Pricing multi-asset options with tempered stable distributions

Abstract

We derive methods for risk-neutral pricing of multi-asset options, when log-returns jointly follow a multivariate tempered stable distribution. These lead to processes that are more realistic than the better known Brownian motion and stable processes. Further, we introduce the diagonal tempered stable model, which is parsimonious but allows for rich dependence between assets. Here, the number of parameters only grows linearly as the dimension increases, which makes it tractable in higher dimensions and avoids the so-called “curse of dimensionality.” As an illustration, we apply the model to price multi-asset options in two, three, and four dimensions. Detailed goodness-of-fit methods show that our model fits the data very well.