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This paper studies the equal risk pricing (ERP) framework for the valuationof European financial derivatives. This option pricing approach is consistentwith global trading strategies by setting the premium as the value such thatthe residual hedging risk of the long and short positions in the option areequal under optimal hedging. The ERP setup of Marzban et al. (2020) isconsidered where residual hedging risk is quantified with convex risk measures.The main objective of this paper is to assess through extensive numericalexperiments the impact of including options as hedging instruments within theERP framework. The reinforcement learning procedure developed in Carbonneau andGodin (2020), which relies on the deep hedging algorithm of Buehler et al.(2019b), is applied to numerically solve the global hedging problems byrepresenting trading policies with neural networks. Among other findings,numerical results indicate that in the presence of jump risk, hedging long-termputs with shorter-term options entails a significant decrease of both equalrisk prices and market incompleteness as compared to trading only the stock.Monte Carlo experiments demonstrate the potential of ERP as a fair valuationapproach providing prices consistent with observable market prices. Analysesexhibit the ability of ERP to span a large interval of prices through thechoice of convex risk measures which is close to encompass the variance-optimalpremium.

Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments