Use the Black-Scholes formula to find the value of a call option on the following stock: Time to expiration Standard deviation Exercise price Stock price Annual interest rate Dividend 6 months 60% per year $57 $64 38 0 Value of the Call Option

Use the Black-Scholes formula to find the value of a call option on the following stock: Time to expiration Standard deviation Exercise price Stock price Annual interest rate Dividend 6 months 60% per year $57 $64 38 0 Value of the Call Option

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

Use the Black-Scholes formula to find the value of a call option on the following stock:
Time to expiration
Standard deviation
Exercise price
Stock price
Annual interest rate
Dividend
Value of the Call Option
6 months
60% per year
$57
$64
38
0

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■ Yegi’s Fine Phones has a current stock price of $30. You need to findthe value of a call option with a strike price of $32 that expires in3 months. Use the binomial model with one period until expiration(i.e., t = 0.25 and n= 1). The factor for an increase in stock price isu = 1.15; the factor for a downward movement is d = 0.85. Whatare the possible stock prices at expiration? ($34.50 or $25.50)What are the option’s possible payoffs at expiration? ($2.50 or$0) What are pu and pd? (0.5422 and 0.4429) What is the currentvalue of the option (assume each month is 1/12 of a year)? ($1.36)
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(a) The table below gives information about European options with a maturity date of 6 months. Type Of option Strike Price Call 65 Call 58 Put 65 Premium 5 8 4 (i) Devise the payoff profile of the hedging strategy from the above for an investor betting on an increase in the stock price and calculate the payoff if the stock price increases to $66 after 6 months. (8 marks) (ii) Suppose that another investor expects a big stock price movement but is not sure of the direction. She however bets that the downward movement is more likely. Devise the corresponding trading strategy and calculate the payoff if the stock price is $55 after 6 months. (8 marks) (b) By analysing the pay off profiles of a protective put strategy and a straddle, discuss in what ways these strategies shield the investor from potential losses.
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