The CTMC-Heston Model : Calibration and Exotic Option Pricing with SWIFT

This work presents an efficient computational framework for pricing a general class of exotic and vanilla options under a versatile stochastic volatility model. In particular, we propose the use of a finite state Continuous Time Markov Chain (CTMC) model which closely approximates the classic Heston model, but enables a simplified approach for consistently pricing a wide variety of financial derivatives. Under this CTMC-Heston model, we show that the shape of implied volatility is preserved (hence an equivalent ability to calibrate market smiles), yet complex derivatives such as Asian options, variance swaps/options, and cliquets may be priced with great efficiency. To accomplish this, we employ Markov chain approximation techniques, which have been gaining traction in recent literature. We expect that this framework has significant practical appeal, given the widespread adoption of Heston's model, and the present difficulty that arises in pricing complex products