Q1 Consider the situation where the Olympus stock price 3 months from the expiration of an option is $29, the exercise price of the option is $27, the risk-free rate is 4% per annum, and the volatility is 16% per annum.

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 European Call using the numbers from Q1 explain your answers analytically.

2. Calculate the new value of the European Put using the numbers from Q1 explain your answer analytically.

3. What is the Theta of the European Call and the Theta of the European Put respectively? Explain your numbers analytically.