Named after Steven Heston, the Heston model is a mathematical model describing the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process.
The Heston Model is one of the most widely used stochastic volatility (SV) models today. Its attractiveness lies in the powerful duality of its tractability and robustness relative to other SV models.
(Heston 1993) proposed the following the model:
dSt = µSt dt + Vt St dWt1
dVt = κ(θ − Vt )dt + σ Vt dWt2
dWt1 dWt2 = ρdt
A practical approach has been adopted since the focus of calibration is quite
practical itself. All the relevant tools are provided to facilitate this calibration
process, including M ATLAB code. This code has been con?ned to the appendix to
keep the main body clutter free and ‘quick-to-read’.