Please write the calculation process, thank you!!!!

1. Which of the following best describes the gamma of an option?

1. The sensitivity of option price to a change in the price of the underlying asset
2. The second partial derivative of the option value with respect to price of the underlying asset
3. The sensitivity of option price to a change in the riskless rate of interest
4. The rate of change in option value with respect to the volatility of the underlying asset
5. The time decay of the option

2. A weather derivatives CDD function has a benchmark temperature of 65 degrees Fahrenheit. The maximum temperature during a day is 85 degrees Fahrenheit and the minimum is 57 degrees Fahrenheit what is the daily CDD?

1. 6
2. 45
3. 77
4. 0
5. 14

3. The lower bound for the price of a put option written on a non dividend paying stock is:

1. S_T Ke^-rt
2. S₀
3. Ke^-rt
4. Ke^-rt - S_T
5. S₀ - S_T

4. Assume that the MILLY100 Index at close of trading yesterday was 7,300 and the daily volatility of the index was estimated as 0.8% per day at that time. The parameters in a GJR GARCH model are = 0.000006, = 0.09, and = 0.90. If the MILLY100 moves by 75 points by close of trading today, what will the new volatility estimate be, per day, if the move is an increase or a decrease?

Increase Decrease

1. 1.0286% 1.0653%
2. 7.5996% 7.6060%
3. 9.0144% 7.9225%
4. 1.0286% 1.4273%
5. 0.8544% 0.9099%

5. A plain vanilla interest rate swap is written on a notional principal of 100m. The swap pays 3.6% per annum in return for the 3-month LIBOR. Payments are made every 6 months and the swap has 10 months remaining to maturity. The 3-month LIBOR 2 months ago was 3.2% per annum. The swap rate for all maturities is currently 3.8% with continuous compounding. What is the value, in Euros, of the swap to the party paying floating?

1. -119,195.16
2. 1,941,376
3. 82,477.03
4. 83,001.04
5. -82,477.00