Apply part (a) under the risk-neutral log-price drift $r-\sigma^2/2$, integrate the maximum and minimum tails using the supplied identities, and simplify the two exponential moments. Fubini then identifies the residual term as $(\sigma^2/2)\int_0^TS_tdt$. Discounted expectations on both sides give exactly the stated pricing identity.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 29L / d / Solution

 Solution (source code)