英文标题：
《Randomisation and recursion methods for mixed-exponential Levy models,
  with financial applications》
---
作者：
Aleksandar Mijatovic, Martijn Pistorius, Johannes Stolte
---
最新提交年份：
2014
---
英文摘要：
  We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Levy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Levy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Levy processes, which includes Brownian motion with drift, Kou\'s double-exponential model and hyper-exponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Levy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.
---
中文摘要：
我们发展了一种新的蒙特卡罗方差缩减方法来估计两种常见的路径依赖泛函的期望：集合的首次通过时间和占用时间。该方法基于列维桥过程集合的首次通过时间概率和预期占用时间的递归近似，部分依赖于时间参数的随机性。我们建立了一般Levy过程的这种递归，并导出了混合指数跳跃扩散的显式形式。混合指数跳跃扩散是Levy过程的一个稠密子类（在弱近似意义下），包括带漂移的布朗运动、Kou的双指数模型和超指数跳跃扩散模型。我们给出了一个高精度的数值实现，并得出了误差估计。通过举例说明，该方法被应用于指数Levy模型和具有指数跳跃的Bates型随机波动率模型下的区间应计项目和障碍期权的估值。与标准蒙特卡罗方法相比，我们发现该方法的效率显著提高。
---
分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--

---
PDF下载：
-->