Non-affine GARCH Option Pricing Models, Variance-Dependent Kernels, and Diffusion Limits*
研究非仿射非高斯GARCH模型在方差依赖指数线性定价核下的定价与弱收敛，推导风险中性动态和泡沫条件，实证表明该定价核与非高斯创新结合的优势。
This paper investigates the pricing and weak convergence of an asymmetric non-affine, non-Gaussian GARCH model when the risk neutralization is based on a variance-dependent exponential linear pricing kernel with stochastic risk aversion parameters. The risk-neutral dynamics are obtained for a general setting and its weak limit is derived. We show how several GARCH diffusions, martingalized via well-known pricing kernels, are obtained as special cases and we derive necessary and sufficient conditions for the presence of financial bubbles. An extensive empirical analysis using both historical returns and options data illustrates the advantage of coupling this pricing kernel with non-Gaussian innovations.