Exchangeability type properties of asset prices

TL;DR

This paper explores how exchangeability properties of asset prices influence option pricing and hedging strategies, especially for basket options driven by Levy processes, introducing semi-static hedging techniques for complex multi-asset options.

Contribution

It provides new insights into the impact of exchangeability on option prices and develops semi-static hedging methods for multi-asset barrier options driven by Levy processes.

Findings

Exchangeability affects basket option prices.

Semi-static hedging techniques for multi-asset options are proposed.

Results are applicable to Levy process-driven asset models.

Abstract

In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular attention is devoted to the case of asset prices driven by Levy processes. Based on this, concrete semi-static hedging techniques for multi-asset barrier options, such as certain weighted barrier spread options, weighted barrier swap options or weighted barrier quanto-swap options are suggested.