Change of numeraire in the two-marginals martingale transport problem

Campi, Luciano, Laachir, Ismail and Martini, Claude (2017) Change of numeraire in the two-marginals martingale transport problem. Finance and Stochastics, 21 (2). pp. 471-486. ISSN 0949-2984

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Abstract

In this paper, we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two-period setting. In particular, we consider the optimal transport plan constructed in Hobson and Klimmek (Finance Stoch. 19:189–214, 2015) as well as the one introduced in Beiglböck and Juillet (Ann. Probab. 44:42–106, 2016) and further studied in Henry-Labordère and Touzi (Finance Stoch. 20:635–668, 2016). We show that in the case of positive martingales, a suitable change of numeraire applied to Hobson and Klimmek (Finance Stoch. 19:189–214, 2015) exchanges forward start straddles of type I and type II, so that the optimal transport plan in the subhedging problems is the same for both types of options. Moreover, for Henry-Labordère and Touzi’s (Finance Stoch. 20:635–668, 2016) construction, the right-monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire.

Item Type:	Article
Official URL:	http://link.springer.com/journal/780
Additional Information:	© 2016 The Authors © CC BY 4.0
Divisions:	Statistics
Subjects:	H Social Sciences > HG Finance
JEL classification:	G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
Date Deposited:	09 Jan 2017 10:16
Last Modified:	12 Dec 2024 01:24
URI:	http://eprints.lse.ac.uk/id/eprint/68783

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