Assignment 2

Using the daily data on the S&P 500 and the 3-month T-bill rate provided in “Hw2 2026 Data.xls”

answer the following questions and round to 2 decimal points. Assume that today is April 7, 2026,

there are 252 trading days per year, and we adopt the assumptions of the Black-Scholes model.

Question 1: From the data provided, (i) what would be the price of a 6-month to maturity at-the- money European call option written on the S&P 500? (ii) What would be the price of a 6-month to

maturity European put option written on the S&P 500? For this question, assume that the S&P 500

does not pay dividends.

Question 2: (i) Find the strike price that would make the prices of a 6-month to maturity European

call and a 6-month to maturity European put equal to each other (or within 160 cents of each other).

(ii) What are the prices of the call and the put for the strike price you found? If you find multiple

strike prices that meet the requirements, choose one of them. The contract specification is provided

at https://www.cboe.com/tradable-products/sp-500/spx-options/spx-specifications/.

Question 3: You believe that there is 50% chance that in 1 month from now the S&P 500 will crash

by 20% or appreciate by 20% (both estimates are monthly returns). You create a portfolio that short

100 6-month European call options and long 200 6-month to maturity European put options with

strike price equal to your answer for Question 2. Given your view, what is the expected return on

your portfolio over the next month?

Question 4: We now consider an American call option written on the S&P 500 with 6-month to

maturity. If the call has a strike price equal to your answer for Question 2, and two dividends of $30

and $40 are paid in 2 months and 4 months from now. What is your best estimate of the price of the

American call?

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