Assume that an option seller (e.g., market maker and financial institution) is selling a European Call option on SPY .

The spot price of SPY is currently $410 (i.e. S0 = $410). The volatility of SPY is 35% (i.e. beta = 0.35). We are interested in valuing SPY option at the end of 6 months (i.e. deltat or T = 6/12 = 0.5). The risk-free rate with continuous compounding is 5% per annum (i.e. r = 0.05). See information below:

Stock/Spot Price	So	$410
Strike Price	K	$410
Time-to-Maturity (6 months)	T	0.5
Volatility	beta	35%
Risk-free Rate	r	5%

Note: the following questions are asking for the one-step binomial option pricing model, not the Black-Scholes-Merton model.

Question 3 - Part (A) [Arbitrage Portfolio Approach]

Based on the information above, apply the Arbitrage Portfolio approach with one-step binomial option pricing model and calculate the value of a European CALL option with an exercise/strike price of $410 (K = $410) and maturity of 6 months (T = 0.5).

Important Instructions and Steps to follow: your answers should show all of the complete steps (i) to (iv) below; show all variables, formula, calculations, and results (for (i) to (iv)) as clear as possible:

Step (i) 1-Step Binomial tree of the stock price with calculation of u and d.

Step (ii) 1-Step Binomial tree of the option price.

Step (iii) Provide discussion to explain how the options sellers (market makers) can construct a risk-free arbitrage portfolio, with calculation of Delta () and the Present Value of Arbitrage Portfolio.

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

[in your answers, show all formula/steps, calculation, and result as clearly as possible]