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

Option Pricing (60 Points)

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.

2.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.

3.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. Calculate the 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. Your well-written response should be formatted according to CSU-Global Guide to Writing and APA Requirements, with any sources properly cite

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