The stock price five months from the expiration of an option is $42, the exercise price of the option is $40, the continuously compounded risk-free interest rate is 11% per annum, and the volatility (o) is 21% per annum. Calculate the price of the option if it is a European call. Calculate the price of the option if it is a European put. a. b.

The stock price five months from the expiration of an option is $42, the exercise price of the option is $40, the continuously compounded risk-free interest rate is 11% per annum, and the volatility (o) is 21% per annum. Calculate the price of the option if it is a European call. Calculate the price of the option if it is a European put. a. b.

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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The stock price 6 months from the expiration of an option is $42, the exercise price of the option is $40, the risk-free rate is 10% per annum, and the volatility is 20% per annum. a) What is the price on a European call? b) What is the price of a European put? c) Check the put-call parity is satisfied.
Consider a European Call Option with a strike of 82. The current price of the underlying asset is 80, and the time to expiry is 5 months. The current market price of the option is 6.22. The risk-free rate is 4.1%. (a) Find the implied volatility of the underlying. Provide all necessary calculations.
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. a) What is the price of the option if it is a European put?
You observe the price of a European put option that expires in nine months and has a strike price of$45 is $3. The underlying stock price is $49.50. The term structure is flat, with all risk-free interestrates being 8%.a. What is the price of a European call option that expires in nine months and has a strike priceof $45? b. You observe next that the price of the call option (in part (a)) in the market is $9.59. Statewhy an arbitrage opportunity exists and explain how you would take advantage of thisopportunity. (Hint: answer should include an outline general strategy, net cost ofstrategy at initiation and net profit at expiration using the numbers in the question)
1. Consider an option on a non-dividend paying stock when the stock price is $30, the exercise price is $28, the annual interest rate is 5%, the annual volatility is 25%, and the time to maturity is 6 months. Show the details of your calculations. a) What is the price of the option if it is a European call?
A stock price is currently $30. It is known that at the end of one year, it will be either $36 and $24. The exercise price of a one-year European call option is $32. The risk-free interest rate is 5% per annum. a. Construct a binomial tree to show the payoff of the call option at the expiration date. b. Based on the binomial tree model, what is the value of the call option?
A European put option on a non-dividend paying stock has strike price of $40 and time to maturity 9 months. Assume the risk-free interest rate is 5% per annum, the volatility is 20% per annum and the current stock price is $38. Using the Black-Scholes model, calculate the price of the European put option.
Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6 months. (a) Calculate u, d, and p for a two-step tree. (b) Value the option using a two-step tree.
Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset.
Consider a European Call option of stock XYZ. The current price of the option is $5.67. This option has 3 months to maturity, and the strike price is $80. Currently, the price of XYZ stock is $65. The 3-month interest rate (annualized, continuously compounded) is 4%. Compute the net payoff to the buyer of the option at the expiration of the options, assuming that: the price of XYZ at maturity is $105 $ the price of XYZ at maturity is $70 $
2. (a) Compute the price of a European call option written on a non-dividend-paying stock. The current stock price is $100 and the volatility of the stock price is 30%. The maturity of the option is in three months and the strike price is $105. The risk free interest rate with continuous compounding is 3% per annum. You should use a three step (period) binomial model to price the option. (b) The option can be replicated by a portfolio consisting of the stock and a risk-free asset. What is the replicating portfolio strategy of the call option? (c) Explain how the delta should change, as the stock price increase and check if this is indeed the case in your tree.
Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset.

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