1. Verify thatSande^(rt)are solutions of the Black-Scholes PDE (8.15) and give an accompanying financial explanation.
   

Using A = Elf/'33 from (8.10) and rearranging, we arrive at 32v av + gazszaSE +16% rV = o. (3.15) This is the famous BikShOII-ES partial differential equation (PDE). It is a rela- tionship between V, S , r and certain partial derivatives of V. Two points are worth raising immediately. (I) The drift parameter pr, in the asset model does not appear in the PDE. (2) We have not yet specied what type of option is being valued. The PDE must he sat ised for any option on S whose value can be expressed as some smooth function WIS, I)