0. Problem 2

   Let C(S)K,T,r, be the Black and Scholes formula for the price of a European call option with current stock price S, strike price K, expiration date T, risk-free rate r, and return volatility . Write down the expressions for the derivatives C/S, 2C/S2, C/r, C/T, C/. How do we call these derivatives? Are you able to derive sign restrictions on these derivatives? If yes, what are these restrictions?

   Problem 3

   • Let P(S)K,T,r, be the Black and Scholes formula for the price of a Eu- ropean put option with current stock price S, strike price K, expiration date T, risk-free rate r, and return volatility . Write down the put-call parity formula for European put and call options with the same strike price, expiration date, and underlying asset.

   • Use the put-call parity and your answers in Problem 2 to derive the ex- pressions for the derivatives P/S, 2P/S2, P/r, P/T, P/. How do we call these derivatives? Are you able to derive sign restrictions on these derivatives? If yes, what are these restrictions?