Derivatives (6)

Respond to the following questions.

1. Given the following, answer the questions that follow.

    S= $100,  K = $95,  r = 8% (and continuously compounded),  σ = 30%,  δ= 0, T = 1 year, and n= 3. 

   a. Confirm that the binomial option price for an American call option is $18.283. (Hint: There is no early exercise. Therefore, a European call would have the same price.)

   b. Demonstrate that the binomial option price for a European put option is $5.979. Verify that put-call parity is satisfied.

   c. Confirm that the price of an American put is $6.678.

1. If S= $120, K = $100, σ = 30%, r = 0, and δ= 0.08, compute the following:

   a. The Black-Scholes call price for 1 year, 2 years, 5 years, 10 years, 50 years, 100 years, and 500 years to maturity. Explain your answer as time to expiration, T, approaches infinity.

   b. Change r from 0 to 0.001. Then repeat a. What happens as time to expiration, T, approaches infinity? Explain your answer and include what, if any, accounts for the change.  

2. Consider this scenario: A bull spread where you buy a 40-strike call and sell a 45-strike call. In addition, σ = 0.30, r = 0.08, δ= 0, and T = 0.5. Calculatethe following:

   a. Delta, gamma, vega, theta, and rho if S= $40.

   b. Delta, gamma, vega, theta, and rho if S= $45.

   c. Are any of your answers to (a) and (b) different? If so, state the reason.

Complete your 2-4 page response using Microsoft Word or Excel. For calculations, you must show work to receive credit.