Can someone assist me in the derivation of the solution to the partial differential equation (PDE) that g must satisfy, including the boundary condition for time T. for April 2014 Qn7, ii) Forward and spot rates as well as the bond price for Qn 10 Sept 2015
Hi PrideW, The Black-Scholes PDE is given on page 46 of the Tables, just swap the f for a g. The boundary condition is DT = g(ST,T) The derivation is covered in the Course Notes but is not required in this question. All the relationships between spot rates, forward rates and bond prices are given on page 44 of the Tables. The spot rate is "derived" from the fact that B(T) = exp(-Ts(T)) is the present value of 1. For the forward rate, start with B(T+h) / B(T) = exp(-h F(T,h)) rearrange and let h tend to 0, since f(T) = lim F(T,h) as h tends to 0 Good luck! John
