基于Bates模型的期权定价的有限元框架

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摘要翻译：
在本文中，我们在一个著名的带跳跃的随机波动率模型Bates模型的框架下，提出了一个期权定价的有限元方法。在该模型中，资产对数收益服从跳跃扩散模型，跳跃分量由复合泊松型Levy过程组成，波动行为由CIR型随机微分方程描述，具有均值回复漂移项和与对数收益相关的扩散分量。与所有的Levy模型一样，期权定价问题可以用一个积分-微分方程来表述：对于Bates模型，定价方程的未知F（S,V,t）（期权价格）依赖于三个独立变量，微分算子部分是抛物型的，而非局部积分算子是关于跳跃的Levy测度计算的。在本文中，我们将给出一个适用于有限元方法的问题的变分形式。对欧式期权的数值计算结果将与不同方法所得结果进行比较。
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英文标题：
《A Finite Element Framework for Option Pricing with the Bates Model》
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作者：
Edie Miglio, Carlo Sgarra
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最新提交年份：
2008
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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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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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英文摘要：
  In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a jump-diffusion model where the jump component consists of a Levy process of compound Poisson type, while the volatility behavior is described by a stochastic differential equation of CIR type, with a mean-reverting drift term and a diffusion component correlated with that of the log-returns. Like in all the Levy models, the option pricing problem can be formulated in terms of an integro-differential equation: for the Bates model the unknown F(S, V, t) (the option price) of the pricing equation depends on three independent variables and the differential operator part turns out to be of parabolic kind, while the nonlocal integral operator is calculated with respect to the Levy measure of the jumps. In this paper we will present a variational formulation of the problem suitable for a finite element approach. The numerical results obtained for european options will be compared with those obtained with different methods.
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PDF链接：
https://arxiv.org/pdf/0812.3083

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关键词：Bates 期权定价 Bate BAT ATE 方法 收益 approach stochastic 波动