A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. Thestock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compoundedrisk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is aEuropean put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation tocalculate the value of this call.

An option is an agreement between two parties granting one the opportunity to buy or sell a security…

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.

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.

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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Question

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.

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4. Which of the below represents the value of an American option in each state? max(Payoff if exercised, Value if held) Payoff if exercised Risk-neutral probability min(Payoff if exercised, Value if held)
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Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04
Select all statements which are correct. The value of a European put option is increasing in the strike price. The value of a European call option is increasing in the strike price. The value of a European put option is increasing in the spot price. The value of a European call option is increasing in the spot price.
Consider a two year put options with strike Price sh. 52 on a stick whose current price is sh.50. suppose there is 2 times steps and each step is one year and in each times steps the price move up or down by 20%. Suppose the risk Free rate is 5% . Calculate value of put assuming; A) Europeans options B) American options
We will derive a two-state put option value in this problem. Data: S0 = $180; X = $190; 1 + r = 1.10. The two possibilities for ST are $210 and $110.a. The range of S is $100 while that of P is $80 across the two states. What is the hedge ratio of the put? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) (The answer for this one is -.80) :)b. Form a portfolio of four shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.) c. What is the present value of the portfolio? (Round your answer to 2 decimal places.) d. Given that the stock currently is selling at $180, calculate the put value. (Do not round intermediate calculations and round your answer to 2 decimal places.)
Using put-call parity, if the price of an At-the-Money Call option maturing in 1 day is $3.14, what is the price of an of an At-the-Money Put option maturing in 1 day (give an approximation)? A. $0.95 B. $2.86 C. $3.14 D.$3.26
Given the following data, show the profit from a strategy involving a straddle for the put, call and combined position. The price of a European call and put option are $5 and $6 respectively. Both of the options have a strike price of $30. Explain why a trader might be willing to enter into a straddle. Please show all work. Please use four decimal places for all calculations.
Put together a Black–Scholes option calculator in Excel to answer the following.(a) What is the call-option value withS0 = $45, K = $48, r = 6%, T = 15 months,and volatility = 40%?(b) What is the put-option value withS0 = $60, K = $65, r = 6%, T = 18 months,and volatility = 20%?(c) What is the put-option value withS0 = $38, K = $40, r = 6%, T = 3 months,and volatility = 60%?(d) What is the call-option value withS0 = $100, K = $95, r = 8%, T = 3 years,and volatility = 40%?
An investor buys a 6-month European call option with an exercise price of $35 for $6, and sells a 6-month European call option with an exercise price of $40 for $4. a) What kind of a spread does this strategy create? Answer in terms of “Bull Spread” versus “Bear Spread”. b) Calculate both the total payoff and profit on this strategy at the expiration of the options. Please use a Table (as in the class notes) to identify the payoff and profit.
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Calculate the Black-Scholes price of a Call option where: S = $50 K = $45 T-t=.25 O = .20 r= .03 Show your work.

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