XYZ Corp. will pay a $2 per share dividend in two months. Its stock price currently is $86 per share. A European call option on XYZ has an exercise price of $78 and 3-month time to expiration. The risk-free interest rate is 0.8% per month, and the stock's volatility (standard deviation) = 22% per month. Find the Black-Scholes value of the American call option. (Hint: Try defining one "period" as a month, rather than as a year, and think about the net-of-dividend value of each share.) (Round your answer to 2 decimal places.) Black-Scholes value of the option $ 7.12

XYZ Corp. will pay a $2 per share dividend in two months. Its stock price currently is $86 per share. A European call option on XYZ has an exercise price of $78 and 3-month time to expiration. The risk-free interest rate is 0.8% per month, and the stock's volatility (standard deviation) = 22% per month. Find the Black-Scholes value of the American call option. (Hint: Try defining one "period" as a month, rather than as a year, and think about the net-of-dividend value of each share.) (Round your answer to 2 decimal places.) Black-Scholes value of the option $ 7.12

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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The current market share price of Belta Airlines plc is $20. Every month, the stock price is expected either to increase by a multiplicative factor u = 1.1, or decrease by d = 0.91. The relevant annual continuously compounded risk-free rate of interest is 6%. 2. (a) What, according to the binomial option pricing model, will be the price of a 3-month European put option on a share of Belta stock, with a strike price of £19.50? (b) (c) What would the price of the put option was American style? If your answers to parts (a) and (b) differ, why do they differ?
The price of a stock, which pays no dividends, is $30 and the strike price of a two-year European call option on the stock is $25. The risk-free rate is 8% (continuously compounded). Which of the following is a precise lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Round your answer to 2 decimal places. a. $8.42 b. $8.76 c. $8.57 d. $8.70
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.
The spot price of a share of XYZ stock is $100. The annual risk-free continuously compounded interest rate is 0.07, and the stock pays no dividends. The annualized standard deviation of the continuously compounded stock return is 0.2. Find the price of a European call option on the stock with strike price $110 and that matures in 4 years.
The price of a European call option on a stock with a strike price of $50.9 is $5.6. The stock price is $40.1, the continuously compounded risk-free rate (all maturities) is 5.2% and the time to maturity is one year. A dividend of $0.6 is expected in six months. What is the price of a one-year European put option on the stock with a strike price equal to the call's strike price? Please state the formula and steps, thanks
Use the binomial tree analysis to value a 6-month American put option with a $65 strike price on Crookshanks Corporation. The shares are currently trading for $60. The annualized continuously compounded risk-free rate is 3%. The volatility of the stock is 57%. You will use the Cox Ross Rubenstein method for computing the binomial tree, and use a time step of 2 months.
1) In a one-period binomial model, assume that the current stock price is $100, and that it will rise to $130 or fall to $70 after one month. The gross one month risk - free rate is 1.02 %. Using risk neutral pricing, what is the price of a 100- strike one-month call option? Round your calculaton for q and 1 - q to four (4) decimal places. a. $14.90 b. $14.71 c. $15.05 d. $15.69 2) In a one-period binomial model, assume that the current stock price is $100, and that it will rise to $120 or fall to $80 after one month. The gross one month risk - free rate is 1.03%. Using risk neutral pricing, what is the price of a 100-strike one-month put option? Round your calculaton for q and 1 - q to three (3) decimal places a. $8.00 b. $8.25 c. $8.50 d. $8.75
The stock price of Heavy Metal (HM) changes only once a month: either it goes up by 24% or it falls by 20.7%. Its price now is $48. The interest rate is 1.2% per month. What is the value of a one-month call option with an exercise price of $48? What is the option delta? The payoffs of the call option can be replicated by buying shares of stock and borrowing. What amount should be invested in stock and what amount must be borrowed? What is the value of a two-month call option with an exercise price of $49? What is the option delta of the two-month call over the first one-month period?
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.

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