Robust Hedging of Options on Local Time

32 Pages Posted: 22 Nov 2015

See all articles by Julien Claisse

Julien Claisse

Independent

Gaoyue Guo

Ecole Polytechnique, Paris

Pierre Henry-Labordere

Natixis - Paris, France

Date Written: November 19, 2015

Abstract

In this paper, we focus on model-free pricing and robust hedging of options depending on the local time, consistent with Vanilla options. This problem is classically approached by means of the Skorokhod embedding problem (SEP), which consists in representing a given probability on the real line as the distribution of a Brownian motion stopped at a chosen stopping time. By using the stochastic control approach initiated in Galichon, Henry-Labordère and Touzi, we recover the optimal hedging strategies and the corresponding prices given by Vallois' embeddings to the SEP. Furthermore, we extend the analysis to the two-marginal case. We provide a construction of two-marginal embedding and some examples for which the robust superhedging problem is solved. Finally, a special multi-marginal case is studied, where we construct a Markov martingale and compute its explicit generator. In particular, we provide a new example of fake Brownian motion.

Keywords: Skorokhod embedding, Model-free pricing, Robust hedging, Local time

Suggested Citation

Claisse, Julien and Guo, Gaoyue and Henry-Labordere, Pierre, Robust Hedging of Options on Local Time (November 19, 2015). Available at SSRN: https://ssrn.com/abstract=2692982 or http://dx.doi.org/10.2139/ssrn.2692982

Julien Claisse

Independent ( email )

Gaoyue Guo

Ecole Polytechnique, Paris ( email )

1 rue Descartes
Paris, 75005
France

Pierre Henry-Labordere (Contact Author)

Natixis - Paris, France ( email )

Paris, Paris 75
France

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
118
Abstract Views
647
rank
297,522
PlumX Metrics