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Implied Volatility Index

Implied Volatility Index . Kyu Won Choi March 2, 2011 Econ 201FS. Implied Volatility Index. Implied Volatility Index With observed option prices, market’s estimate of the volatility is found Black-Scholes-Merton pricing formula C t observed = C t BSM (p(t), K, T-t, r,  t )

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Implied Volatility Index

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  1. Implied Volatility Index Kyu Won Choi March 2, 2011 Econ 201FS

  2. Implied Volatility Index • ImpliedVolatility Index • With observed option prices, market’s estimate of the volatility is found • Black-Scholes-Merton pricing formula Ctobserved= CtBSM (p(t), K, T-t, r, t) • Depending on the validity of model • Chicago Board Options Exchange (CBOE)’s Market Volatility Index • VIX: Model-free implied volatility for S&P 500 index • Developed by Whaley (1993) • VXN: Model-free implied volatility for Nasdaq 100 index • Since September 2003 • Expected future market volatility over the next 30-day of risk-neutral world

  3. Contents • Leverage Effect & Volatility Feedback Effect • S&P 500 and VIX • Nasdaq 100 and VXN • Jump Detection using RV and BV • Difference between Annualized RV and Annualized VIX • Volatility Risk Premium • Relationship between VIX and VXN

  4. Data Set • Daily closing values of the VIX from 1/3/2000 to 12/31/2010 • Total of 2767days • S&P 500 Prices from 1/3/2000 to 12/31/2010 • Nasdaq 100 Daily Closing Prices from 9/22/2003 to 12/31/2010 • Total of 1834 days • Daily closing values of VXN from 9/22/2003 to 12/31/2010

  5. S&P 500 Index and VIX

  6. S&P 500 Index Returns

  7. Returns and Volatility • Negative and asymmetric relationship btwreturns and volatility • Asymmetric effect when returns decline/volatility increases • Leverage Effect: negative (positive) returns increase financial leverage, stocks riskier, driving up volatility (down) • impact of the lagged returns on the current volatilities (current returns on future volatilities) • Volatility Feedback hypothesis: an increase in volatility leads to a decrease in return • impact of the current volatilities on the future returns • Time-varying risk premiums • Can use GARCH model

  8. Correlation between S&P 500 Index Returns and VIX (negative)

  9. Between return and change in VIX(asymmetry)

  10. Realized Volatility of S&P 500

  11. Bipower Volatility of S&P 500 Index

  12. Relative Jump Contribution

  13. Annualized VIX

  14. The Difference btw Annualized RV and Annualized VIX

  15. Nasdaq 100 Index and VXN

  16. Nasdaq 100 Returns

  17. Correlation between NDX Returns and VXN (negative)

  18. Movement of VIX and VXN

  19. Scatter Plot of VIX and VXN

  20. Further study • VXD (based on DJIA), VSTOXX in France, VDAX-NEW in Germany • Frequency data of them • Look for the relationship • Jump option pricing models • Co-jumping process ? • An implied volatility index follows a stochastic process • Option valuation for stochastic volatility • Time-varying risk premium?

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