Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Abstract

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.

9 pages, 2 figures, 1 table

References in corpus (4)

• The statistical properties of the volatility of price fluctuations
• Volatility in Financial Markets: Stochastic Models and Empirical Results
• Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence
• A path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models