Change of numeraire in the two-marginals martingale transport problem

Luciano Campi (), Ismail Laachir () and Claude Martini ()
Additional contact information
Luciano Campi: London School of Economics and Political Sciences
Ismail Laachir: Zeliade Systems
Claude Martini: Zeliade Systems

Finance and Stochastics, 2017, vol. 21, issue 2, No 5, 486 pages

Abstract: 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.

Keywords: Robust hedging; Model-independent pricing; Model uncertainty; Optimal transport; Change of numeraire; Forward start straddle; 91G20; 91G80 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s00780-016-0322-2

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