You think that there is an arbitrage opportunity on the market. The current stock price of Wesley corp. is $20 per share. A one- year put option on Wesley corp. with a strike price of $18 sells for $3.33, while the identical call sells for $7. The one-year risk- free interest rate is 8%. Assuming that the put option is fairly priced, compute the fair price of the call option and explain what you must do to exploit this arbitrage opportunity and what will be your gain.

You think that there is an arbitrage opportunity on the market. The current stock price of Wesley corp. is $20 per share. A one- year put option on Wesley corp. with a strike price of $18 sells for $3.33, while the identical call sells for $7. The one-year risk- free interest rate is 8%. Assuming that the put option is fairly priced, compute the fair price of the call option and explain what you must do to exploit this arbitrage opportunity and what will be your gain.

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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A call option on Rosenstein Corporation stock has a market price of $7. Thestock sells for $31 a share, and the option has an exercise price of $25 a share.a. What is the exercise value of the call option?b. What is the premium on the option?
You work on a proprietary trading desk of a large investment bank, and you have been asked for a quote on the sale of a call option with a strike price of $53 and one year of expiration. The call option would be written on a stock that does not pay a dividend. From your analysis, you expect that the stock will either increase to $73 or decrease to $38 over the next year. The current price of the underlying stock is $53, and the risk-free interest rate is 5% per annum. What is this fair market value for the call option under these conditions? Do not round intermediate calculations. Round your answer to the nearest cent. $
A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 − $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 − $1.00 =…
Required: You are attempting to value a call option with an exercise price of $80 and one year to expiration. The underlying stock pays no dividends, its current price is $80, and you believe it has a 50% chance of increasing to $90 and a 50% chance of decreasing to $70. The risk-free rate of interest is 5%. Consider one share of stock and two written calls. Calculate the call option's value using the two- state stock price model. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of the call
A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 - $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 - $1.00 =…
A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 − $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 − $1.00 =…
You are attempting to value a call option with an exercise price of $105 and one year to expiration. The underlying stock pays no dividends, its current price is $105, and you believe it has a 50% chance of increasing to $127 and a 50% chance of decreasing to $83. The risk-free rate of interest is 10%. Calculate the call option’s value using the two-state stock price model. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.
You are attempting to value a call option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $136 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%. Calculate the call option's value using the two-state stock price model. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.
You are attempting to value a call option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $136 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%. Calculate the call option's value using the two-state stock price model. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. > Answer is complete but not entirely correct. Value of the call option $ 12.73 x
You would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of $109 at year- end. XYZ currently sells for $109. Over the next year the stock price will increase by 12% or decrease by 12%. The T-bill rate is 6%. Unfortunately, no put options are traded on XYZ Co. a. Suppose the desired put option were traded. How much would it cost to purchase? (Do not round intermediate calculations and round your final answer to 2 decimal places.) Cost to purchase b. What would have been the cost of the protective put portfolio? (Do not round intermediate calculations and round your final answer to 2 decimal places.) Cost of the protective put portfolio c. What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = 109? Show that the payoff to this portfolio and the cost of establishing the portfolio match those of the desired protective put. (Do not round…
Optival’s stock is currently trading at $60 per share with a historical volatility of 20%. The risk-free rate is 4%. Consider a European call and put option on Optival’s stock with an exercise price of $55 that expires in 2 years. Use excel or a similar program to determine the option price using the Black-Scholes formula. (a): What is the value the European call and put option on Optival’s stock with a strike price of $60? (b): To the nearest cent, how much does the option value change for the following adjustments to the input values: ∆ in Call Value ∆ in Put Value ↑ stock price by $1 to $61 ↑ strike price by $1 to $56 ↑ the rF by 1% to 5% ↑ volatility by 1% to 21% ↑ time to maturity by 1 yr (c): Why does the value of the call increase by less than $1 when the stock price increases by $1? (d): To the nearest percent and holding all else constant, how high would the risk-free rate need to be for a 1 year increase in time to maturity to have a negative impact on the value of…
A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 − $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 − $1.00…

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