Q4 (Exercise 12.3) Let S = $100, K = $120, σ = 30%, r = 0.08, and 8 = 0. a. Compute the Black-Scholes call price for 1 year to maturity and for a variety of very long times to maturity (use T=1, 2, 5, 10, 50, 100, 500). What happens to the option price as T→ ∞o? b. Set 8 = 0.001. Repeat (a). Now what happens to the option price? What accounts for the difference?

Q4 (Exercise 12.3) Let S = $100, K = $120, σ = 30%, r = 0.08, and 8 = 0. a. Compute the Black-Scholes call price for 1 year to maturity and for a variety of very long times to maturity (use T=1, 2, 5, 10, 50, 100, 500). What happens to the option price as T→ ∞o? b. Set 8 = 0.001. Repeat (a). Now what happens to the option price? What accounts for the difference?

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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H2. Using the Black-Scholes model (BSOPM), compute the standard deviation that is implied by the following call option data as: the time to the option's maturity is 0.25 years, the price of the underlying option asset is RM30, the continuously compounded risk-free interest rate is 0.12. the exercise or striking price is RM30, and the cost or premium of the call is RM1.90.
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).
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?
Use the Black-Scholes model to value a call option with the following data: Price $34 Exercise price 30 Risk-free rate 0.04 time to expiry 0.5 0.31557 0.099584 0.762113 0.538972 0.777004 0.705047 Post your answer with 2 decimal places 5 0² d1= d2= Nd1= Nd2=
4. Consider an exchange option. Suppose the initial prices (time 0) of the two stocks are S =S2 = 100 and a =0.40,. Suppose also that the returns on the stocks are uncorrelated. Assume no dividends and final maturity of the option is T = 2 year: (a) Using the closed-form expressions for the price of these options, identify the price of the exchange option when o = 0, a2 =0.20, ag =0.40, and @2 =0.60. (b) Is there a trend in the price? Intuitively, why is this the case?
Q2: Given the following inputs for YMMV: Interest rate 3.25 Dividend rate 3.00 Spot Price Volatility (%) 30.21 12.00 Strike Price 30.00 Expiry (months) T Option type 12 European Put a) Compute u, d, Pup; Pdn, Construct a 3 step tree and price the option.
1. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.
2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.
Using put-call parity, if the price of an At-the-Money Call option maturing in 1 day is $3.14, what is the price of an of an At-the-Money Put option maturing in 1 day (give an approximation)? A. $0.95 B. $2.86 C. $3.14 D.$3.26
Please solve in 30 minutes Assume the three-period binomial model (t = 0, 1, 2, 3) where S0 = 4, u = 2, d = 1/2 and r = 1/4. Consider a digital option that pays off $10 at time three if the stock price exceeds $7, but nothing otherwise. Find the value of this option at time zero?
Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e.,u= 2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchasse the security at the end of two periods for a price of 150. My main question is what should the no-arbitrage price of the call be? Can I have complete detail and formula please.
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.

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