Quantification of the model risk in finance and related problems

Event type: Thesis defence (Thèse Ismail Laachir)
Start at: july 02, 2015
Place: 15h00, Salle 2.2.34
Responsible team: OC

The main objective of this thesis is the study and quantification of model risk. In the first chapter, we are interested in model-independent pricing and hedging of complex financial products, when a set of “vanilla” instruments are available in the market. We follow the optimal transport approach for the computation of the option bounds and the super (sub)-hedging strategies. We characterize a family of optimal martingale probability measures, under which the exotic option price attains the model-free bounds. We devote special interest to the case of positive martingales stressing in particular some symmetry relations. In the second chapter, we approach the model risk problem from an empirical point of view studying the optimal management of a natural gas storage and quantifying the impact of that risk on the gas storage value. The last chapter concentrates on the basis risk, which arises when one hedges a contingent claim written on a non-tradable but observable asset using a portfolio of correlated tradable assets. This problem is linked to the celebrated Föllmer-Schweizer decomposition which can be deduced from the resolution of a special backward stochastic differential equations (BSDEs) driven by a càdlàg martingale. When this martingale is a Brownian motion, the related BSDEs are strongly related to semi-linear parabolic PDEs. We formulate a deterministic problem generalizing those pdes to the general context of martingales and we apply this methodology to discuss some properties of the Föllmer-Schweizer decomposition. We also give an explicit expression of such decomposition of the option payoff when the underlying prices are exponential of additive processes.