Quantum algorithms for pricing derivatives
Event details
| Date | 29.11.2023 |
| Hour | 15:15 › 16:15 |
| Speaker | Alessandro Luongo (https://www.quantumlah.org/people/profile/L-Alessandro) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Computational Mathematics Seminar
Abstract: We present new quantum algorithms for pricing financial derivatives in both single-period and multi-period financial markets. In the context of single-period markets we introduce three distinct algorithms. The initial two methods leverage a linear program-based formulation of the pricing problem, employing the quantum zero-sum game algorithm and the quantum simplex algorithm as essential subroutines. The third algorithm introduces a novel market assumption, which, while less stringent than market completeness (which is a standard assumption in many market models), enables the application of quantum linear systems solvers, potentially leading to significant speedups. For multi period markets we discuss a quantum version for the famous least-squares Monte Carlo (LSM) algorithm. Our algorithm achieves a nearly quadratic speedup in the runtime compared to the LSM algorithm under some mild assumptions. Our quantum algorithm can be applied to American option pricing, and we analyze a case study for the common situation of Brownian motion and geometric Brownian motion processes. Based on: https://arxiv.org/abs/2111.15332 and https://arxiv.org/abs/2209.08867 .
Abstract: We present new quantum algorithms for pricing financial derivatives in both single-period and multi-period financial markets. In the context of single-period markets we introduce three distinct algorithms. The initial two methods leverage a linear program-based formulation of the pricing problem, employing the quantum zero-sum game algorithm and the quantum simplex algorithm as essential subroutines. The third algorithm introduces a novel market assumption, which, while less stringent than market completeness (which is a standard assumption in many market models), enables the application of quantum linear systems solvers, potentially leading to significant speedups. For multi period markets we discuss a quantum version for the famous least-squares Monte Carlo (LSM) algorithm. Our algorithm achieves a nearly quadratic speedup in the runtime compared to the LSM algorithm under some mild assumptions. Our quantum algorithm can be applied to American option pricing, and we analyze a case study for the common situation of Brownian motion and geometric Brownian motion processes. Based on: https://arxiv.org/abs/2111.15332 and https://arxiv.org/abs/2209.08867 .
Practical information
- General public
- Free
Organizer
- Bernard Kapidani
Contact
- Bernard Kapidani