有限差分解假设方法在最小二乘蒙特卡洛中的应用
Finite-Difference Solution Ansatz approach in Least-Squares Monte Carlo
AI总结：
本文提出利用一维有限差分解构造条件预期延续收益的假设，用于改进最小二乘蒙特卡洛的准确性和稳定性，该方法在局部和随机波动率模型下被证明可作为控制变量降低均方误差，从而减少定价误差。
摘要：
本文提出了一种简单但有效且高效的方法，以提高最小二乘蒙特卡洛的准确性和稳定性。核心思想是利用一维有限差分解构造条件预期延续收益的假设，用于线性回归。该方法连接了求解后向偏微分方程与蒙特卡洛模拟，旨在实现两者的优势互补。在涵盖局部和随机波动率模型的一般设定下，该假设被证明可作为控制变量，降低均方误差，从而减少最终定价误差。我们通过现实案例展示了该技术，包括百慕大期权、最差发行人可赎回票据以及估值调整下的欧式期权预期正暴露。
英文摘要：
This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the finite-difference solution from one dimension, to be used in linear regression. This approach bridges between solving backward partial differential equations and Monte Carlo simulation, aiming at achieving the best of both worlds. In a general setting encompassing both local and stochastic volatility models, the ansatz is proven to act as a control variate, reducing the mean squared error, thereby leading to a reduction of the final pricing error. We illustrate the technique with realistic examples including Bermudan options, worst of issuer callable notes and expected positive exposure on European options under valuation adjustments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
