Volatility Derivatives

Size: px

Start display at page:

Download "Volatility Derivatives"

Maud Harrell
8 years ago
Views:

1 Volatility Derivatives George Skiadopoulos Dept. of Banking and Financial Management, University of Piraeus & Financial Options Research Centre, University of Warwick Presentation at the Derivatives Forum 3 February, 2008 Athens Based on A series of talks for academics & practitioners at Cass Business School/ City University, INSEAD, Warwick University, Chicago/ Bachelier Society. Boston University, New York University/ Courant Institute of Mathematics. Federal Reserve Bank of N. York. RISK Magazine s Quant Congresses in London & N. York. A number of academic publications: Journal of Banking and Finance, Journal of Futures Markets, REDR. It has also been advertised on the CBOE website 2 1

on A series of talks for academics & practitioners at Cass Business School/ City University, INSEAD, Warwick University, Chicago/ Bachelier Society.

2 Implied Volatility Indices. Outline Volatility Derivatives. Products: Implied vol. derivatives, variance/volatility swaps. Pricing. Some ongoing research. 3 Implied Volatility: Definition & Properties O = f ( S, K, r τ, τσ, ) M t BS t t, imp, t On any given date, the observed implied volatility is a function of the strike and the expiry date of the option. Non-flat implied volatility surface. In addition, the implied volatility surface moves over time (Skiadopoulos et al., REDR, 1999). 4 2

3 Implied Volatility: Definition & Properties O = f ( S, K, r τ, τσ, ) M t BS t t, imp, t On any given date, the observed

3 European Style S&P 100 Options (XEO) Implied Volatility Surface 5 Implied Volatility Indices: Is the Game worth the Candle? Implied volatility indices have mushroomed over the last years. U.S.: VIX, VXO, VXN, VXD, RVX. Europe: VDAX, VDAX-New, VSTOXX, VX1, VX6, VCAC, VAEX, VBEL, VSMI. They eliminate measurement errors & can be used As the underlying asset to implied volatility derivatives. As a leading indicator for the stock market. To forecast the realised volatility. To calculate Value-at-Risk. 6 3

Europe: VDAX, VDAX-New, VSTOXX, VX1, VX6, VCAC, VAEX, VBEL, VSMI.

4 Implied Vol Indices: Indicative Graphs VIX and VDAX 02/02/01 02/08/01 02/02/02 02/08/02 02/02/03 02/08/03 02/02/04 02/08/04 02/02/05 02/08/05 02/02/06 02/08/06 VIX VDAX 7 GVIX & Investor s Gauge of Fear (Skiadopoulos, AFE, 2004) atm implied volatility /10/00 21/12/00 7/02/01 Greek Volatility Indices and FTSE/ASE-20 10/04/01 28/05/01 11/07/01 6/09/01 25/10/01 12/12/01 4/02/02 2/04/02 24/05/02 10/07/02 Vol index (closing prices) 13/09/02 18/10/02 20/12/02 FTSE/ASE FTSE/ASE

5 Implied Volatility Derivatives A growing class of volatility derivatives. They are written on an implied volatility index. Many pricing models have been developed. Dotsis, Psychoyios, and Skiadopoulos (JBF, 2007). They can be used for Speculation & Hedging volatility risk (Psychoyios and Skiadopoulos, JFM, 2006). 9 The CBOE Implied Volatility Derivatives VIX & VXD, VXN, RVX futures (Mar 04/ Apr 05/Jul 07). Underlying: VIX / VXD/ VXN/ RVX. Expiries: Up to six near-term serial months & five months on the February quarterly cycle. Multiplier: $1000. VIX, VXN & RVX options (Feb 06/ Sep 07). Exercise style: European. Expiries: up to three near-term months & up to three additional months on the February quarterly cycle. # of strikes: three with spacing of $2.50. Multiplier: $

9 The CBOE Implied Volatility Derivatives VIX & VXD, VXN, RVX futures (Mar 04/ Apr 05/Jul 07). Underlying: VIX / VXD/ VXN/ RVX.

