Parameter Averaging of Quadratic SDEs With Stochastic Volatility

35 Pages Posted: 10 Feb 2009

See all articles by Leif B. G. Andersen

Leif B. G. Andersen

Bank of America Merrill Lynch

Nicolas A. Hutchings

Banc of America Securities LLC

Date Written: February 9, 2009

Abstract

In an influential series of papers, V. Piterbarg demonstrates how to perform time-averaging of parameters in a class of diffusion models with linear local volatility and orthogonal stochastic volatility. In this paper, we consider how to extend the applicability of parameter-averaging techniques to a setting where i) the local volatility function has non-zero convexity; and ii) the correlation between the stochastic volatility process and the underlying asset is non-zero and deterministic. These extension are based on classical small-noise SDE expansions and are of practical use in a number of markets -- foreign exchange being a good example -- where empirical observations of volatility smile moves indicate the presence of non-linear local volatility. For efficient calibration of the time-averaged model, we also derive accurate call option pricing approximations for assets with constant-parameter quadratic local volatility overlaid with (correlated) Heston-type stochastic volatility. Several numerical tests probe the accuracy of the parameter-averaging techniques and the various option pricing approximations.

Keywords: Time-averaging, local-stochastic volatility, quadratic local volatility, Heston process

JEL Classification: G12, G13

Suggested Citation

Andersen, Leif B.G. and Hutchings, Nicolas A., Parameter Averaging of Quadratic SDEs With Stochastic Volatility (February 9, 2009). Available at SSRN: https://ssrn.com/abstract=1339971 or http://dx.doi.org/10.2139/ssrn.1339971

Leif B.G. Andersen (Contact Author)

Bank of America Merrill Lynch ( email )

One Bryant Park
New York, NY 10036
United States
646-855-1835 (Phone)

Nicolas A. Hutchings

Banc of America Securities LLC ( email )

United States

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