Pricing of basket options I
Pricing of high-dimensional options is a deep problem of the Theoret- ical Financial Mathematics. In this article we give a transparent and self contained treatment of this problem. Namely, we present and study a new class of Levy driven models of stock markets. In our opinion, any market model should be based on a transparent and intuitively easily acceptable pre-axiomatic concept. In our case this is the system of stochastic equa- tions (2). Our market model is based on the principle of inheritance, i.e. for the particular choice of parameters it coincides with known mod- els. Also, our model is effectively numerically realisable. For the class of models proposed, we give an explicit representations of characteristic functions. This allows us us to construct a sequence of approximation formulas to price basket options. We show that our approximation for- mulas have almost optimal rate of convergence in the sense of respective n-widths.