+ Implied Volatility Index Kyu Won Choi March 2, 2011 Econ 201FS
Feb 23, 2016
+
Implied Volatility Index Kyu Won Choi
March 2, 2011Econ 201FS
+ Implied Volatility Index
Implied Volatility Index With observed option prices, market’s estimate of the volatility is
found Black-Scholes-Merton pricing formula
Ctobserved = Ct
BSM (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
+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
+Data Set
Daily closing values of the VIX from 1/3/2000 to 12/31/2010 Total of 2767 days
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
+ S&P 500 Index and VIX
+ S&P 500 Index Returns
+Returns and Volatility
Negative and asymmetric relationship btw returns 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
+Correlation between S&P 500 Index Returns and VIX (negative)
+Between return and change in VIX(asymmetry)
+Realized Volatility of S&P 500
+Bipower Volatility of S&P 500 Index
+Relative Jump Contribution
+Annualized VIX
+The Difference btw Annualized RV and Annualized VIX
+ Nasdaq 100 Index and VXN
+ Nasdaq 100 Returns
+Correlation between NDX Returns and VXN (negative)
+Movement of VIX and VXN
+Scatter Plot of VIX and VXN
VIX VXNMean 20.66
2524.1188
Standard Deviation
10.7854
9.6296
Skewness 2.2256
2.3771
Kurtosis 9.0324
10.3726
+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?