A binomial tree is used to value a European call option. The strike price is $90 and the option expires 6 months from now. The underlying stock price is modeled by a binomial tree with volatility o = 0.2, time step dt = 0.25, and number of time steps n = 2. The risk-free interest rate is %3D r = 0.04. (a) Find p, q, u and v. (b) If the current stock price is $100, find the current value of the option.

A binomial tree is used to value a European call option. The strike price is $90 and the option expires 6 months from now. The underlying stock price is modeled by a binomial tree with volatility o = 0.2, time step dt = 0.25, and number of time steps n = 2. The risk-free interest rate is %3D r = 0.04. (a) Find p, q, u and v. (b) If the current stock price is $100, find the current value of the 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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Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. If the price of the call option is 7.17, describe the arbitrage that would be possible, and calculate the profit that would result.
D4) Consider a two-step binomial tree. What is the delta of the put option if: the futures price is S = 1682.00, the risk-free rate is r = 2.90%, the strike price is K = 1757.00, the maturity is T = 12 months and the tree parameters are u = 1.1357 and d = 0.8620? (keep 4 decimals in your 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.
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.
Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. What would the price of the call option ‘c’ need to be for put-call parity to hold?
Using the binomial call option model to find the current value of a call option with a $25 exercise price on a stock currently priced at $26. Assume the option expires at the end of two periods, the riskless interest rate is ½ percent per period. What are the hedge ratios?
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
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.
The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money.) If the interest rate is 8%, what is the risk-neutral valuation of the call option?
The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money).
A call option with X = $50 on a stock currently priced at S = $55 is selling for $10. Using a volatility estimate of σ = .30, you find that N(d1 ) = .6 and N(d2 ) = .5. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than .30? Explain.
Consider the following data for a certain share. Current Price = S0 = Rs. 80 Exercise Price = E = Rs. 90 Standard deviation of continuously compounded annual return = \sigma = 0.5 Expiration period of the call option = 3 months Risk – free interest rate per annum = 6 percent a. What is the value of the call option? Use the normal distribution table. b. What is the value of a put option?

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