Past exam of the martingales and financial mathematics course of the University of Oxford / 2009 / B / 5 / a / Solution

Write $\tau =T-t$. In the Black-Scholes formula, both $d_1$ and $d_2$ depend on $x,K$ only through $\log (x/K)$. Replacing them by $\lambda x,\lambda K$ leaves that ratio unchanged. Each prefactor in the put formula acquires the same factor $\lambda$, givingThis is degree-one homogeneity of the European put option price in its spot and strike together.