Question 3 (Marks: 50) For the stock that corresponds to your Group, select an option expiry date among the available ones in the market so that T> 0.5 years. Given the spot price of the stock (So), select three strike prices K₁, K₂ and K3 near the money such that K₁ < K₂ < K3. a) Pricing Call and Put options with strike price K₂ and maturity T (in detail calculations). The time horizon should be divided into 5 intervals of duration 4t, each. Consider that the stock price may increase by 1 and decrease by da on each time interval. The volatility of the stock price is the historical volatility found in Question 2, part (c). - Calculate analytically the p* probability Draw the binomial tree for the stock price evolution Provide and explain the formula of calculating the probabilities of reaching each node Price the European Call and Put Options (show the required trees; explain) Price the American Call and Put Options (show the required trees; explain) Comment on the difference of the premiums b) Pricing Call and Put options with strike prices K₁, K₂ and K, and maturity T. The time horizon should be divided into 15 intervals now of duration 4t, each. Consider that the stock price may increase by u, and decrease by u, on each time interval. The volatility of the stock price is again the historical volatility found in Question 2, part (c). Calculate analytically the p" probability Price the European Call and Put Options of strike price K₁7. Price the European Call and Put Options of strike price K₂. Price the European Call and Put Options of strike price K3. Compare the European Call and Put premiums for strike price K₂ of (a) and (b) Explain the difference between the calculated premiums and those in the market. c) Given the premiums c; and p; (i = 1,2,3) that correspond to the options with strike prices K₁, K₂ and K3 that have been already calculated, built the following trading strategies and discuss their suitability: Option (K₂) and underlying asset. i) Covered Call and ii) Protective Put Multiple options (K₁, K3) of the same type. i) Bull Spread with Calls and ii) Bear Spread with Puts Combinations. i) Strip (K₂) and Butterfly Spread (K₁, K₂, K3) Note: For the risk-free rate you can use the United States 52 Week Bill Yield®.