Please show all work. Put option elasticity is defined as [% change in option price]/[% change in stock price] = (S/P)*(delta). The following information is given for the European put option on Schlumberger (SLB). Current Stock Price = $86.89, Strike Price = $90, r_C=1.0% (continuously compounded interest rate), T = 19 days, Sigma = 30.35% (annualized implied volatility).

(a) At time 0, if Robert own 10,000 shares of SLB, how many units (an integer) of European put options does Robert buy for (delta) hedging his stock position?

(b) Based on the Black-Scholes model, what is the current price of this European put option?

(c) What is the estimated option elasticity [i.e., (S/P)*P/S] based on the above formula?

(d) Robert buys 10,000 shares of SLB at $86.89/share. He will hold his stock and initial put option positions. (from parts a and b) for 19 days. If the stock price is $100 when the European put option expires in 19 days, what is the net profit/loss for Robert if he liquidates all of his positions (including all shares and put options) on the expiration date? (Note: P_T = max(0, X-S_T) when the put option expires.)

(e) Find the current price of the corresponding European call option.