Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms

We introduce a quantum algorithm to compute the market risk of financial derivatives. Previous work has shown that amplitude estimation can accelerate derivative pricing quadratically in target error and we extend this quadratic scaling advantage computation. show employing gradient algorithms deliver further number associated sensitivities, usually called greeks. By numerically simulating on derivatives practical interest, demonstrate not only successfully estimate greeks examples studied, but resource requirements be significantly lower practice than what is expected by theoretical complexity bounds. This additional computation lowers estimated logical clock rate required for from Chakrabarti et al. [Quantum 5, 463 (2021)] factor ~7, 50MHz 7MHz, even modest industry standards (four). Moreover, if have access enough resources, parallelized across 60 QPUs, which case each device achieve same overall runtime as serial execution would ~100kHz. Throughout work, summarize compare several different combinations classical approaches could used computing