Pricing of basket options I

TL;DR

This paper introduces a new class of Lévy-driven market models based on linear stochastic systems, providing explicit characteristic functions and near-optimal approximation formulas for pricing high-dimensional basket options.

Contribution

It proposes a transparent, inheritable Lévy-driven model with explicit characteristic functions and efficient approximation formulas for basket option pricing.

Findings

Explicit characteristic functions for the models

Near-optimal convergence rates of approximation formulas

Effective numerical realizability of the models

Abstract

Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a transparent and intuitively easily acceptable concept. In our case this is a linear system of stochastic equations. Our market model is based on the principle of inheritance, i.e. for the particular choice of parameters it coincides with known models. Also, the model proposed is effectively numerically realizable. For the class of models under cosideration, 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 formulas have almost optimal rate of convergence in the sense of respective n-widths.