If $K_1\leq K_2$, then pointwise
$$
(S_T-K_1)^+\geq(S_T-K_2)^+.
$$
The positive pricing formula under the <T-forward measure> gives
$$
C_t^{T,K}=B_t^T\mathbb E_{Q^T}[(S_T-K)^+\mid\mathcal F_t].
$$
Therefore $C_t^{T,K_1}\geq C_t^{T,K_2}$, so the call price is non-increasing in strike.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 211 / 2 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-211/2/c/solution