Calibrating and Pricing with a Stochastic-Local Volatility Model

Posted: 30 Nov 2012 Last revised: 17 Mar 2015

See all articles by Yu Tian

Yu Tian

Monash University

Zili Zhu

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation)

Geoffrey Lee

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation)

Fima Klebaner

Monash University

Kais Hamza

Monash University

Date Written: June 30, 2014

Abstract

In this paper, we present our study on using the hybrid stochastic-local volatility (SLV) model for option pricing. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In this paper, we provide detailed discussion on the implementation of the calibration and pricing procedures. The implemented SLV model is used for pricing exotic options in the FX market. Pricing results are presented for the SLV model in direct comparison with the pure local volatility and pure stochastic volatility models. The SLV model is shown to match market traded implied volatility surfaces very well and to improve the pricing accuracy for market traded barrier options.

Keywords: local volatility, stochastic volatility, leverage function, calibration, exotic options pricing

JEL Classification: C6, D4, G12

Suggested Citation

Tian, Yu and Zhu, Zili and Lee, Geoffrey and Klebaner, Fima and Hamza, Kais, Calibrating and Pricing with a Stochastic-Local Volatility Model (June 30, 2014). Journal of Derivatives, Spring 2015, Vol. 22, No. 3: pp. 21-39, DOI: 10.3905/jod.2015.22.3.021, Available at SSRN: https://ssrn.com/abstract=2182411 or http://dx.doi.org/10.2139/ssrn.2182411

Yu Tian (Contact Author)

Monash University ( email )

Melbourne, Victoria VIC 3800
Australia

Zili Zhu

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation) ( email )

Gate 5 Normanby Road
Clayton
Melbourne, Australian Capital Territory 3168
Australia
61 3 95458003 (Phone)
61 3 9545 8080 (Fax)

Geoffrey Lee

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation) ( email )

41 Boggo Rd
Dutton Park, Queensland
Australia

Fima Klebaner

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

Kais Hamza

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

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