2) Consider a stock whose current price is $100 and volatility is 20% p.a. The stock isexpected to pay a dividend of $2 in one month's time. The risk-free rate is 5% p.a.continuously compounding.(a)Using a two-period binomial tree, what is the value of a 2-monthAmerican call whose exercise price is $101?(b) Using a two-period binomial tree, what is the value of a 2-monthAmerican put whose exercise price is $101?

An option is a type of financial instrument that is based on the value of underlying securities,…

Answered: Consider a stock whose current price is…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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2. Two-step Binomial Tree St=100 Step: n=0 Su=105 Sd=95.23 (Bonus question, maturity n=1 Suu=110.25 Sud=Sdu=100 Sdd=90.70 n=2 Consider the above two-step binomial tree, with each step being three months, At=0.25. The stock price is shown on the tree. The annual risk-free rate is 5%. u= Su/St=1.05, d=1/u. There is no dividend from the stock. 1) Consider an at-the-money European call option (S=K) with six-month maturity a) What is the payoff to this call option at the expiration date at each possible stock price? b) Calculate the call option fair value today. 2) Consider a European put option with six-month maturity and a strike price of $90. a) What is the payoff to this put option at the expiration date at each possible stock price? b) Calculate the put option fair value today. ) Calculate at-the-money American call option (S-K) with six-month
Suppose the risk-free return is 5.3% and the market portfolio has an expected return of 10.2% and a standard deviation of 16%. Loblaw Companies Limited stock has a beta of 0.32. What is its expected return? The expected return is%. (Enter your response as a percent rounded to two decimal places.)
If the interest rate on T Bills is 2% and the market risk premium is 6%, what is the CAPM-implied expected return on a stock with a beta of 1.25? Enter your answer as a percentage rounded to 2 decimal places.
The level of the Syldavian market index is 21,600 at the start of the year and 26,100 at the end. The dividend yield on the index is 4.3%. a. What is the return on the index over the year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Retur b. If the interest rate is 5%, what is the risk premium over the year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Risk Premium % Real Return % c. If the inflation rate is 7%, what is the real return on the index over the year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) %
You use the usual forward tree model for stocks to construct a binominal tree for modeling the price movements of the stock. You are given: i) The length of the period is 1 year ii) The initial stock price is 100 iii) The stock' s volatility is 30% iv) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 5% v) The continuously compounded risk-free interest rate is 5% Calculate the price of a two-year 100-strike American call option on the stock. Possible Answers A 11.40 B 12.09 C 12.78 D 13.47 E 14.16
The market price of a security is $50. Its expected rate of return is 10%. The risk-free rate is 5%, and the market risk premium is 8%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity. (Round your answer to 2 decimal places.)
For a two-period binomial model, you are given: Each period is one year. The current price for a non dividend-paying stock is 20. u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock price goes up. d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock price goes down. The continuously compounded risk-free interest rate is 5%. Calculate the price of an American call option on the stock with a strike price of 22.
The risk-free rate of return is 5%, the required rate of return on the market is 10%, and High-Flyer stock has a beta coefficient of 1.8. If the dividend per share expected during the coming year, D1, is $3.60 and g = 5%, at what price should a share sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Currently, the risk-free return is 2 percent, and the expected market rate of return is 11 percent. What is the expected return of the following three-stock portfolio? Do not round intermediate calculations. Round your answer to two decimal places. Investment Beta $ 200,000 1.0 100,000 0.1 700,000 2.9 %
The current price of a non-dividend-paying biotech stock is $140 with a volatility of 25%. The risk-free rate is 4%. For a 3-month time step: (a) What is the percentage up movement? (b) What is the percentage down movement? (c) What is the probability of an up movement in a risk-neutral world? (d) What is the probability of a down movement in a risk-neutral world? Use a two-step tree to value a 6-month European call option and a 6-month European put option. In both cases the strike price is $150. Answer: (For (a) to (d), answer XX.XX if the answer is XX.XX% or 0.XXXX; for the option prices: please round you answers to the second decimal places.) (a, (c) (d) Price of the Call: Price of the Put: % % % %
Suppose the stock price is currently $75. For the next six months there is 7.5% probability that the stock will appreciate 8% with 4% annualized drift. The risk-free rate is 1.53% per year with continuous compounding. The dividend yield is 1 p.a.%. Value the following option using binomial tress and 12-time steps. a.) What is the value of a six-month European put option with a strike price of $86. b.) What is the value of a six-month American put option with a strike price of $70. c.) What is the value of a six-month European call option with a strike price of $86. d.) What is the value of a six-month European put option with a strike price of $70. e.) Estimate how high the minimum strike price must be for it to be optimal to exercise the put option immediately.
Perform all calculations with excel: ABC Corporation is currently trading at $40, with volatility\ sigma 30%, r = 5%, and no dividends. Assume that the ABC stock price can be modeled according to a three period binomial approach with T = 9 months and n = 3, so that the stock price moves every 3 months. 1. Build out the binomial tree for ABC. 2. What is the value of an American put option with strike price 40? 3. What is the value of a European call option with strike price 50?

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