a) 50 Points: Derive all the formulas given in the slides for the Greeks of call and put options on a stock as the underlying (that are on p. 18 of Section 6 of the slides). Hints: - One you've derived the formula for the call, the one for the put will follow by put-call parity. - To derive the formulas for the and Vega of a call, start by showing that S0(d+)=KerT(d) b) 20 Points : Verify that the Black-Scholes PDE holds: Ct+rSCS+22S2CSSrC=0, where S is the current stock price, C is the call option price, and Cs,CSS,Ct are its , and Theta Greeks. a) 50 Points: Derive all the formulas given in the slides for the Greeks of call and put options on a stock as the underlying (that are on p. 18 of Section 6 of the slides). Hints: - One you've derived the formula for the call, the one for the put will follow by put-call parity. - To derive the formulas for the and Vega of a call, start by showing that S0(d+)=KerT(d) b) 20 Points : Verify that the Black-Scholes PDE holds: Ct+rSCS+22S2CSSrC=0, where S is the current stock price, C is the call option price, and Cs,CSS,Ct are its , and Theta Greeks