Pricing and hedging option

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The thesis under study focus on pricing and hedging European options. We propose an -hypergeometric model with uncertain volatility (UV) by which we derive a worst-case scenario for option pricing. The approach is based on the connection between a certain class of nonlinear partial differential equations of Hamilton-Jacobi-Bellman type (G-HJB), that govern the nonlinear expectation of the UV model [50] and that provide an alternative to the difficult model calibration problem of UV models, and second-order backward stochastic differential equations (2BSDEs). Moreover, we formulate a concrete model that is solved numerically using the deep learning method by Beck et al. [6] and exploiting the link between fully nonlinear G-HJB equations and 2BSDE. Finally we highlight several option Hedging strategies as Delta hedging, Delta-Sigma hedging and the Hedging by perturbation analysis.