A Threshold for Quantum Advantage in Derivative Pricing

Pricing multi-asset derivatives by finite difference method on a quantum computer

Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this paper, we focus on derivative pricing based on solving the Black-Scholes partial differential equation by finite difference method (FDM), which is a suitable approach for some types of derivatives but suffers from the {\it curse of dimensionality}, that is, exponential growth of complexity in the case of multiple underlying assets. We propose a quantum algorithm for FDM-based pricing of multi-asset derivative with exponential speedup with…

一种适用于含时哈密顿量的路径积分方法及其在衍生品定价中的应用

A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing

本文将半经典路径积分方法推广至含时哈密顿量，并以 Black-Karasinski 利率模型验证其准确性与效率，为衍生品定价提供替代完全数值格式的可行方案。

Quantum computational finance: Monte Carlo pricing of financial derivatives

Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant probability distributions can be prepared in quantum superposition, the payoff functions can be implemented via quantum circuits, and the price of financial derivatives can be extracted via quantum measurements. We show how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimat…

使用量子信号处理的衍生品定价

Derivative Pricing using Quantum Signal Processing

本文提出基于 Quantum Signal Processing (QSP) 的方法，将金融衍生品收益直接编码至量子振幅以避免昂贵的量子算术，显著降低了 T-gates、逻辑量子比特等资源需求，为在量子计算机上实现衍生品定价的量子优势提供了更高效的途径。

Quantum Computation for Pricing Caps using the LIBOR Market Model

The LIBOR Market Model (LMM) is a widely used model for pricing interest rate derivatives. While the Black-Scholes model is well-known for pricing stock derivatives such as stock options, a larger portion of derivatives are based on interest rates instead of stocks. Pricing interest rate derivatives used to be challenging, as their previous models employed either the instantaneous interest or forward rate that could not be directly observed in the market. This has been much improved since LMM was raised, as it uses directly observable interbank offered rates and is expected to be more precise.…

Pricing multi-asset derivatives by variational quantum algorithms

Pricing a multi-asset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of derivatives, the computational complexity increases exponentially as the number of underlying assets increases in some classical methods, such as the finite difference method. Therefore, there are efforts to reduce the computational complexity by using quantum computation. However, when solving with naive quantum algorithms, the target derivative price is emb…