6 A Look at the Market /26/04 6/26/04 9/26/04 Shortest VIX Futures 12/26/04 3/26/05 6/26/05 9/26/05 12/26/05 3/26/06 6/26/06 9/26/06 12/26/ /26/04 6/26/04 9/26/04 VIX futures Open Interest 12/26/04 3/26/05 6/26/05 9/26/05 12/26/05 3/26/06 6/26/06 9/26/06 12/26/06 11 Other types of Volatility Derivatives Variance/Volatility Swaps: forward contracts. They are based on the realised variance/volatility of a stock index. Payoff at maturity: (RV t,t - SR t,t ) * L Variance futures: CBOE S&P month variance futures. CBOE S&P month variance futures. 12 6

12/26/06 11 Other types of Volatility Derivatives Variance/Volatility Swaps: forward contracts.

7 Ongoing Research Konstantinidi, E., Skiadopoulos, G. and Tzagkaraki, E. (2007): Can the Evolution of Implied Volatility be Forecasted? Evidence from European and US Implied Volatility Indices, Working Paper, University of Piraeus. Point-wise forecasting. Interval forecasting. Trading Games 13 Point Forecasts: VIX futures (Konstantinidi et al., 2007) VIX Panel A: Economic Variables Model Point Forecasts Shortest 2nd Shortest Sharpe Ratio % CI (-0.05, 0.11) (-0.06, 0.10) A p % CI (-0.51, 1.00) (-0.45, 0.67) Panel B: AR(1) Point Forecasts Shortest 2nd Shortest Sharpe Ratio % CI (-0.10, 0.06) (-0.12, 0.04) A p % CI (-0.96, 0.25) (-0.81, 0.13) Panel C: VAR Point Forecasts Shortest 2nd Shortest Sharpe Ratio % CI (-0.09, 0.06) (-0.10, 0.06) A p % CI (-0.93, 0.52) (-0.71, 0.40) 14 7

Trading Games 13 Point Forecasts: VIX futures (Konstantinidi et al., 2007) VIX Panel A: Economic Variables Model Point Forecasts Shortest 2nd Shortest Sharpe Ratio 0.03 0.0175 95% CI (-0.05, 0.

8 Recap There is a growing interest in volatility derivatives markets. Underlying index. Derivative products. We have overviewed The underlying asset. The products Some research useful to academics and practitioners. 15 Bibliography Dotsis, G., Psychoyios, D., and Skiadopoulos, G. (2007): "An Empirical Comparison of Continuous-Time Models of Implied Volatility Indices", Journal of Banking and Finance, 31:12, pp Konstantinidi, E., Skiadopoulos, G. and Tzagkaraki, E. (2007): Can the Evolution of Implied Volatility be Forecasted? Evidence from European and US Implied Volatility Indices, Working Paper, University of Warwick. Psychoyios, D., and Skiadopoulos, G. (2006): Volatility Options: Hedging Effectiveness, Pricing, and Model Error, Journal of Futures Markets, 26:1, pp Skiadopoulos, G. (2004): The Greek Implied Volatility Index: Construction and Properties, Applied Financial Economics, 14:16, pp Skiadopoulos, G. (2001): Volatility Smile Consistent Option Models: A Survey, International Journal of Theoretical and Applied Finance, 4:3, pp Skiadopoulos, G., Hodges, S., and Clewlow, L. (1999): The Dynamics of the S&P 500 Implied Volatility Surface, Review of Derivatives Research, 3:3, pp

(2007): "An Empirical Comparison of Continuous-Time Models of Implied Volatility Indices", Journal of Banking and Finance, 31:12, pp. 3584-3603. Konstantinidi, E., Skiadopoulos, G. and Tzagkaraki, E.

9 Thank you for your attention & time!

The Greek Implied Volatility Index: Construction and. Properties *

The Greek Implied Volatility Index: Construction and Properties * George Skiadopoulos ** This Draft: 27/08/2003 - Comments are very welcome Abstract There is a growing literature on implied volatility