Question 2. The Binomial Option Pricing [30\%] This question is based on the following information and assumptions: - The spot price of SPY is $395(S0=$395). - The volatility of SPY is 22%(=0.22). - The options sellers (market makers and financial institutions) are valuing a European Call option with the exercise/strike price of $420(K=$420) and maturity of 3 months (T=3/12=0.25). - The risk-free rate with continuous compounding is 4% per annum (r=0.04). 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 $420(K=$420) and maturity of 3 months (T=3/12= 0.25). Important instructions and steps to follow: your answers should include all of the complete steps (i) to (iv) below; show all variables, formula, binomial trees, calculations, discussions and results (for (i) to (iv)) as clearly as possible: - Step (i) Present the 1-Step Binomial tree of the stock price with calculation of " u " and " d ". - Step (ii) Present the 1-Step Binomial tree of the option price. - Step (iii) Provide detailed discussions on 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). [Show your answers, formula, steps/calculations, and discussions as clearly as possible] Question 2. The Binomial Option Pricing [30\%] This question is based on the following information and assumptions: - The spot price of SPY is $395(S0=$395). - The volatility of SPY is 22%(=0.22). - The options sellers (market makers and financial institutions) are valuing a European Call option with the exercise/strike price of $420(K=$420) and maturity of 3 months (T=3/12=0.25). - The risk-free rate with continuous compounding is 4% per annum (r=0.04). 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 $420(K=$420) and maturity of 3 months (T=3/12= 0.25). Important instructions and steps to follow: your answers should include all of the complete steps (i) to (iv) below; show all variables, formula, binomial trees, calculations, discussions and results (for (i) to (iv)) as clearly as possible: - Step (i) Present the 1-Step Binomial tree of the stock price with calculation of " u " and " d ". - Step (ii) Present the 1-Step Binomial tree of the option price. - Step (iii) Provide detailed discussions on 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). [Show your answers, formula, steps/calculations, and discussions as clearly as possible]
