The price of a non-dividend paying stock is now $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 4% per annum with continuous compounding. a. Calculate the risk-neutral probability p of an up-move over each three-month period b. Calculate the value of a six-month European call option with a strike price of $42 c. Calculate the value of a six-month European put option with a strike price of $42 d. If the six-month put option was American instead of European, how would you expect its value to be different (higher, the same, or lower) than the European one? Please explain

The price of a non-dividend paying stock is now $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 4% per annum with continuous compounding. a. Calculate the risk-neutral probability p of an up-move over each three-month period b. Calculate the value of a six-month European call option with a strike price of $42 c. Calculate the value of a six-month European put option with a strike price of $42 d. If the six-month put option was American instead of European, how would you expect its value to be different (higher, the same, or lower) than the European one? Please explain

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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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.
You Consider a stock with a price of $50 that is expected to increase by 6% or decrease by 8% each month over the next two months. Having a risk-free rate at 3% per year with continuous compounding, calculate the value of a two-month European put option with a strike price of $55. Repeat your calculations for a two-month American put option with a strike price of $55. Show clearly all your calculations and results with the use of the relevant equations and graphs. Discuss your investment decision in each case separately.
Determine the risk-neutral value of a eight-month European put option to sell a FLB (First Local Bank) share for a price of R400 when the current price is R420, the interest rate is 10%, and the volatility of the security is 0.28?
The market price of a security can be modelled by assuming that it will either increase by 25% or decrease by 15% each month, independently of price movement in other months. No dividends are payable in the next two months. The continuously compounded monthly risk-free rate of interest is 1%. The current market price of the security is 127. a.) Use the binomial model to calculate the value of a two-month European put option on the security with strike price of 125. b.) Calculate the value of a two-months American put option on the same security with the same strike price. c.) Calculate the value of a two-months American call option on the same security with the same strike price.
Suppose the call option of Tesla company has an exercise price of $200 and expires in 90 days. Assume the current price of Tesla stock is $240, with a standard deviation of 40% per year. The risk-free interest rate is 6.18% per year. First, using the Black-Scholes formula, compute the price of the call. And then use put-call parity to compute the price of the put with the same strike and expiration date. Based on put-call parity, what should be the put option price? $ 2.65 $ 1.78 $ 3.69 $ 4.22 None of the above
The price of a stock is currently $37. Over the next half year, the price is anticipated to rise to $42 or decline to $36. The upside has a 60% probability of occurring. The risk-free interest rate is 5% p.a.. What is the price of a six month call option with an exercise price of $38?
The market price of JS stock is currently $30. It is known that at the end of three months it will be either $33 or $27. The risk-free interest rate is 8% per annum with continuous compounding. (a) Use a one-step binomial tree to calculate the value of a three-month European put option on the JS stock with a strike price of $31? Use no-arbitrage arguments (you need to show how to set up the riskless portfolio). (b) Use the same one-step binomial tree and your results from (a) to determine the price of a three-month American put option on the JS stock with a strike price of $31
Consider a two-period binomial model in which a non-dividend-paying stock currently trades at £35. Over each of the next two six-month periods, the share price is expected to go up by 12% or down by 9%. The risk-free interest rate is 6% per annum with continuous compounding. Calculate the value of a one-year European put option with a strike price of £36, using a two-period binomial tree method.
C. Draw a graph of the SML and locate the projects (A) and (B) on the graph. 5. Effective Annual Yield (EAY) and Effective Annual Rate (EAR) A. You plan to invest $1,000 for one year and you have the opportunity to invest it at a 12 percent APR, compounded monthly. Alternatively, you could invest the funds at an annual rate of 12.3 percent compounded semiannually. What is the EAY of each alternative? (Hint: You need to carry your answer to at least the fourth decimal place.) Which investment should be chosen? 2

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