Quantum Binomial Tree, An Effective Method for Probability Distribution Loading for Derivative Pricing

Efficiently generating or loading probability distributions on quantum computers is a foundational task in Quantum Monte Carlo methods. While the quantum amplitude estimation algorithm offers a quadratic speed-up over classical Monte Carlo techniques, this advantage can be negated if the probability distribution is not effectively loaded. Moreover, any practical approach must be flexible enough to accommodate a wide range of market models�a requirement unmet by existing methods. In this paper, we propose a novel and efficient approach for loading probability distributions tailored to derivative pricing. The proposed method, the Quantum Binomial Tree, serves as a quantum analog of the classical Binomial Tree model. This approach enables exponential scaling in the number of Monte Carlo paths, while retaining an overall quadratic speed-up compared to classical algorithms. We demonstrate how the Quantum Binomial Tree framework can load prominent financial models�including the local volatility model, and the Heston model onto a quantum computer. Furthermore, this paper includes a detailed implementation for option pricing under time-dependent volatility, as well as numerical results.