arXiv subjects
Publications and source records attributed to Ismail Laachir.
In this work, inspired by the Archer-Mouy-Selmi approach, we present two methodologies for scoring the stress test scenarios used by CCPs for sizing their Default Funds. These methodologies can be used by risk managers to compare different sets of scenarios and could be particularly useful when evaluating the relevance of adding new scenarios to a pre-existing set.
We describe a robust calibration algorithm of a set of SSVI slices (i.e. a set of 3 SSVI parameters $θ, ρ, φ$ attached to each option maturity available on the market), which grants that these slices are free of Butterfly and 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, parsimonious solution to the smile problem, which has the potential to become a benchmark one.
The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general c{à}dl{à}g 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{ö}llmer-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.
In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan constructed in \cite{HobsonKlimmek2013} as well as the one introduced in \cite{BeiglJuil} and further studied in \cite{BrenierMartingale}. We show that, in the case of positive martingales, a suitable change of numeraire applied to \cite{HobsonKlimmek2013} 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 \cite{BrenierMartingale}'s construction, the right monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire. An application to stochastic volatility models is also provided.
In this paper we provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows to prove existence and uniqueness for linear backward stochastic differential equations driven by a general càdlàg martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of Föllmer and Sondermann (1986) to the partial information framework and we show how our result fits in the approach of Schweizer (1994).