THESIS
2013
xiii, 172 pages : illustrations ; 30 cm
Abstract
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...[
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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.
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