 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/ii/paper-4/28j/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

For positive spot, strike, volatility and maturity, the Black-Scholes formula is

C = S_{0} Φ (d_{1}) - K e^{- r T} Φ (d_{2}), P = K e^{- r T} Φ (- d_{2}) - S_{0} Φ (- d_{1}),

where

d_{1} = [lo g (S_{0} / K) + (r + σ^{2} /2) T] / (σ T)

and

d_{2} = d_{1} - σ T

. Degenerate zero-volatility or zero-maturity cases are obtained by limits.

 New to topics? Read the docs here!