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?

am. 116.

Given the following information, predict the European call option's new price after the risk free rate changes. Initial call option price = $3 Initial risk free rate = 9.9% Rho = 9 New risk free rate = 9.5%   (required precision 0.01 +/- 0.01)   Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r   Recall that rho is defined as the partial derivative of the option's price with respect to the risk free rate. (i.e. rho = ∂π / ∂r).

b) Suppose you are given the following information: Current market price of a share= R200 000 Option’s exercise price = R300 000 Time until the option expires= 5 yrs Risk free rate =4% Standard deviation of the returns on the share= 0.35 Required: i. Calculate d1 and d2 ii. Suppose N(d1) =0.7517 and N(d2) =0.4602; calculate the price of the call option on the share

Consider the 1-period binomial model with a bond with A(0) = 60 and A(1) = 70 and a stock with S(0) = 4X and S^u(1) 6Y and S^d(1) = 3Z. = 1. What is the price (payoff) C(1) of a call option with strike price 28? 2. same... with strike price 45? 3. same... with strike price 72? 4. Set up a system of linear equations to determine a replicating portfolio for the call option from part 2 (strike price 45). 5. Solve it and determine the price C(O). 6. Compute, tabulate, and plot the price C(O) as you vary the strike price of the option from 28, 29, ..., 71, 72.

2. Calculate the put premium according to put-call parity which gives no arbitrage opportunity. Explain what transaction would you do if the put premium is below/above the put premium you calculated. European call option premium: c = $2 Stock price today: So- $30 Life of option: T=0.5 Risk-free rate for maturity T with continous compounding: r= 8% Strike price: K= Decide on the K value yourself (carefully). No dividends paid during life of option.

<Urgent> please answer M9,M10,M11

4d) Price the European call having strike 60 GBP. Use the two-periods binomial model with u = 1.1, d = 0.9 and ∆t = 1. Assume that the risk free rate is 5%, and the current price of the underlying asset is 50 GBP.