金融工程研究中心学术报告:Mathematics behind volatility index VIX

报告人:香港科技大学 Yue Kuen KWOK (郭宇权)教授



报告摘要: Volatility of the stochastic dynamics of an asset price process is the standard deviation of the logarithm of asset price returns. The volatility of financial assets is a hidden stochastic process derived from observable asset prices. Fund managers may explore investment opportunities on trading volatility instead of directional moves of asset prices. The Chicago Board of Options Exchange launched the volatility index of the S&P 500 stock index (ticker symbol VIX), which is formally defined as the square root of the risk neutral expectation of the integrated variance of the S&P 500 over the next 30 calendar dates. The goal of the VIX is to compute model free volatility measure implied by the traded stock option prices. The dynamics of VIX is highly correlated with market anxiety and sentiment, so VIX bears the nickname “fear gauge”. In this talk, we discuss the mathematics behind the construction of VIX, and how VIX can be expressed in terms of weighted average of traded option prices. Under the affine Heston model on stochastic volatility, VIX is related to a linear relation of the instantaneous variance. We also discuss pricing models of VIX futures and options under the consistent model approach and direct modeling approach.

报告人简介:Yue Kuen Kwok (郭宇权) is a Professor in the Department of Mathematics, the Hong Kong University of Science and Technology (HKUST). He is the founding director of MSc degree in Financial Mathematics and the current director of BSc degree in Mathematics and Economics at HKUST. Professor Kwok’s research interests concentrate on pricing and risk management of financial derivatives. He has published more than 100 research articles in major research journals in financial mathematics and mathematical sciences. In addition, he is the author of two books on quantitative finance: “Mathematical Models of Financial Derivatives”, second edition, (2008), and “Saddlepoint Approximation Methods in Financial Engineering” (2018), both published by Springer Verlag. He has provided consulting services to a number of financial institutions on various aspects of derivative trading and credit risk management. He has served in the editorial boards of Journal of Economic and Dynamics Control, Asian-Pacific Financial Markets and International Journal of Financial Engineering. He received his PhD degree in Applied Mathematics from Brown University in 1985.


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