英文标题：
《Fluctuation identities with continuous monitoring and their application
to price barrier options》
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作者：
Carolyn E. Phelan, Daniele Marazzina, Gianluca Fusai, Guido Germano
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最新提交年份：
2017
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英文摘要：
We present a numerical scheme to calculate fluctuation identities for exponential L\\\'evy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential L\\\'evy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener-Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-$z$ domain) as the monitoring time step approaches zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme.
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中文摘要：
我们提出了一个数值格式来计算连续监测情况下指数L拞evy过程的涨落恒等式。这包括接触单个上部或下部屏障的斯皮策标识，以及两个屏障出口问题的更困难情况。这些恒等式在Fourier-Laplace域中给出，需要进行数值逆变换。因此，我们填补了主要研究离散监控案例的文献中的一个空白；事实上，目前还没有处理连续情况的数值方法。作为一种激励性应用，我们通过指数利维过程建模的基础资产，对障碍期权进行持续监控。我们对该方法进行了详细的误差分析，并给出了误差界，以说明基于sinc的快速Hilbert变换用于Wiener-Hopf分解的截断误差是如何限制性能的。当监测时间步长接近零时，通过将我们的新技术的结果与离散监测情况（在Fourier-$z$域）的结果进行比较，我们表明，连续监测的误差收敛代表了离散监测方案的一个极限。
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分类信息：

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
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