6. A call option with X=90 sells for $6 which is consistent with stock volatility of 20%. The delta of the call is 0.6. A put option on the same stock has identical maturity and exercise and sells for $3, which also is consistent with stock volatility 20%.

a. (10 points] Suppose you believe that the volatility of the underlying stock will actually be 15%, and you sell a straddle (i.e.. sell one call and sell one put) to speculate on your belief. What will be the delta of your position?

b. (10 points) Instead of a straddle, you decide to establish a delta-neutral portfolio that will profit if the implied volatility on both options decreases to 15%. What is the appropriate ratio of calls to puts? Will you be long or short each option?

c. [10 points] Will you gain or lose on your delta-neutral position from part b) if the implied volatility of the options after a month is still 20%? Suppose the stock price hasn't changed.