Pick a stock or a stock index. From the data, you chose above pick the option with the highest gamma from your option sample

1. What does gamma capture, in words?
2. What is the impact of a jump of 3% on the price of the underlying on the value of your chosen option in dollars?
3. Imagine you are short 1000 of these options, your manager comes to your office and says you need to hedge out the gamma risk. To hedge you are only allowed to use an option with a delta of 0.1 and gamma 0.20, what position in this option contract do you need to take?
4. Your manager now comes back and realizes he forgot to hedge delta, what can you do to hedge out the delta without changing the gamma?
5. Why does your method for (4) work?
6. Use the data on your chosen underlying asset above.

a) Graph the implied volatility as a function of strike price for short maturity (less than 4 months) and long maturity options (maturity greater than one year).

b) Comment on the implied volatility function for each maturity.

c) Describe the implied volatility surface implied by the long and short options and give an explanation of the shape.

d) Use the implied volatility of the at-the-money option to calculate the price of an out-of-the-money option. Is it different from the quoted price, if so, why?