Pricing Multi-Asset Options with Multivariate Variance Gamma and Normal Inverse Gaussian Processes Using the Fourier Space Time-Stepping Method
We use a multivariate variance gamma process developed by Jun Wang (2009) and a similarly constructed multivariate normal inverse Gaussian process to price multi-asset options and calculate greeks with the Fourier space time-stepping (FST) method introduced by Jackson, Jaimungal, and Surkov (2007). The prices are checked against Monte Carlo simulations to demonstrate their accuracy, and we see a marked improvement in computational efficiency. Included are options on the spark spread, the crack spread, and the crush spread, as well as other exotic options that are difficult to price with existing methods. We also adopt a parameter estimation method by Cervellera and Tucci (2016) for variance gamma processes, and adapt it for use with normal inverse Gaussian processes, to make parameter estimates for the marginal processes that are robust with respect to small perturbations of the data.