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

31 Pages Posted: 28 Oct 2019

See all articles by Alvaro Leitao Rodriguez

Alvaro Leitao Rodriguez

University of Coruña - Department of Mathematics - M2NICA

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Luis Ortiz-Gracia

University of Barcelona

Multiple version iconThere are 2 versions of this paper

Date Written: October 18, 2019

Abstract

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.

Keywords: Heston Model, CTMC, Markov Chain Approximation, Regime Switching, Option Pricing, Calibration, Wavelets, SWIFT, Stochastic Volatility, Asian Options, Variance Swaps

JEL Classification: C63

Suggested Citation

Leitao Rodriguez, Alvaro and Kirkby, Justin and Ortiz-Gracia, Luis, The CTMC-Heston Model: Calibration and Exotic Option Pricing with SWIFT (October 18, 2019). Available at SSRN: https://ssrn.com/abstract=3471806 or http://dx.doi.org/10.2139/ssrn.3471806

Alvaro Leitao Rodriguez (Contact Author)

University of Coruña - Department of Mathematics - M2NICA ( email )

Campus Elvina s/n
A Coruna, 15071
Spain

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

Luis Ortiz-Gracia

University of Barcelona ( email )

Diagonal, 690
08034 Barcelona
Spain

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