arXiv 1405.73422014-05-28q-fin.PR

动态方差-Gamma模型下的期权定价

Option Pricing in a Dynamic Variance-Gamma Model

Lorenzo Mercuri, Fabio Bellini

发表信息：: Journal of Financial Decision Making (2011) vol. 7, n.1 pp. 37-51 - ISSN: 1790-4870

摘要：

本文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Gamma混合密度是随时间变化的，并遵循仿射GARCH模型，试图捕捉波动冲击的持续性和更高阶的条件动力学在一个吝啬的方式。我们选择一个等价鞅测度通过条件Esscher变换的Buhlmann等。（1996），并表明，这种变化的措施导致一个类似的动态的混合分布。该模型允许一个递归过程的终端对数价格的特征函数的计算，从而允许半分析定价在赫斯顿和南迪（2000年）。从实证的角度来看，我们检查这个模型的能力，校准SPX期权数据，我们比较它与赫斯顿和南迪（2000年）模型和克里斯托弗森，赫斯顿和雅各布斯（2006年）模型，这是基于逆高斯新息。此外，我们提供了一个详细的比较与几个变种的赫斯顿和南迪模型，显示方差伽马创新的优越性，也从历史的MLE估计的角度来看。

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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