论文标题
微笑的量子定价：量子计算机上局部波动率模型的实现
Quantum Pricing with a Smile: Implementation of Local Volatility Model on Quantum Computer
论文作者
论文摘要
在先前的论文中已经讨论了量子算法在蒙特卡洛模拟中的应用。但是，到目前为止，此类论文中讨论的定价模型是黑色choles模型，这很重要，但很简单。因此，考虑如何在金融机构中实施实践中使用的更复杂的模型是有动力的。然后，我们考虑了本地波动率（LV）模型，其中基础资产价格的波动依赖于价格和时间。我们提出两种类型的实施。一种是每次寄存器的方式，它在以前的大多数论文中都采用。通过这种方式，生成资产价格路径所需的每个随机数（RN）都会在分离的寄存器上生成，因此所需的Qubit号码与RN的数量成正比增加。另一个是在作者以前的作品中提出的prn-on-a-a-a-a-n-n-n-negister方式。这样，在寄存器上生成的一系列伪随机数（PRN）用于生成资产价格的路径，因此随着电路深度的权衡，所需的量子数将减少。我们详细介绍了这两个实现的电路图，并估算了所需的资源：量子数和T计数。
Applications of the quantum algorithm for Monte Carlo simulation to pricing of financial derivatives have been discussed in previous papers. However, up to now, the pricing model discussed in such papers is Black-Scholes model, which is important but simple. Therefore, it is motivating to consider how to implement more complex models used in practice in financial institutions. In this paper, we then consider the local volatility (LV) model, in which the volatility of the underlying asset price depends on the price and time. We present two types of implementation. One is the register-per-RN way, which is adopted in most of previous papers. In this way, each of random numbers (RNs) required to generate a path of the asset price is generated on a separated register, so the required qubit number increases in proportion to the number of RNs. The other is the PRN-on-a-register way, which is proposed in the author's previous work. In this way, a sequence of pseudo-random numbers (PRNs) generated on a register is used to generate paths of the asset price, so the required qubit number is reduced with a trade-off against circuit depth. We present circuit diagrams for these two implementations in detail and estimate required resources: qubit number and T-count.
