Option Pricing with Quadratic Volatility: A Revisit

25 Pages Posted: 10 Apr 2008 Last revised: 14 Aug 2008

Date Written: February 7, 2008

Abstract

This paper considers the pricing of European options on assets that follow a stochastic differential equation with a quadratic volatility term. We correct errors in the existing literature, extend the pricing formulas to arbitrary root configurations, and list alternative representations of option pricing formulas to improve computational performance. Our exposition is based entirely on probabilistic arguments, adding a fresh perspective and new intuition to the existing PDE-dominated literature on the subject. Our main tools are martingale methods and shift of probability measure; the fact that the underlying process is typically a strict local martingale is carefully considered throughout the paper.

Keywords: Quadratic SDE, option pricing, local martingale, volatility smiles

JEL Classification: G13, C63

Suggested Citation

Andersen, Leif B.G., Option Pricing with Quadratic Volatility: A Revisit (February 7, 2008). Available at SSRN: https://ssrn.com/abstract=1118399 or http://dx.doi.org/10.2139/ssrn.1118399

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)

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