Analytical Option Pricing for Time Dependent Quadratic Local Volatility Models

38 Pages Posted: 24 May 2011 Last revised: 10 Mar 2012

Date Written: May 22, 2011

Abstract

In this note we develop accurate analytical pricing formulas for time dependent quadratic local volatility models. We derive a set of exact simple analytical expressions for option prices when parameters are constant and provide novel and simpler proofs to already exisiting results. We then build a general framework for deriving analytical expansions for time dependent local volatility models and use these to deduce averaging formulas which enable us to transform any time-dependent quadratic volatility model onto an equivalent constant parameter one. We show the accuracy of these methods through numerical examples.

Keywords: Quadratic Volatility, Time-Dependent Parameters, Parameter Averaging, Smart Expansion

Suggested Citation

Chibane, Messaoud, Analytical Option Pricing for Time Dependent Quadratic Local Volatility Models (May 22, 2011). Available at SSRN: https://ssrn.com/abstract=1850205 or http://dx.doi.org/10.2139/ssrn.1850205

Messaoud Chibane (Contact Author)

Neoma Business School ( email )

1 Rue du Maréchal Juin
Mont Saint Aignan Cedex, 76825
France

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