If the value is independent of spot, both spatial derivatives vanish. The <Black-Scholes equation> reduces to $V_t-rV=0$, so \b[$\boxed{V(S,t)=Ae^{r(t-T)}}$], where $A$ is an arbitrary constant. A constant terminal payoff is therefore discounted at the <interest rate> $r$; its separation constant is $\lambda=0$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 48 / 2 / a / Solution

 Solution (source code)