Lévy模型中回撤及其持续时间的模拟：基于stick-breaking高斯近似
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
AI总结：
本文提出一种基于stick-breaking高斯近似的模拟算法，用于高效计算指数Lévy模型中回撤及其持续时间的期望泛函，并通过SBG耦合获得Wasserstein距离界，显著降低高跳跃活动下的计算复杂度。
摘要：
我们开发了一种计算方法，用于计算指数Lévy模型中回撤及其持续时间的期望泛函。该方法基于一种新颖的模拟算法，用于一般Lévy过程的高斯近似的状态、上确界及上确界达到时间的联合分布。我们为应用中出现的各种局部Lipschitz和不连续收益函数限定了偏差，并分析了相应的蒙特卡洛和多级蒙特卡洛估计器的计算复杂度。针对Lévy过程的蒙特卡洛方法（使用高斯近似）已在Lipschitz收益函数情形下得到分析，在该情形下，当跳跃活动性高时，我们算法的计算复杂度比现有方法低至两个数量级。我们方法的核心是某些Wasserstein距离的界，这些界通过Lévy过程与其高斯近似之间的新颖SBG耦合获得。基于专用GitHub仓库中实现的数值性能与我们的理论界表现出良好的一致性。
英文摘要：
We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel simulation algorithm for the joint law of the state, supremum and time the supremum is attained of the Gaussian approximation of a general Lévy process. We bound the bias for various locally Lipschitz and discontinuous payoffs arising in applications and analyse the computational complexities of the corresponding Monte Carlo and multilevel Monte Carlo estimators. Monte Carlo methods for Lévy processes (using Gaussian approximation) have been analysed for Lipschitz payoffs, in which case the computational complexity of our algorithm is up to two orders of magnitude smaller when the jump activity is high. At the core of our approach are bounds on certain Wasserstein distances, obtained via the novel SBG coupling between a Lévy process and its Gaussian approximation. Numerical performance, based on the implementation in the dedicated GitHub repository, exhibits a good agreement with our theoretical bounds.
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