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.
Suppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoidarbitrage?
7) Consider a European call option on a -dividend-paying stock where the stock price is $40, the strıke price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. A dividend of $1 is expected in 3 months' time a. Calculate u, d̟ and p for a two-step tree b. Value the option using a two-step tree. c. Value the option with 5 time steps using DerivaGem software.
Suppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. Required: (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoid arbitrage?
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 an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. What is the value of the option. Provide all necessary calculations.
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
Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. (a) What is the evolution of the prices of the underlying asset in time? Show it on a binomial tree.

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