 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/29k/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The digital call option and digital put option indicators partition the possible terminal stock prices:

1_{{S_{T} \geq K}} + 1_{{S_{T} < K}} = 1.

D_{call} (t, S_{t}) + D_{put} (t, S_{t}) = e^{- r (T - t)} .

At time zero, part b gives

D_{call} (0, S_{0}) = e^{- r T} Φ (d_{-})

, so

D_{put} (0, S_{0}) = e^{- r T} (1 - Φ (d_{-})) = e^{- r T} Φ (- d_{-}) .

 New to topics? Read the docs here!