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摘要翻译：
金融期权定价的路径积分技术大多基于可以根据福克-普朗克微分方程重新构造的模型，因此忽略跳跃，只描述漂移和扩散。我们提出了一种方法来调整路径积分传播子和期权价格本身的公式，使跳跃过程与通常的漂移和扩散项一起考虑。特别地，我们重点研究了随机波动率模型，如指数Vasicek模型，并对该模型的定价公式和传播子进行了扩展，使其在给定跳跃大小分布的情况下引入跳跃扩散。该模型包含了Black-Scholes模型之外的非高斯涨落，并且得到了挥发物的对数正态分布，这与超统计分析的结果是一致的。用Monte Carlo模拟验证了本文的结果。
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英文标题：
《Generalized pricing formulas for stochastic volatility jump diffusion
models applied to the exponential Vasicek model》
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作者：
L.Z.J.Liang, D.Lemmens and J. Tempere
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最新提交年份：
2010
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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：
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.
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PDF链接：
https://arxiv.org/pdf/1011.1175
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