7. We sell a put option on a stock and we delta hedge with the underlying stock.

a. Do we buy or sell the underlying stock.

b. Do we benefit or not from realized volatility (movement/gamma)?

c. What about an upward shift in the implied volatility (perception of future volatility instead of realized volatility), do we benefit or not if the shift occurs after we have initially sold the put?

Separately, assume we buy a call option on 100 shares. The call option has a premium of 8.60 $ per share and thus we pay 860 dollars. The stock price is 100 dollars per share. The delta is currently .50.

d. How many shares of stock do we sell?

In one month, the stock price drops to 90, and the Call price drops to 3.20 per share. The new Delta is .30.

e. How many shares do we buy or sell in order to re-hedge?

f. How many dollars did we win or lose during that first month?