Option Pricing and Spikes in Volatility: Theoretical and Empirical Analysis

This paper considers a financial market where the asset prices and the corresponding volatility are driven by a multidimensional mixture of Wiener shocks and Poisson jumps. While implied volatility is characterized by spikes, the existing models rely on the restrictive assumption of positive jumps in volatility. To overcome this inadequacy, the present paper introduces normally distributed jumps in the logvariance process. The model proposed is able to mimic empirically observed spikes in volatility and, consequently, improves upon the existing literature as it replicates the main features of both the stock return series and the corresponding option prices. After estimating the stock returns via the Efficient Method of Moments, the expression for the valuation of a plain vanilla European call option is derived, using the no-arbitrage argument. S&P500 option prices are used to assess quantitatively the empirical performance of the innovative features of the proposed model. The estimates indicate that spikes in volatility introduce a significant improvement in option pricing and provide evidence for stochastic jump risk premia.