Joining the Heston and a Three-Factor Hull-White Model: A Closed-Form Approach

Posted: 21 Jun 2014 Last revised: 28 Jan 2017

See all articles by Roman Horsky

Roman Horsky

Das Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

Tilman Sayer

Advanced Logic Analytics

Date Written: June 20, 2014

Abstract

In this article, we present an innovative hybrid model for the valuation of equity options. Our approach includes stochastic volatility according to Heston (1993) and features a stochastic interest rate that follows a three-factor short rate model based on Hull-White (1994). Our model is of affine structure, allows for correlations between the stock, the short rate and the volatility processes and can be fitted perfectly to the initial term structure. We determine the zero bond price formula and derive the analytic solution for European type options in terms of characteristic functions needed for fast calibration. We highlight the flexibility of our approach, by comparing the price and implied volatility surfaces of our model with the Heston model, where we in particular focus on the correlation structure. Our approach forms a comprehensive market model with an intuitive correlation structure that connects both the equity and interest market to the market volatility.

Keywords: Option valuation, Heston model, two-factor Hull-White model, Stochastic volatility, Stochastic interest rate, Analytic solution

Suggested Citation

Horsky, Roman and Sayer, Tilman, Joining the Heston and a Three-Factor Hull-White Model: A Closed-Form Approach (June 20, 2014). International Journal of Theoretical and Applied Finance, Vol. 18, No. 8, 2015, Available at SSRN: https://ssrn.com/abstract=2456980 or http://dx.doi.org/10.2139/ssrn.2456980

Roman Horsky

Das Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM ( email )

Fraunhofer-Platz 1
Kaiserslautern, 67663
Germany

Tilman Sayer (Contact Author)

Advanced Logic Analytics

London
United Kingdom

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