大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Topics in Volatility and Forecasting (Day 1)

Ser-huang Poon (University of Manchester)

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4. Topics in Volatility and Forecasting (Day 1)

Two Day Seminar　(CSFI・大証寄附研究部門共催)

Topics in Volatility and Forecasting (Day 1)

Ser-huang Poon (University of Manchester)

8月23日（木）(Day 1)

16:20-17:50 Ser-huang Poon (University of Manchester)
http://php.portals.mbs.ac.uk/spoon.aspx
Title: "Stochastic volatility with self-exciting jumps: Risk Premium and Hedging Implications"

Abstract: We introduce self-exciting jumps to Heston stochastic volatility process to capture the market behaviour after a big equity price drop, and estimate risk premium for jumps and stochastic volatility from equity return series and option data. Instead of using option prices directly, we use cumulants and the nuber of factors implied by the SPX vol surface. We use particle filter nested in an EM framework for the joint estimation. The evidence of high skewness in 2008 shows time varying jump intensity plays a very important role in the crisis period and explained most of the risk premium, while in other period, stochastic variance accounts for most of the risk premium.

In the second part, we use the joint characteristic function of equity price and state variables to produce a consistent pricing framework for contingent claims on both equity and VIX. Based on linear approximation of jump size, we show that one factor models lead to a constant correlation for VIX futures of all maturity. In the multi-factor models, we demonstrate how to calculate the optimal hedging ratio for VIX option using VIX future. Finally, we derived the unconditional correlation term strucuture of VIX future implied by the model based on the stationary distribution of the state variables. The empirically observed pattern of VIX correlation suggests the two-factor model is adequate for short maturity VIX options but more factors are necessary if longer maturity VIX derivatives are to be priced and hedged accurately.

8月24日（金）(Day 2)
http://www-csfi.sigmath.es.osaka-u.ac.jp/structure/activity/seminar.php?id=87