by Delphine Lautier, Julien Ling and Franck Raynaud

We examine the impact of two financial crises on commodity derivative markets: the subprime crisis and the bankruptcy of Lehman Brothers. These crises are “external” to the commodity markets because they occurred in the financial sphere. Still, because commodity markets are now highly integrated with each other and with other financial markets, such events could have had an impact. In order to fully comprehend this possible impact, we rely on tools inspired by the graph theory that allow for the study of large databases. We examine the daily price fluctuations recorded in 14 derivative markets from 2000 to 2009 in three dimensions: the observation time, the space dimension – the same underlying asset can be traded simultaneously in two different places – and the maturity of the transactions. We perform an event study in which we first focus on the efficiency of the price shock’s transmission to the commodity markets during the crises. Then we concentrate on whether the paths of shock transmission are modified. Finally, relying on the measure proposed by Bonacich (1987) for social networks, we focus on whether the centrality of the price system changes.

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by Ivar Ekeland, Yiming Long & Qinglong Zhou

In economic theory, and in optimal control, it has been customary to discount future gains at a constant rate δ > 0 (…). That future gains should be discounted is well grounded in fact. On the one hand, humans prefer to enjoy goods sooner than later (and to suffer bads later than sooner), as every child-rearing parent knows. On the other hand, it is also a reflection of our own mortality: 10 years from now, I may simply no longer be around to enjoy whatever I have been promised. These are two good reasons why people are willing to pay a little bit extra to hasten the delivery date, or will require compensation for postponement, which is the essence of discounting. On the other hand, there is no reason why the discount rate should be constant, i.e. why the discount factor should be an exponential e−δt.

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by Romuald ELIE & Gilles-Edouard ESPINOSA

Considering a positive portfolio diffusion X with negative drift, we investigate optimal stopping problems of the form (…) This paper unifies optimal selling rules observed by [5] for quadratic absolute distance criteria with bang-bang type ones observed in [1, 4, 9]. More precisely, we provide a verification result for the general stopping problem of interest and derive the exact solution for two classical criteria f of the literature. (…). These results reinforce the idea that optimal stopping problems of similar type lead easily to selling rules of very different nature. Nevertheless, our numerical experiments suggest that the practical optimal selling rule for the relative quadratic error criterion is in fact very close to immediate selling.

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by Jean-François Chassagneux, Romuald Elie & Idris Kharroubi

This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value, which dominates the claim of interest, is the so-called facelift transform of the claim. We investigate under which conditions the super-replication price and strategy of a large class of claims coincide with the exact replication price and strategy of the facelift transform of this claim. In dimension 1, we observe that this property is satisfied for any local volatility model. In any dimension, we exhibit a necessary and sufficient condition for this property, which combines the dynamics of the stock together with the characteristics of the closed convex set of constraints. The obtention of this condition relies on the introduction of the notion of first order viability property for linear parabolic PDEs. We investigate in details several practical cases of interest: multidimensional Black Scholes model, non-tradable assets or short selling restrictions.

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by Céline Grislain-Letrémy & Sabine Lemoyne de Forges

Prevention policies against flood, such as dams or levees, are commonly designed by local jurisdictions and for most they exert externalities on neighboring jurisdictions. Each jurisdiction chooses its collective prevention effort depending on the insurance system that covers its inhabitants. As uniform insurance depends on all insureds’ risk, it enables a partial integration of prevention externalities by jurisdictions. We determine under which condition uniform insurance Pareto dominates actuarial insurance.

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