Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task in financial institutions, and its speed-up will provide a large business impact. Recently, applications of quantum computing to financial problems have been started to be investigated. In this paper, we first propose a quantum algorithm for Bermudan option pricing. This method performs the approximation of the continuation value, which is a crucial part of Bermudan option pricing, by Chebyshev interpolation, using the values at interpolation nodes estimated by quantum amplitude estimation. In this method, the number of calls to the oracle to generate underlying asset price paths scales as $\widetilde{O}(\epsilon ^{-1})$ , where ϵ is the error tolerance of the option price. This means the quadratic speed-up compared with classical Monte Carlo-based methods such as least-squares Monte Carlo, in which the oracle call number is $\widetilde{O}(\epsilon ^{-2})$ .

中文翻译：

---

通过量子幅度估计和切比雪夫插值的百慕大期权定价

金融衍生品的定价，特别是百慕大期权等早期可行使期权的定价，是金融机构一项重要但繁重的数字任务，其加速将对业务产生巨大影响。最近，已经开始研究量子计算在金融问题上的应用。在本文中，我们首先提出了一种用于百慕大期权定价的量子算法。该方法使用由量子幅度估计估计的插值节点处的值，通过切比雪夫插值来执行延续值的近似，这是百慕大期权定价的关键部分。在这种方法中，为生成基础资产价格路径而调用预言机的次数为 $\widetilde{O}(\epsilon ^{-1})$，其中 ε 是期权价格的容错度。