Q.3 Consider now that Olympus time parameter is increasing from t=3/12 to t= 6/12. All the other stock parameters remain the same.

1. Calculate the new value of the Call using the numbers from Q1 and explain your answers analytically. 2. Calculate the new value of the Put using the numbers from Q1 and explain your answer analytically. 3. What is the Theta of the Call and the Theta of the Put respectively? Explain your numbers analytically.

Q.1 Consider the situation where the Zeus stock price 3 months from the expiration of an option is $32, the exercise price of the option is $30, the risk-free rate is 6% per annum, and the volatility is 25% per annum.

a. Calculate the price of the European Call and European Put respectively. b. If the quoted price of the call is $2.75, can you argue that the call is undervalued? c. If the quoted price of the put is $1.98, can you argue that the put is overvalued? d. Show by the means of well-drawn diagrams that Option-Pricing is a ZERO-SUM game. Explain your answers analytically.