Computational & Applied Mathematics & Statistics Events
[PAST EVENT] Mathematics Colloquium - Ed Chadraa, William & Mary
Access & Features
- Free food
- Open to the public
Title:
Estimating Variance Swap Payoff and Volatility Index using Continuous-Time GARCH Processes
Abstract:
Trading futures on S&P 500 volatility index and variance swap began on CBOE Futures Exchange in 2004. S&P 500 Volatility Index (Ticker: VIX) is a popular measure of the stock market's expectation of volatility. S&P 500 Variance Futures (Ticker: VA) is another derivative product that recently gained popularity that allows one to speculate on or hedge risks associated with volatility.
Volatility cannot be observed therefore it is difficult to assess which models are better. Among the models that have proven the most successful are the GARCH (Generalized Auto-Regressive Conditionally Heteroskedastic) models, introduced by Engle (1982) and later generalized by Bollerslev (1986). Various attempts have been made to capture the stylized features of financial time-series using continuous-time models. A family of continuous-time GARCH processes, developed by Brockwell et. al. (2006), exhibit many of the characteristic features of observed financial time-series.
In this presentation, one-step forecasted values of VIX are computed using discrete-time GARCH and continuous-time GARCH models to investigate the effectiveness of the models. Also, we compared the payoff estimations for three-year variance swap contracts using past closing prices of the S&P 500 index to provide insight into which model outperforms the other.
Sponsored by: Mathematics