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This article presents a deep reinforcement learning approach to price andhedge financial derivatives. This approach extends the work of Guo and Zhu(2017) who recently introduced the equal risk pricing framework, where theprice of a contingent claim is determined by equating the optimally hedgedresidual risk exposure associated respectively with the long and shortpositions in the derivative. Modifications to the latter scheme are consideredto circumvent theoretical pitfalls associated with the original approach.Derivative prices obtained through this modified approach are shown to bearbitrage-free. The current paper also presents a general and tractableimplementation for the equal risk pricing framework inspired by the deephedging algorithm of Buehler et al. (2019). An $\epsilon$-completeness measureallowing for the quantification of the residual hedging risk associated with aderivative is also proposed. The latter measure generalizes the one presentedin Bertsimas et al. (2001) based on the quadratic penalty. Monte Carlosimulations are performed under a large variety of market dynamics todemonstrate the practicability of our approach, to perform benchmarking withrespect to traditional methods and to conduct sensitivity analyses.

Equal Risk Pricing of Derivatives with Deep Hedging