2) Consider a stock whose current price is $100 and volatility is 20% p.a. The stock isexpected to pay a dividend of $2 in one month's time. The risk-free rate is 5% p.a.continuously compounding.(a)Using a two-period binomial tree, what is the value of a 2-monthAmerican call whose exercise price is $101?(b) Using a two-period binomial tree, what is the value of a 2-monthAmerican put whose exercise price is $101?

An option is a type of financial instrument that is based on the value of underlying securities,…

Answered: Consider a stock whose current price is…

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 stock, the current price (S.) of which is $30. We model stock-price evolution using a Binomial model. In every three-month period, u = 1.1052 and d = 0.9048. The risk free rate of interest is 5% per annum continuously compounded. The four-step Binomial tree is shown below: 44.75 40.50 36.64 36.64 33.16 33.16 30 30.00 30.00 27.15 27.15 24.56 24.56 22.22 20.11 Node Time: 0.0000 0.2500 0.5000 0.7500 1.0000 A European-style exotic derivative has been written on this stock. The derivative has one year to expiry. Denote by S;, S2, S; and S4 the stock price after three, six, nine and twelve months respectively. The payoff to the derivative is specified as follows: [max(S2,S,)–min(S,,S,) if S, 2 30 Рayoff 3D max(S,S,S,)-S, if S, < 30 Required: Using a four-step Binomial framework and the risk-neutral approach, calculate the current value of this exotic derivative. Use continuous compounding for all present value calculations. Show all working.
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: 1 period of 1 year. 4 subperiods, each 3 months. 12 subperiods, each 1 month.
The next question is based on the following data for a two-period binomial model. • The stock's price S is $100. After three months, it either goes up and gets multiplied by the factor U = 1.14, or it goes down and gets multiplied by the factor D = 1/U. Options mature after T = 0.5 year and have a strike price of K = $96. • The continuously compounded risk-free interest rate r is 1.6 percent per year. Today's price of an American put option is: [round to two decimal places]
You use the standard binomial model and the following information to construct a one-period binomial tree for modeling the price movements of a nondividend-paying stock. (The tree is sometimes called a forward tree.) The period is six months. The initial stock price is $75. The stock's volatility is 25%. • The continuously compounded risk-free interest rate is 8%. At the beginning of the period, an investor owns an American put option on the stock. The option expires at the end of the period. Determine the smallest integer-valued strike price for which an investor will exercise the put option at the beginning of the period. A) 85 B) 86 O) 87 D) 88 E) 89
Indicate whether the following statements are true or false (circle one). Use 1 or 2 sentences to discuss why it is so. (a) If R, is simple 1-month return, then the annualized return is 12 x R, after assuming all R = R. True False Why? (b) Let and r GSA be continuously compounded 1 - month returns for Goldman Sachs Group (GS) and American International Group (AIG). If we construct a portfolio using the share ain[0, 1] for GS, the portfolio cc return is ľ AIG = 0x*y +(1-x)*r True False Why? (c) In 5. (b)., if 5% quantile of the portfolio cc return is given as AIG, GS, r 40.05 = -0.5, then 5% monthly Value-at-Risk for the $10,000 investment in this portfolio is $10,000 × (-0.5) = -$ 5,000. True False r
For a two-period binomial model, you are given: Each period is one year. The current price for a non dividend-paying stock is 20. u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock price goes up. d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock price goes down. The continuously compounded risk-free interest rate is 5%. Calculate the price of an American call option on the stock with a strike price of 22.
Assume the Black-Scholes framework. Let S be a stock such that S(0) = 21, the dividend rate is δ = 0.02, the risk free rate is r = 0.05, and the volatility is σ = 0.2. (a) Calculate the expected payoff of a 6 month call with strike price 17. (b) Calculate the cost of such a call. (c) Calculate the cost of a 6 month put with strike price 17. (d) Calculate the price of a derivative that pays |S(0.5) − 17| in six months
You have a stock trading at $100. The stock follows a lognormal distribution: with drift of 20% and volatilty of 30%. The risk free rate is 2%. What is the risk-neutral probability for a 3- month 100 put to expire in the money? Find N(-d2). Compare the results.
You model a stock price S(t) using a stochastic process, with t measured in years. Your model implies that the risk-neutral distribution for the stock price at t = 4 has probability density function fs(4)(x) = x-40 {} 50 if 40 < x < 50 else Assume that interest is compounded continuously at nominal rate r = : 2.0%. Calculate the price of the stock at time 0 to the nearest pence. Do not enter the pound sign.
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 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?
The current spot price of a stock is $89.00, the expected rate of return is 9.8%, and the volatility of the stock is 18%. The risk-free rate is 3.3%. Assume the log-normal model. (a) Calculate the Delta A. and Vega v. of a European call with strike $94.00 expiring in 14 months. Enter your solution for A, to three decimal places. Enter your solution for v. as a dollar value to two decimal places. Ac = Vc = (b) Calculate the Delta A, and Vega v, of a European straddle with strike $94.00 expiring in 14 months. Enter your solution for As to three decimal places. Enter your solution for v, as a dollar value to two decimal places. As =

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