Volatility trading with the quadratic normal model in the oil options market

Abstract

The paper applies the recently developed quadratic normal model (QNM) to oil options. This three-parameter model assumes parabolic local volatility and extends the Bachelier model to a much broader class of “fat-tailed” distributions with two additional parameters related to skewness and kurtosis. The primary focus of this paper is to demonstrate how this model can be efficiently calibrated to option prices and used by volatility arbitrageurs in managing their portfolios. We calibrate model parameters daily to market prices of WTI options over an extensive twenty-five year period and analyze the dynamics and stability of parameters over time. We show two primary applications of the model for delta-hedging of market-making portfolios and for pricing over-the-counter options.