Let St denote the price of Google (GOOG) at time t. The spot price of GOOG is $400. The risk-free rate is 5%. Assume that St follows the log-normal model, with expected rate of return 10% and daily volatility of 1%. Assume there are 256 trading days a year.

(a) Compute the Delta and Gamma of an at-the-money 6-month European put option on GOOG. (Gamma might be close to 0, but it is not 0.)

(b) Suppose at t = 0 the price of GOOG jumps by $10 instantaneously, while everything else remains the same. Estimate how much the put option price changes using the Delta you computed in part (a).

(c) Is this estimate an over-estimate or under-estimate? Justify your answer with only part (a); that is, without comparing (b) to the actual change in the two put prices when the spot goes from 400 to 410.