FINTECH THRUST SEMINAR | Quantum Monte Carlo Algorithm for Solving Black-Scholes PDEs for High-Dimensional Option Pricing in Finance and Its Complexity Analysis
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Quantum Monte Carlo Algorithm for Solving Black-Scholes PDEs for High-Dimensional Option Pricing in Finance and Its Complexity Analysis
Abstract:
In this talk we present a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs with correlation for high-dimensional option pricing. The payoff function of the option is of general form and is only required to be continuous and piece-wise affine (CPWA), which covers most of the relevant payoff functions used in finance. We provide a rigorous error analysis and complexity analysis of our algorithm. In particular, we prove that the computational complexity of our algorithm is bounded polynomially in the space dimension d of the PDE and the reciprocal of the prescribed accuracy ε. Moreover, we show that for payoff functions which are bounded, our algorithm indeed has a speed-up compared to classical Monte Carlo methods. Furthermore, we present numerical simulations in one and two dimensions using our developed package within the Qiskit framework tailored to price CPWA options with respect to the Black-Scholes model, as well as discuss the potential extension of the numerical simulations to arbitrary space dimension. This talk is based on joint work with Jianjun Chen and Yongming Li.
Ariel Neufeld is a Tenured Associate Professor in mathematics at the Nanyang Technological University in Singapore. He received his PhD in mathematics in May 2015 at ETH Zurich, where he spent half of his PhD at the Columbia University in the City of New York. Prior to joining NTU he was a postdoctoral researcher at ETH Zurich. His research focuses on model uncertainty in financial markets and distributionally robust optimization, machine learning algorithms and their applications in finance and insurance, financial and insurance mathematics, as well as stochastic analysis and stochastic optimal control.