Jeff is so optimistic about his employer’s stock that on Feb. 19, he sold one hundred contracts of European put options on Google at the premium of $4.73 apiece (see the selected options in the table below). There is no dividend expected before the put option expires on the following January 20, and the stock price was $61.72 at the time of the trade. The risk free rate is 2% per annum.
Google Stock price on August 19: $61.72
Options Expiring Friday, January 20
Calls Puts Price Volume Open Interest Strike Price Volume Open Interest $ 6.60 6 43 $ 60.00 $ 3.60 10 871 $ 2.95 9 277 $ 65.00 $ 4.73 300 1349 $ 1.73 15 886 $ 70.00 $ 9.97 4 205
(1) What is the implied volatility underlying this European put based on the BlackScholes-Merton model?
(2) Jeff decides to engage in dynamic delta hedging against her short puts with daily rebalancing. Assume that the stock price of Google follows a log-normal distribution with the volatility determined from the previous part of the question. What will be a simulated path of the daily stock prices for Shell and the corresponding daily trades that Jeff must take to achieve delta neutrality?
(3) What is the net present value of entire exercise of delta hedging? Is this what you would have expected corresponding to a perfect delta hedging?