9. Consider a European put option on a stock, with a $30 strike and 1-year to expiration. The stock does not pay dividends, and its current price is $25. Suppose the volatility of the stock is 20%. The continuously compounded risk-free interest rate is 7%. Use a two-period binomial tree to calculate the following: (all the intermediary calculation steps are required) (a) All possible stock prices. (b) The option premium (without the use of A and B).

9. Consider a European put option on a stock, with a $30 strike and 1-year to expiration. The stock does not pay dividends, and its current price is $25. Suppose the volatility of the stock is 20%. The continuously compounded risk-free interest rate is 7%. Use a two-period binomial tree to calculate the following: (all the intermediary calculation steps are required) (a) All possible stock prices. (b) The option premium (without the use of A and 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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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.
4. Consider a stock with a current price of S0 = $60. The value of the stock at time t = 1 can take one of two values: S1,u = $100, S1,d = $40. The price of a risk-free bond that pays out $1 in period t = 1 is $0.90. (a) Using a one-step binomial tree, write down the possible payoffs of a put option on stock S with strike K = $60 and maturity t = 1. (b) What is the price of this put option? (c) What is the price of a call option with strike K = $60 and maturity t = 1? Please use put-call parity to find the call price.
In this problem we assume the stock price S(t) follows Geometric Brownian Motion described by the following stochastic differential equation: dS = µSdt + o Sdw, where dw is the standard Wiener process and u = 0.13 and o = current stock price is $100 and the stock pays no dividends. 0.20 are constants. The Consider an at-the-money European call option on this stock with 1 year to expiration. What is the most likely value of the option at expiration? Please round your numerical answer to 2 decimal places.
Consider an American put option (K=$100) expiring in one year on a stock trading for $84. The return volatility on the stock is 27.3% and the riskless rate is 5%. Find the price of the option using a Binomial Model with two steps. (Respond with two decimal places, such as "-12.34") 26.59 Correct Answer: 18.28
Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = 0.34. What would be the appropriate values for u and d if your binomial model is set up using: a. 1 period of 1 year. b. 4 subperiods, each 3 months. c. 12 subperiods, each 1 month. Note: Do not round intermediate calculations. Round your answers to 4 decimal places. Subperiods At = T/n u = exp(σ√ At) d = exp(-σ√ At) a. 1 1/1 = 1 b. 4 1/4 = 0.25 C. 12 1/12 0.0833
Consider shorting a call option c on a stock S where S = 24 is the value of the stock, K = 30 is the strike price, T = ½ is the expiration date, r = 0.04 is the continuously compounded interest rate per year, and  = 0.3 is the volatility of the price of the stock. Determine the delta ratio Δ .
In this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $D per share at the expiration date of the option.a. What is the value of a stock-plus-put position on the expiration date of the option?b. Now consider a portfolio comprising a call option and a zero-coupon bond with the same maturity date as the option and with face value (X + D). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio regardless of the stock price.c. What is the cost of establishing the two portfolios in parts (a) and (b)? Equate the costs of these portfolios, and you will derive the put-call parity relationship.
Assume the price of an non-dividend stock is $40, the annual volatility of the stock is 20%, and the continuous compound risk-free interest rate is 5%. What's the price of a European put option on this stock with delivery price of $40 with 1-year expiration? (The standard normal distribution table is in the attachment or you can use excel function NORMSDIST, and please keep the results with 3 decimal places.) (BS Model-Option Pricing)
Consider a stock with a current price of P = $27.Suppose that over the next 6 months the stockprice will either go up by a factor of 1.41 or downby a factor of 0.71. Consider a call option on thestock with a strike price of $25 that expires in6 months. The risk-free rate is 6%.(1) Using the binomial model, what are the endingvalues of the stock price? What are the payoffsof the call option?
Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.) Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value GA $ $ $ 48 60 0.07 0.04 0.50 0.26
Consider a 11-period binomial model with R=1.02, S0 = 100, and u= 1.05. Compute the value of a European call option on the stock with strike K = 102. The stock does not pay dividends.
Imagine all investors are risk-neutral and we have the following binomial tree: 0 Stock: So= 80 1 100 72 2 120 90 86.4 64.8 Using the risk-neutral option valuation approach, calculate the price of a two-year put option on this stock with a strike price $92. Assume that the risk-free rate is 3% per year. Also assume the stock does not pay a dividend. Pick the closest number.

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