Volatility derivatives, as a special class of financial derivatives whose underlying asset is the volatility, have witnessed increasing popularity over the last decades. Among assorted measurements of volatility, the Volatility Index (VIX) launched by the Chicago Board Options Exchange (CBOE) is most closely followed by investors, and its derivatives, namely, the VIX futures and options, are the most actively traded products. Therefore, a solid understanding of the VIX index as well as accurate and efficient pricing of the VIX futures and options are called for. This thesis serves as a self-contained monograph on this topic. A systematic and comprehensive introduction to the VIX index is first presented. Then, the exact closed form pricing formulas for the VIX futures and optio...[ Read more ]

Volatility derivatives, as a special class of financial derivatives whose underlying asset is the volatility, have witnessed increasing popularity over the last decades. Among assorted measurements of volatility, the Volatility Index (VIX) launched by the Chicago Board Options Exchange (CBOE) is most closely followed by investors, and its derivatives, namely, the VIX futures and options, are the most actively traded products. Therefore, a solid understanding of the VIX index as well as accurate and efficient pricing of the VIX futures and options are called for. This thesis serves as a self-contained monograph on this topic. A systematic and comprehensive introduction to the VIX index is first presented. Then, the exact closed form pricing formulas for the VIX futures and options are derived under the stochastic volatility model with simultaneous jumps and the 3/2 plus jumps stochastic volatility model, respectively. Furthermore, the saddlepoint approximation pricing formulas of different orders are proposed for the VIX futures and options under the stochastic volatility model with simultaneous jumps, which are brand-new in the area of VIX derivatives pricing. Finally, results from numerical tests are reported.