Calibration of Stochastic Volatility Models: An Optimal Control Approach

26 Pages Posted: 21 Oct 2012

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Ling Tang

affiliation not provided to SSRN

Xingye Yue

affiliation not provided to SSRN

Date Written: April 30, 2012

Abstract

We aim to calibrate stochastic volatility models from option prices. We develop an optimal control approach to recover the risk neutral drift term of stochastic volatility. An efficient numerical algorithm is given. Numerical results and empirical studies are presented to demonstrate our algorithm. In contrast to existing literature, we do not assume that the stochastic volatility model has special structure, so our algorithm applies to calibration of general stochastic volatility models. In addition, our empirical results reveal that the risk neutral process of volatility recovered from market prices of options on S&P $500$ index is indeed linearly mean-reverting.

Keywords: calibration, stochastic volatility model, option prices, optimal control, inverse problem

JEL Classification: G12, G13

Suggested Citation

Dai, Min and Tang, Ling and Yue, Xingye, Calibration of Stochastic Volatility Models: An Optimal Control Approach (April 30, 2012). Available at SSRN: https://ssrn.com/abstract=2009342 or http://dx.doi.org/10.2139/ssrn.2009342

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Ling Tang

affiliation not provided to SSRN ( email )

Xingye Yue

affiliation not provided to SSRN ( email )

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