Characteristic Functions and Fourier Transform Pricing
Document ID: 2008-928 (previously 2008/008)
Published on: 31st July 2008
Author: Graeme Lawson
When deriving many now classical financial economic models, Black-Scholes-Merton no-arbitrage arguments are often applied and extended to multiple state variables (asset price, volatility e.t.) in order to derive a valuation equation. These arguments result in a partial differential equation (P.D.E.) description of an options value throughout it’s existence, that is usually solved using solid and well understood mathematical engineering techniques such as Fourier & Laplace transforms. These arguments/techniques have successfully been employed to derive successful and celebrated models such as the Heston stochastic volatility model, and probability densities for various model frameworks via the solution of Fokker-Plank/Kolomogorov equation. The aim of this note is to support forthcoming technical notes, in that it aims to introduce or explain these techniques, first in the Black-Scholes-Merton context, and then in the stochastic volatility context.
