Department of Computer Science, University College London
COMP0043 Numerical Methods for Finance
Prof Guido Germano
Main summer / standard assessment sitting 2021–2022
Answers
1. Drift-diffusion processes (32 marks)
a) The Ornstein-Uhlenbeck process fulfils the stochastic differential equation (SDE)
dX(t) = αOU(μOU X(t))dt + σOUdW(t).
Omitting the dependence of X and W on t, this is a drift-diffusion (or Itˉo) process
dX = μ(X, t)dt + σ(X, t)dW.
According to Itˉo’s formula, a function Y (X, t) satisfies the SDE
dY =
