2. (a) Compute the price of a European call option written on a non-dividend-payingstock. 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. Therisk free interest rate with continuous compounding is 3% per annum. You shoulduse 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-freeasset. 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 thisis indeed the case in your tree.

(a) Pricing the European Call Option with a Binomial TreeWe'll use a three-step (period) binomial…

Answered: 2. (a) Compute the price of a European…

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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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 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.
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)
Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.
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 $
Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $63.00 currently and pays an annual dividend of $1.92. The standard deviation of the stock’s returns is 0.21 and risk-free interest rate is 5.0%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal
Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $62.50 currently and pays an annual dividend of $1.47. The standard deviation of the stock's returns is 0.14 and risk-free interest rate is 3.5%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal places.) $ Put value
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. 1. а. b.
You observe a €50 price for a non-dividend-paying stock. The call option has two years to mature, the periodically compounded risk-free interest rate is 5%, the exercise price is €50, u = 1.356, and d = 0.744. Assume the call option is European-style.Compute the current PUT option value
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%. (b) You believe the true volatility is 28.4%. Is the option under-priced or overpriced? Hence what position should you take in option to make money. Explain. (Please provide Screenshots.)
Use the following data for a fictitiously named company OPPS to answer the questions that follow: — The current stock price S is $23. — The time to maturity T is six months. — The continuously compounded, risk-free interest rate r is 5 percent per year. — European option prices are given in the following table: Strike Price Call Price Put Price K1 = $17.5 6.00 0.10 K2 = 20 4.00 0.50 K3 = 22.5 2.00 1.00 K4 = 25 1.00 2.50 You buy a call option with strike price K2 = 20 and sell a call option with strike price of K3 = 22.5. Then which of the following statements is INCORRECT? The derivative has zero-profit when the stock price at expiration is $21.5. You have set up a call spread. You have set up a bullish spread. The maximum loss is –$2 for a stock price at expiration less than or equal to $20. The maximum profit is $0.5 for a stock price at expiration greater than or equal to $22.5.
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.

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