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 HenryLabordère 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 Mathematics Subject Classification (2010) 91G20 · 91G80 JEL Classification G13

This paper focuses on the valuation and hedging of gas storage facilities, using a spot-based valuation framework coupled with a financial hedging strategy implemented with futures contracts. The contributions of this paper are two-fold. Firstly, we propose a model that unifies the dynamics of the futures curve and spot price, and accounts for the main stylized facts of the US natural gas market such as seasonality and the presence of price spikes in the spot market. Secondly, we evaluate the associated model risk, and show not only that the valuation is strongly dependent upon the dynamics of the spot price, but more importantly that the hedging strategy commonly used in the industry leaves the storage operator with significant residual price risk.

The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general càdlàg martingales. When the martingale is a standard Brownian motion, the natural deterministic analysis is provided by the solution of a semilinear PDE of parabolic type. A significant application concerns the hedging problem under basis risk of a contingent claim g(X T , S T ), where S (resp. X) is an underlying price of a traded (resp. non-traded but observable) asset, via the celebrated F öllmer-Schweizer decomposition. We revisit the case when the couple of price processes (X, S) is a diffusion and we provide explicit expressions when (X, S) is an exponential of additive processes.

We describe a robust calibration algorithm of a set of SSVI maturity slices (i.e. a set of 3 SSVI parameters θ t , ρ t , ϕ t attached to each option maturity t available on the market), which grants that these slices are free of Butterfly and of Calendar-Spread arbitrage. Given such a set of consistent SSVI parameters, we show that the most natural interpolation/extrapolation of the parameters provides a full continuous volatility surface free of arbitrage. The numerical implementation is straightforward, robust and quick, yielding an effective and parsimonious solution to the smile problem, which has the potential to become a benchmark one.We thank Antoine Jacquier and Stefano De Marco for useful discussions and remarks. All remaining errors are ours.

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