A Hybrid Stochastic Volatility Model Incorporating Local Volatility

2012 Fourth International Conference on Computational and Information Sciences (ICCIS)

4 Pages Posted: 4 Jun 2012 Last revised: 28 Jan 2014

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)

Fima Klebaner

Monash University

Kais Hamza

Monash University

Date Written: June 3, 2012

Abstract

In this paper, we present our study on a hybrid stochastic volatility model incorporating local volatility for pricing options in the foreign exchange (FX) market. The hybrid stochastic-local volatility model (SLV) could match the implied volatility surface well and meanwhile shows the flexibility for pricing exotic options. The difficulty in implementing the SLV model lies in the calibration of the leverage function, which can be roughly seen as a ratio between the local volatility and the conditional expectation of stochastic volatility. We will illustrate our implementation of the SLV model and show the pricing performance for exotic options.

Keywords: implied volatility, local volatility, stochastic-local volatility, leverage function

JEL Classification: C6, D4, G12

Suggested Citation

Tian, Yu and Zhu, Zili and Klebaner, Fima and Hamza, Kais, A Hybrid Stochastic Volatility Model Incorporating Local Volatility (June 3, 2012). 2012 Fourth International Conference on Computational and Information Sciences (ICCIS), Available at SSRN: https://ssrn.com/abstract=2074675 or http://dx.doi.org/10.2139/ssrn.2074675

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)

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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