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摘要翻译：
有据可查的是，一个试图捕捉普通期权市场价格行为的基础资产价格过程模型需要同时表现出扩散和跳跃特征。本文假定资产价格过程$S$是具有cadlag路径的马尔可夫过程，并提出了一种计算资产在预先确定的走廊上交易时应计对数收益的实现方差规律的方案。因此，我们得到了在这样的市场中波动性衍生品和基于走廊实现方差的衍生品的定价和套期保值算法。考虑的模型类别很大，因为它包括跳扩散和Levy过程。我们证明了该格式的弱收敛性，并详细描述了S$为CEV过程（连续轨迹）、方差gamma过程（独立增量跳跃）和无限活动跳跃扩散（间断增量依赖轨迹）等特征情形下算法的实现。
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英文标题：
《Volatility derivatives in market models with jumps》
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作者：
A. Mijatovic, H. Lo
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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英文摘要：
It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process $S$ is Markov with cadlag paths and propose a scheme for computing the law of the realized variance of the log returns accrued while the asset was trading in a prespecified corridor. We thus obtain an algorithm for pricing and hedging volatility derivatives and derivatives on the corridor-realized variance in such a market. The class of models under consideration is large, as it encompasses jump-diffusion and Levy processes. We prove the weak convergence of the scheme and describe in detail the implementation of the algorithm in the characteristic cases where $S$ is a CEV process (continuous trajectories), a variance gamma process (jumps with independent increments) or an infinite activity jump-diffusion (discontinuous trajectories with dependent increments).
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PDF链接：
https://arxiv.org/pdf/0905.3326
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