27.6. A 6-month Asian average strike call option on a nondividend paying stock based on the arithmeticaverage of quarterly prices is modeled with a 2-period binomial tree. You are given:(1) The stock price is 60.(ii) o= 0.3(iii) The continuously compounded risk-free interest rate is 0.04.(iv) The binomial tree is constructed using forward prices.Calculate the risk-neutral probability of an option payoff greater than 0.

Volatility = 30% Risk free rate = 0.04 or 4% Stock Price = 60 2 Period Binomial Period Time Period…

A 6-month Asian average strike call option on a nondividend paying stock based on the arithmetic ge of quarterly prices is modeled with a 2-period binomial tree. You are given: ) The stock price is 60. ) o= 0.3 ) The continuously compounded risk-free interest rate is 0.04. w) The binomial tree is constructed using forward prices. alculate the risk-neutral probability of an option payoff greater than 0.

A 6-month Asian average strike call option on a nondividend paying stock based on the arithmetic ge of quarterly prices is modeled with a 2-period binomial tree. You are given: ) The stock price is 60. ) o= 0.3 ) The continuously compounded risk-free interest rate is 0.04. w) The binomial tree is constructed using forward prices. alculate the risk-neutral probability of an option payoff greater than 0.

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 following information is given about an Option on a stock: S(0)=$31, X=$34, rf=9%, variance (sigma squared)=20%, T=182.5 days, Dividend $1.75 in 45 days (1) Calculate the price of a European put option using the Black-Scholes pricing model (show all workings including d1, d2, N(d1), N(d2)) (2) Calculate the price of the corresponding European call option (hint: put call parity) (3) Suppose you feel that the put option is overpriced. What strategy should you use to exploit the apparent mispricing? (4) The market has entered a state of significant volatility, and you believe the implied volatility is incorrect. You believe it should be 10% higher. What trade would you undertake to exploit this arbitrage
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
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 .
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 an n = 1 step binomial tree with T = 1. Suppose r, the annualized risk-free rate is 9 %, and delta, the annualized dividend rate is 8 %. Also suppose the annualized standard deviation of the continuously compounded stock return, sigma, is 35 %. Suppose further that the initial stock price, S = $110. Compute American call option prices for K = $ 55, $ 66, $ 77, $ 88,$ 99, $ 110, $ 121. a) Determine the American call premium, when K = $ 55 55 b) Determine the American call premium, when K = $ 66 | c) Determine the American call premium, when K = $ 77 d) Determine the American call premium, when K = $ 88 ? ? ? ?
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?
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?
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 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.
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 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 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).

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