A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate values for u, d, and p when a six-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree. 78.41 79.85 80.04 79.57

A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate values for u, d, and p when a six-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree. 78.41 79.85 80.04 79.57

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter20: Financing With Derivatives

Section20.A: The Black-scholes Option Pricing Model

Problem 1P

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A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate values for u, d, and p when a 6-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree.
The current spot price of a stock is $89.00, the expected rate of return is 9.8%, and the volatility of the stock is 18%. The risk-free rate is 3.3%. Assume the log-normal model. (a) Calculate the Delta A. and Vega v. of a European call with strike $94.00 expiring in 14 months. Enter your solution for A, to three decimal places. Enter your solution for v. as a dollar value to two decimal places. Ac = Vc = (b) Calculate the Delta A, and Vega v, of a European straddle with strike $94.00 expiring in 14 months. Enter your solution for As to three decimal places. Enter your solution for v, as a dollar value to two decimal places. As =
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.
A stock has a price of $37 and an annual return volatility of 59 percent. The risk-free rate is 3.13 percent. Perform calculations in Excel. a. Calculate the European call and European put option prices with a strike price of $38.00 and a 90-day expiration. (Use 365 days in a year. Do not round Intermediate calculations. Round your answers to 2 decimal places.) Call premium Put premium b. Calculate the deltas of the European call and European put. (Use 365 days In a year. A negative value should be Indicated by a minus sign. Do not round Intermediate calculations. Round your answers to 4 decimal places.) Call delta Put delta
A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.
The stock price is currently $30. Each month for the next two months it is expected to increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off [max(30 — St； 0)]2, where St is the stock price in two months? If the derivative is American-style, should it be exercised early?
A stock is currently trading at $42. Over the next 3 periods, it is expected to go up by 10% or down by 10%. Assume that the risk-free rate of interest is 6% per annum. a. What is the value of a three-month American call option with an exercise price of $40? b. What is the value of a three-month American put option with an exercise price of $46?
The current price of a non-dividend paying stock is $50. Use a two-step tree to value a European put option on the stock with a strike price of $50 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 50%. What is the value of the option according to the two-step binomial model. Please enter your answer rounded to two decimal places (and no dollar sign).
XYZ stock is currently traded at $40. Consider a put option on XYZ with $38 exercise price expiring in 6 months. Estimate the price of the option using two-period BOPM. Assume the stock price can go up by 10% and down by 15% each period (i.e., (6 months) / (2 periods) = 3 months). The annual risk-free interest rate is 6%. please use excel and show formulas. thanks!
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
A company stock whose current price is $192 is expected to either increase to $242 or decrease to $185 over the next nine months with equal probability. Compute the price of a nine-month at-the-money European put option. Use the fact that the riskless rate is 3.3% per year with continuous compounding. Express your answer with two decimals.
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