The 4/2 Stochastic Volatility Model
21 Pages Posted: 14 Nov 2014 Last revised: 17 Aug 2016
Date Written: March 16, 2016
We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is mathematically and computationally tractable, thereby enabling an efficient pricing procedure. This called for using the Lie symmetries theory for PDEs; doing so allowed us to extend known results on Bessel processes. Finally, we provide an exact simulation scheme for the model; this is useful in view of the numerical applications.
Keywords: Stochastic volatility; Volatility modelling; Lie's symmetries; Laplace Transform; Exact Simulation
JEL Classification: C6, C63, G1, G12, G13
Suggested Citation: Suggested Citation