Equal Risk Pricing of Derivatives with Deep Hedging

Abstract: This article presents a deep reinforcement learning approach to price and hedge financial derivatives. This approach extends the work of Guo and Zhu (2017) who recently introduced the equal risk pricing framework, where the price of a contingent claim is determined by equating the optimally hedged residual risk exposure associated respectively with the long and short positions in the derivative. Modifications to the latter scheme are considered to circumvent theoretical pitfalls associated with the original approach. Derivative prices obtained through this modified approach are shown to be arbitrage-free. The current paper also presents a general and tractable implementation for the equal risk pricing framework inspired by the deep hedging algorithm of Buehler et al. (2019). An $\epsilon$-completeness measure allowing for the quantification of the residual hedging risk associated with a derivative is also proposed. The latter measure generalizes the one presented in Bertsimas et al. (2001) based on the quadratic penalty. Monte Carlo simulations are performed under a large variety of market dynamics to demonstrate the practicability of our approach, to perform benchmarking with respect to traditional methods and to conduct sensitivity analyses.