Question 2. The Binomial Option Pricing

Assume that you are an options seller (e.g., a financial institution) who is selling a European Call option on Silver ETF (Silver Exchange Traded Fund). Assume that the underlying asset is Silver ETF with no storage cost and no dividend. The risk-free rate with continuous compounding is 4% per annum (i.e. r = 0.04). See information below:

Stock/Spot Price	S0	$160
Strike Price	K	$190
Maturity date of Forward Contract (3 months)	T	3/12 (or 0.25)
Volatility		60%
Risk-free Rate	r	4%
Dividend	q	0

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

Question 2 - Part (A) [Arbitrage Portfolio Approach] [16%] 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 $190 (K = $190) and maturity of 3-month (T = 3/12 or 0.25).

Note: 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) Discuss how the options sellers (market makers) can construct a riskfree arbitrage portfolio, with calculation of Delta () and calculation of the Present Value of Arbitrage Portfolio.

Step (iv) Final result of the No-Arbitrage Option Price (based on the Arbitrage Portfolio Approach). [Show your answers, formula, steps/calculations, and discussions as clear as possible]

Question 2 - Part (B) [Risk-Neutral Valuation Approach] [16%] Based on the information above, apply the Risk-Neutral Valuation approach with onestep binomial option pricing model and calculate the value of a European CALL option with an exercise/strike price of $190 (K = $190) and maturity of 3-month (T = 3/12 or 0.25).

Note: your answers should show all of the complete steps 1 to 2 below; show all variables, formula, calculations, and results (for steps 1 and 2) as clear as possible:

Step 1 calculation of Risk-Neutral Probability (p) with binomial tree of the option price

Step 2 calculation of Risk-Neutral Valuation and final result of the No- Arbitrage Option Price (based on the Risk-Neutral Valuation Approach). [Show your answers, formula, steps/calculations, and discussions as clear as possible]