Consider a stock with a price of $120 and a standard deviation of 20 percent. The stock will pay a dividend of $5 in 40 days and a second dividend of $5 and 130 days. The current risk-free rate is 5 percent per annum. An American call on this stock has an exercise price of $150 and expires in 100 days. Price the American call option using the Black-Scholes Model. Show all calculations. Question 5 [20 marks] ABC is currently trading at $78 per share. Your previous calculation of the historical volatility for ABC indicated an annual standard deviation of return of 27 percent, but examining the implied volatility of several ABC options reveals an increase in annual volatility to 32 percent. There are two traded options series that expire in 245 days as show in the following table: X = 75 X = 80 Call Put Call Put DELTA 0.6674 -0.3326 0.574 -0.426 GAMMA 0.0176 0.0176 0.019 0.019 The options have $75 and $80 strike prices respectively. The current 245-day riskfree interest rate is 4.75 percent per annum, and you hold 2,000 shares of ABC. Construct a portfolio that is DELTA - and GAMMA- neutral using the call options written on ABC. Show all calculations.