose Amazon stock is trading for 500 per share,...Ch. 20 - Consider the data for IBM options in Problem 3....Ch. 20 - You are watching the option quotes for your...Ch. 20 - Explain why an American call option on a...Ch. 20 - Consider an American put option on XAL stock with...Ch. 20 - The stock of Harford Inc. is about to pay a 0.30...Ch. 20 - Suppose the SP 500 is at 900, and a one-year...Ch. 20 - Suppose the SP 500 is at 900, and it will pay a...Ch. 20 - Prob. 29PCh. 20 - Suppose that in July 2009, Google were to issue 96...
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- What is the price of a European CALL option that is expected to pay a dividend of $2 in three months with the following parameters? s0 = $40d = $2 in 3 monthsk = $42 r = 10%sigma = 20%T = 0.5 years (required precision 0.01 +/- 0.01)arrow_forwardConsider a 2-year EUROPEAN PUT with a strike price of $65 on a stock whose current stock price is $60. Suppose that there are two time steps, and in each time step the stock price either moves up by 20% or moves down by 20%. Also suppose that risk-free rate is 5% per annum with continuous compounding . What is the value of the European put option?arrow_forwardWhich of the following statements is (are) TRUE? Select one or more alternatives: If the AUD trades at a forward premium relative to the NZD, we would expect the NZD risk-free rate to be higher than the AUD risk-free rate. If the 1-year AUD risk-free rate is higher than the 1-year NZD risk-free rate then the value of the NZD will rise relative to the AUD over the next year. Assuming it doesn't hedge, a New Zealand based company importing Australian products will suffer if the value of the AUD rises relative to the NZD. □ If covered interest rate parity holds, then uncovered interest rate parity must also hold.arrow_forward
- Suppose that the price of a stock today is at $25. For a strike price of K = $24 a 3-month European call option on that stock is quoted with a price of $2, and a 3-month European put option on the same stock is quoted at $1.5 Assume that the risk-free rate is 10% 3. per annum. (a) Does the put-call parity hold?arrow_forwardThe share price of your favourite company is currently traded at a price of £40 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, drift ?=0.15 and volatility ?=0.24. You decide to buy a European call option with a strike price of £42 and an expiration date of two years from now. What is the no-arbitrage price for this option?arrow_forwardThe share price of your favourite company is currently traded at a price of £60 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, drift µ = 0.15 and volatility o = 0.24. You decide to buy a European call option with a strike price of £63 and an expiration date of two years from now. What is the no-arbitrage price for this option? State your answer to the nearest pence. Do not enter the pound sign.arrow_forward
- The share price of your favourite company is currently traded at a price of £60 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, drift μ= 0.15 and volatility o = 0.24. You decide to buy a European call option with a strike price of £63 and an expiration date of two years from now. What is the no- arbitrage price for this option? State your answer to the nearest pence. Do not enter the pound sign.arrow_forwardYou are an investor in the world where short-selling assets is prohibited. Suppose that the price of asset X in period 0 is $200. This asset will pay a dividend of $8 one year from now in period 1. Let the riskless interest rate from 0 to period q be 5%.Assume the price for a future contract delivery in period 1 is $210. a) Can you make an arbitrage profit when $210 is the price? If so, state specifically what financial transaction? b) Now, assume the price for a futures contract with delivery in period 1 is K190. Can you make an arbitrage profit when this is the price? If so, state specifically what financial transaction you would make in 0 and period 1 to realize a profit. If not, explain?arrow_forwardA one-month European put option on a non-dividend-paying stock is currently selling for $2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities, if any, are there for an arbitrageur? no opportunities; the put is fairly priced. an arbitrage strategy exists that could generate profit with a present value of at least $0.25. An arbitrageur should lend $49.50 for one month, buy the stock, and write the put option An arbitrageur should borrow $47.00 for one month, sell the stock, and write the put optionarrow_forward
- Suppose you pay 10 to buy a European (K = 100, t = 2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is (a) 110; (b) 98.arrow_forwardConsider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.arrow_forwardThe risk-free rate is 8% per annum with continuous compounding. The price of stock CPU is $30. CPU currently does not pay a dividend. You use a two-step tree to price a European put on CPU with a strike price of $32. The option expires in six months. If you estimate that u=1.1 and d=0.9, what is the price of your put? A.$1.50 B.$2.24 C.$1.88 D.$2.56arrow_forward
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