论文标题
使用LIBOR市场模型的定价盖量子计算
Quantum Computation for Pricing Caps using the LIBOR Market Model
论文作者
论文摘要
LIBOR市场模型（LMM）是广泛使用定价利率衍生品的模型。虽然黑色 - choles模型以定价股票衍生品（例如股票期权）而闻名，但较大的衍生品是基于利率而不是股票的。定价利率衍生品通常具有挑战性，因为他们以前的模型采用了无法直接在市场上观察到的瞬时利息或远期利率。自LMM提出以来，这已经得到了很大的改善，因为它使用了可直接可观察的银行间的汇率，预计将更加精确。最近，量子计算已用于加快选项定价任务，但很少在结构化的利率导数上。鉴于利率衍生品市场的规模和LMM的广泛使用，我们采用量子计算来基于LMM的利率衍生工具，CAPS。由于CAPS的定价与不同的男高音的路径依赖性蒙特卡洛迭代有关，这对于许多复杂的结构化衍生物来说是常见的，因此我们开发了杂交经典量子方法，该方法应用了量子幅度估计算法来估算上一个男高音的期望。我们表明，与纯经典的蒙特卡洛方法相比，混合方法仍然显示出更好的收敛性，为具有更大多样性的衍生物多样性提供了有用的案例研究。
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. Recently, quantum computing has been used to speed up option pricing tasks, but rarely on structured interest rate derivatives. Given the size of the interest rate derivatives market and the widespread use of LMM, we employ quantum computing to price an interest rate derivative, caps, based on the LMM. As caps pricing relates to path-dependent Monte Carlo iterations for different tenors, which is common for many complex structured derivatives, we developed our hybrid classical-quantum approach that applies the quantum amplitude estimation algorithm to estimate the expectation for the last tenor. We show that our hybrid approach still shows better convergence than pure classical Monte Carlo methods, providing a useful case study for quantum computing with a greater diversity of derivatives.
