Eirini Konstantinidi 1 , George Skiadopoulos 2 , and Emilia Tzagkaraki 1

1. Can the Evolution of Implied Volatility be Forecasted? Evidence from European and U.S. Implied Volatility Indices Eirini Konstantinidi1, George Skiadopoulos2, and Emilia Tzagkaraki1 1,2 Dept. of Banking and Financial Management, University of Piraeus 2 Financial Options Research Centre, University of Warwick International Workshop in Economics and Finance 2007 15 June, 2007

2. Outline • Motivation – Main Contributions – Implied Volatility Indices . • The Data Set. • Daily horizons: Point forecasts. • In-sample & Out-of-sample performance: Models & Metrics. • Daily horizons: Interval forecasts. • Construction: Historical/ Monte Carlo Simulation. • Accuracy: Statistical Test & Trading Games. • Monthly horizons. • Conclusions. Konstantinidi Eirini (University of Piraeus) 2 / 24

3. Motivation • Implied volatilities change over time. • Is it important to know whether changes in implied volatility • are predictable? • Asset pricing. • Predictability of asset prices. • Option trading strategies. • Market efficiency. • The empirical evidence is mixed. • This paper contributes to this ongoing discussion. Konstantinidi Eirini (University of Piraeus) 3 / 24

4. Main Contributions • Extensive data set of European and U.S. implied volatility indices • is employed. • Point & Interval forecasts are formed. • Horse race among alternative model specifications is performed. • Economic significance in the CBOE volatility futures markets is • assessed. • Predictability across various horizons is examined. Konstantinidi Eirini (University of Piraeus) 4 / 24

5. Implied Volatility Indices • Implied volatility indices have mushroomed over the last years. • US: VIX, VXO, VXN, VXD • Europe: VDAX, VSTOXX, VX1, VX6 • They eliminate measurement errors and can be used: • As the underlying asset to implied volatility derivatives. • In strategies with stocks and options. • To forecast the realized volatility. • To calculate Value-at-Risk. • The properties of implied volatility indices have been studied in • continuous and discrete time. • Unanswered Question: Can the dynamics of implied volatility • indices be forecasted? Konstantinidi Eirini (University of Piraeus) 5 / 24

6. The Data Set • Daily / Monthly data (closing prices) on implied volatility indices • & economic variables. • 02/02/2001 – 17/03/2005: In-sample point forecasts. • 18/03/2005 – 08/01/2007: Out-of-sample point forecasts. • Daily data (settlement prices) on volatility futures. • 18/03/2005 – 08/01/2007: Interval forecasts & Trading games. • VIX & VXD futures • Underlying assets: VIX & VXD. • Contract size: VIX*1000 & VXD*1000. • The three shortest series are constructed. Konstantinidi Eirini (University of Piraeus) 6 / 24

7. The Data Set: Implied Volatility Indices Konstantinidi Eirini (University of Piraeus) 7 / 24

8. The Data Set: Economic Variables Konstantinidi Eirini (University of Piraeus) 8 / 24

9. Daily Horizon:Point Forecasts

10. Economic Variables: Contemporaneous Relationships Konstantinidi Eirini (University of Piraeus) 10 / 24

11. Economic Variables: Predictive Power Konstantinidi Eirini (University of Piraeus) 11 / 24

12. Autoregressive Model Konstantinidi Eirini (University of Piraeus) 12 / 24

13. VAR: Spillover Effects & Predictive Power Konstantinidi Eirini (University of Piraeus) 13 / 24

14. PCA: Predictive Power Konstantinidi Eirini (University of Piraeus) 14 / 24

15. Out-of-Sample Performance Konstantinidi Eirini (University of Piraeus) 15 / 24

16. Daily Horizons: Interval Forecasts

17. Interval Forecasts • Interval forecasts are constructed. • By Historical Simulation: N = 250. • By Monte Carlo (MC) Simulation. • For different significance levels: p =1%, 5%. • MC requires a stochastic process. • Dotsis et al. (2006): Merton’s (1976) model provides the best fit. • We increase the sample by the new observation & the model is re-estimated. • The quality of the constructed intervals is assessed by statistical • tests and trading games. Konstantinidi Eirini (University of Piraeus) 17 / 24

18. Interval Forecasts: Christoffersen’s (1998) Test Konstantinidi Eirini (University of Piraeus) 18 / 24

19. Interval Forecasts: Economic Significance • Trading game with VIX / VXD futures. • Trading Rule: Go long (short) if closer to the lower (upper) bound. • Use also Bollinger bands. • Deduct transaction costs. • Calculate average returns & Sharpe ratios. • Bootstrap the p-values. Konstantinidi Eirini (University of Piraeus) 19 / 24

20. Trading Game & VIX Futures: Results Market Sharpe Ratio: 0.922 Konstantinidi Eirini (University of Piraeus) 20 / 24

21. Monthly Horizons

22. Predictability over Monthly Horizons Konstantinidi Eirini (University of Piraeus) 22 / 24

23. Conclusions • Can the evolution of implied volatility indices be forecasted? • Point & Interval forecasts. • Plethora of data sets have been used. • Alternative techniques have been employed. • Parametric predictive regressions (economic variables, spillovers). • Non-parametric specification (PCA). • Historical / MC simulation: Forecast intervals & Trading game with volatility futures Konstantinidi Eirini (University of Piraeus) 23 / 24

24. Conclusions (Cont’d) • In-sample performance: Results • Depend on the horizon. • Depend on the model specification. • Results do not depend on size. • Out-of-sample performance: Results • No superior performance to the random walk model. • Trading games: No economic significance. • Implication: CBOE volatility futures markets are efficient. Konstantinidi Eirini (University of Piraeus) 24 / 24

25. Thank you for your attention !!!