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学术讲座:Pure Jump Models for Pricing and Hedging VIX Derivatives

 

学术讲座:Pure Jump Models for Pricing and Hedging VIX Derivatives
时间:2017-5-10 16:00-17:00
地点:博学925
摘要:Recent non-parametric statistical analysis of high-frequency VIX data (Todorov and Tauchen (2011)) reveals that VIX dynamics is a pure jump semimartingale with infinite jump activity and infinite variation. To our best knowledge, existing models in the literature for pricing and hedging VIX derivatives do not have these features. This paper fills this gap by developing a novel class of parsimonious pure jump models with such features for VIX based on the additive time change technique proposed in Li et al. (2016). We time change the 3/2 diffusion by a class of additive subordinators with infinite activity, yielding pure jump Markov semimartingales with infinite activity and infinite variation. These processes have time and state dependent jumps that are mean reverting and are able to capture stylized features of VIX. Our models take the initial term structure of VIX futures as input and are analytically tractable for pricing VIX futures and European options via eigenfunction expansions. Through calibration exercises, we show that our model is able to achieve excellent fit for the VIX implied volatility surface which typically exhibits very steep skews. Comparison to two other models in terms of calibration reveals that our model performs better both in-sample and out-of-sample. We explain the ability of our model to fit the volatility surface by evaluating the matching of moments implied from market VIX option prices. To hedge VIX options, we develop a dynamic strategy which minimizes instantaneous jump risk at each rebalancing time while controlling transaction cost. Its effectiveness is demonstrated through a simulation study on hedging Bermudan style VIX options.
演讲人简介:李凌飞,香港中文大学系统工程与工程管理学院助理教授。2007年在北京大学数学学院金融数学系获得学士学位,后在美国西北大学工业工程与管理系获得硕士和博士学位。20126月开始在香港中文大学任教,研究兴趣为金融工程,数理金融,计算金融。曾在金融数学,运筹管理以及科学计算著名期刊Mathematical Finance, Finance and Stochastics, Operations ResearchSIAM Journal on Scientific Computing发表多篇学术论文。现主持两项由香港研资局资助的基金项目。