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

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter12: The Cost Of Capital

Section: Chapter Questions

Problem 26P

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Problem 4 Consider a stock with current price $60. You are given: • Dividends of $1 each will be paid every three months; the next dividend will be paid in 2 months. • σ = 0.3. ⚫ The continuously compounded risk-free interest rate is 4%. Use the Black-Scholes methodology to price a nine-month at-the-money European put option on the stock.
Question 3: 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
INV4 2b Lon Musky Corp. stock sells today for $50 per share, and the risk-free rate is 5% per year, continuously compounded. Six months from now, the price will be either $60 or $45. Using the binomial approach, find the value of a European put option with an exercise price of $50.
QUESTION 1 A one-month European put option on a non-dividend-paying stock is currently selling for $1.5. The stock price is $37, the strike price is $43, and the risk-free interest rate is 5% per annum. What is the minimum arbitrage profit you can make in today's value? (Keep to 2 decimal places)
Suppose that an American put option with a strike price of $70.0 and maturity of 4.0 months costs $13.2. The underlying stock price equals 55. The continuously compounded risk-free rate is 8.5 percent per year. What is the potential arbitrage profit from buying a put option on one share of stock? 1.9783 no arbitrage profit available 3.8117 4.2693 1.80
V3. Consider a European call option on Allana Inc. stock. The option matures in 8 months and its strike price is $50. Current stock price per Allana Inc.’s share is $50. Allana Inc. will pay $2 dividend per share in 2 month and $3 per share in 6 months and the risk free rate is 3% per annum with continuous compounding for all maturities. Assume that the standard deviation of Allana Inc.’s stock return is 30% per year. The Black-Scholes value of this call option is ______. $18.31 $15.17 $6.92 $5.24 $2.96
INV4 2a Lon Musky Corp. stock sells today for $50 per share, and the risk-free rate is 5% per year, continuously compounded. Six months from now, the price will be either $60 or $45. Using the binomial approach, find the value of a European call option with an exercise price of $50.
2. a. Calculate the price of a four-month European put option on a non- dividend-paying stock with a strike price of $60 when the current stock price is $55, the continuously compounded risk-free interest rate is 10% per annum, and the volatility is 31% per annum. b. Calculate the price of the put option if a dividend of $2.50 is expected in three months.
Problem 1. Assume that the interest rate is 5%, continuously compounded annually, and consider call and put options of both American and European style expiring in 6 months on non-dividend paying stock. For each of the following scenarios, check if you can find an arbitrage opportunity and, if you can, describe it: (i) The strike price of a European put option is $3 and the option is traded at $4. (ii) The shares are traded at $3 and the American call option is traded at $3.20.
25 A non-dividend-paying stock, currently priced at $125 per share, can either go up by $25 or down $25 in a year. Consider a one-year European call option with a strike price of $135. The continuously- compounded risk-free interest rate is 8%. Use a one-period binomial model to determine the current price VC (0) of the call option. (a) About 8.60 (b) About 9.52 (c) About 9.76 (d) About 9.81
Question 4 - A stock price is currently worth $20. It is known that at the end of a 6 month period it is expected to go up by 8% or down by 5%. The risk-free interest rate is 4% per annum with continuous compounding. Use a two-step tree to calculate the value of a 1-year American exotic option whose payoff is payoff max (S+ ST - S²; 0). State in which node the option is early exercised.
4. The current price of Leamington plc stock is £3.00. Leamington plc is not expected to pay a dividend in the foreseeable future. Over the next six months, the price is equally likely either to increase by 25% or to fall by 20%. The riskless rate is 7.5% per annum, continuously compounded. Consider a European call option on Leamington plc stock with strike price £3.25 and time to maturity six months. The risk-neutral probability of exercise for the European call option is * 0.36 0.47 0.50 0.53 0.64