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Detecting Jump Activity on Ultra-High Frequency VIX Data

  • Yueh-Neng Lin Department of Finance National Chung Hsing University 250, Kuo-Kuang Road, Taichung, Taiwan
  • Jeremy C. Goh Lee Kong Chian School of Business Singapore Management University 50 Stamford Road, Singapore 178899
The study indicates that a continuous component and infinite activity jumps are present in the ultra-high frequency VIX data, especially when taking into account the impact of market microstructure noise on various statistics. The degree of jump activity is in the range from 1.71 to 1.95, indicating a very high degree of jump activity. The total quadratic variation can be split into a continuous component of 29% and a jump component of 71%, which by construction is attributable to small and large jumps. The study further examines two jump-diffusion models in the Levy process class using front-month VIX futures data from Q2 2006 to Q3 2009. Using one-day lagged structural parameters, modeling finite-activity jumps is important for pricing. But for simple trading strategies, incorporating infinite-activity jumps yields the best performance with an average absolute error of one-and-a-half to two volatility points each day.

  • Yueh-Neng Lin
  • Jeremy C. Goh
The study indicates that a continuous component and infinite activity jumps are present in the ultra-high frequency VIX data, especially when taking into account the impact of market microstructure noise on various statistics. The degree of jump activity is in the range from 1.71 to 1.95, indicating a very high degree of jump activity. The total quadratic variation can be split into a continuous component of 29% and a jump component of 71%, which by construction is attributable to small and large jumps. The study further examines two jump-diffusion models in the Levy process class using front-month VIX futures data from Q2 2006 to Q3 2009. Using one-day lagged structural parameters, modeling finite-activity jumps is important for pricing. But for simple trading strategies, incorporating infinite-activity jumps yields the best performance with an average absolute error of one-and-a-half to two volatility points each day.
Ultra-high frequency VIX,Infinite jump activity,Finite jump activity,Brownian motion,VIX futures,Quadratic variation