Quantum Option Profit and Loss Encoding for Risk Assessment

In the financial sector, risk measurement of derivative options has long been a focal point of research. However, traditional risk measurement methods face bottlenecks of low computational efficiency and high complexity. Quantum algorithms, leveraging the properties of quantum superposition and interference, hold promise for enabling parallel exploration of multi-solution spaces in risk assessment, offering more efficient and accurate solutions. Nevertheless, current quantum devices are challenged by noise and errors, posing difficulties in achieving true quantum advantage in the short term. This paper proposes a Quantum Option Profit and Loss Encoding (QOPLE) method for risk analysis, conducting an in-depth study of its application in the risk assessment of European call options, which are widely used in the options market. A Quantum Option Risk Assessment (QORA) model is constructed based on this method. Compared to classical approaches, this model has the potential for quadratic speedup and is more suitable for current NISQ (Noisy Intermediate-Scale Quantum) devices in terms of resource utilization. Finally, we demonstrate the calculation results of risk assessment for European call options using IBM Qiskit. Simulation results show that by appropriately configuring the model's sampling qubits, an accuracy of up to 99<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> can be achieved, while the number of ancillary qubits required by the model is reduced by at least 15<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> compared to existing quantum algorithms.