Question 1. The Binomial Option Pricing

The spot price of SPY is currently $440 (i.e. S0 = $440). The volatility of SPY is 45% (i.e.

= 0.45). We are interested in valuing SPY option at the end of 3 months (i.e. t or T = 3/12 = 0.25). The risk-free rate with continuous compounding is 4% per annum (i.e. r = 0.04).

Question 1 - Part (A) [Arbitrage Portfolio Approach]

Apply the Arbitrage Portfolio approach with one-step binomial tree and calculate the value of a European CALL option on SPY with an exercise/strike price of $470 (i.e., K = $470) and T = 0.25.

Note: your answers should show all of the complete steps, formula, and calculations as follows:

Binomial tree of the stock price with calculation of u and d. Binomial tree of the option price.

Binomial tree of the arbitrage portfolio, with discussion of how the arbitrage portfolio is constructed, calculation of Delta ( ), and calculation of the Present Value of Arbitrage Portfolio.

Final result of the No-Arbitrage Option Price (based on the Arbitrage Portfolio Approach).