英文标题：
《Decomposition formula for jump diffusion models》
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作者：
Raul Merino, Jan Posp\\\'i\\v{s}il, Tom\\\'a\\v{s} Sobotka and Josep Vives
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最新提交年份：
2019
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英文摘要：
In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston (1993) SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models - models utilizing a variance process postulated by Heston (1993). In particular, we inspect in detail the approximation formula for the Bates (1996) model with log-normal jump sizes and we provide a numerical comparison with the industry standard - Fourier transform pricing methodology. For this model, we also reformulate the approximation formula in terms of implied volatilities. The main advantages of the introduced pricing approximations are twofold. Firstly, we are able to significantly improve computation efficiency (while preserving reasonable approximation errors) and secondly, the formula can provide an intuition on the volatility smile behaviour under a specific SVJ model.
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中文摘要：
本文推导了标的资产价格过程中具有有限活动跳跃的模型（SVJ模型）的期权定价公式的一般分解。这是Alos（2012）对Heston（1993）SV模型的著名结果的扩展。此外，还为一类流行的SVJ模型引入了期权价格的显式近似公式，该模型利用了Heston（1993）假设的方差过程。特别是，我们详细检查了具有对数正态跳跃大小的Bates（1996）模型的近似公式，并与行业标准的傅立叶变换定价方法进行了数值比较。对于该模型，我们还根据隐含波动率重新推导了近似公式。引入的定价近似值的主要优点有两个。首先，我们能够显著提高计算效率（同时保留合理的近似误差），其次，该公式可以提供特定SVJ模型下波动率微笑行为的直觉。
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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：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
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