Esscher transform and the duality principle for multidimensional semimartingales

TL;DR

This paper explores the duality principle in multidimensional option pricing using Esscher transforms on general semimartingales, enabling simplified valuation of complex options like swaps and quantos, with explicit jump model calculations.

Contribution

It introduces a novel application of Esscher transforms to construct dual measures for multidimensional semimartingale models, extending the duality principle to more general asset processes.

Findings

Dual measures constructed via Esscher transforms for multidimensional semimartingales

Relation of swap and quanto options to standard options through duality

Explicit calculations provided for jump process models

Abstract

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here, we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. As an application, we can relate swap and quanto options to standard call and put options. Explicit calculations for jump models are also provided.