英文标题：
《Option Pricing in a Dynamic Variance-Gamma Model》
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作者：
Lorenzo Mercuri and Fabio Bellini
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最新提交年份：
2014
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英文摘要：
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying to capture persistence of volatility shocks and also higher order conditional dynamics in a parsimonious way. We select an equivalent martingale measure by means of the conditional Esscher transform as in Buhlmann et al. (1996) and show that this change of measure leads to a similar dynamics of the mixing distribution. The model admits a recursive procedure for the computation of the characteristic function of the terminal logprice, thus allowing semianalytical pricing as in Heston and Nandi (2000). From an empirical point of view, we check the ability of this model to calibrate SPX option data and we compare it with the Heston and Nandi (2000) model and with the Christoffersen, Heston and Jacobs (2006) model, that is based on Inverse Gaussian innovations. Moreover, we provide a detailed comparison with several variants of the Heston and Nandi model that shows the superiority of the Variance-Gamma innovations also from the point of view of historical MLE estimation.
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中文摘要：
我们提出了一个离散时间随机波动率模型，其中对数收益率的条件分布是方差Gamma，即具有Gamma混合密度的正态方差均值混合。我们假设伽马混合密度是时变的，并遵循仿射Garch模型，试图以一种节省的方式捕捉波动冲击的持续性和高阶条件动力学。我们通过条件Esscher变换选择了一个等价的鞅测度，如Buhlmann等人（1996）所述，并表明这种测度的变化导致了混合分布的类似动力学。该模型允许使用递归程序计算终端对数价格的特征函数，从而允许使用Heston和Nandi（2000）中的半解析定价。从经验的角度来看，我们检查了该模型校准SPX期权数据的能力，并将其与Heston和Nandi（2000）模型以及基于逆高斯创新的Christoffersen、Heston和Jacobs（2006）模型进行了比较。此外，我们还与Heston和Nandi模型的几种变体进行了详细比较，从历史最大似然估计的角度也显示了方差伽马创新的优越性。
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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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