VIX Derivatives Valuation Under GARCH-type Models

Volatility,as an important indicator describing the dynamic changes of the financial market,has a profound impact on participants' decisions such as investment strategies,asset management,and risk hedging.Model-based and model-free volatility measures are the two approaches popularized by both academia and industry,and the Chicago Board Options Exchange(CBOE)volatility index(VIX),which can measure market volatility and investor sentiment accurately and dynamically in real-time,has effectively become the barometer in the US stock market and even the global financial market.At the same time,the VIX derivatives released by CBOE offer additional investment and hedging opportunities for financial market participants,which bring tremendous challenges and opportunities for volatility research,together with ample investment outlets.This thesis proposes and analyses a wide class of GARCH-type models with mixed frequency data and hybrid structure.These models incorporate volatility components,jumps,and realized volatility to effectively capture the long memory and thick tail of financial time series and then significantly improve their volatility forecasting abilities.This thesis is the first work that analytically obtains the links between conditional variances of multi-factor GARCH models and VIX,and it further establishes the closed-form pricing formula of VIX derivatives through the connections.In addition,we empirically explore the role of affine structure in the VIX derivatives pricing and compare the pricing performance of EGARCH,GJR-GARCH,and NGARCH models.This thesis is organized as follows.First of all,we describe in Chapter 1 the background,motivation,contents,and contribution of our studies,and present in chapter 2 the derivatives pricing models and risk-neutral measures.In chapter 3,we apply the generalized affine realized volatility model to obtain the VIX term structure expression and VIX futures pricing formula.Our empirical studies in this chapter find that including realized volatility can substantially improve the forecasting of VIX and the pricing of its futures within these models.Chapter 4 nests multiple volatility components and jump in the generalized affine realized volatility model and studies their contribution in describing VIX and its futures data.To this end,we theoretically derive the closed-form solution for VIX futures pricing and empirically show that the realized volatility,volatility components,and jump can provide an evident improvement in VIX forecasting and its futures pricing;more importantly,these three models features are complements rather than substitutes.Chapter 5 further investigates the VIX derivatives valuation performance offered by the nonaffine dynamics.We find strong empirical evidence that the valuation superiority of the nonaffine specification,especially the EGARCH model,is significant and robust.However,we also find evidence in favor of the affine model in pricing VIX options of high values.Finally,in chapter 6,we present a brief conclusion of this thesis and a discussion of future research.