Option Pricing with Quadratic Volatility: A Revisit
25 Pages Posted: 10 Apr 2008 Last revised: 14 Aug 2008
Date Written: February 7, 2008
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: Suggested Citation