Tag: VIX

Volatility

Introduction

Historical volatility and implied volatility.
Read: Part I, Part II

Nifty volatility

Density plots of historical volatility over different horizons.
Read: NIFTY Volatility, Historical Perspective
Charts that are updated often: Volatility and VIX Charts

Dollar ETF volatilities

When you convert Indian indices to dollars, their volatility profile changes.
Read: INDA vs. SPY Observed Volatility

VIX – Implied Volatility Index

Do VIX indices across markets have any relationship with each other?
Read: India VIX vs. SPX VIX

Can a simple VIX based trading strategy avoid market losses?
Read: Macro Volatility and the NIFTY 50, VIX and Equity Index Returns, Part I, Part II.

Can VIX be predicted using a simple model?
ARMA + GARCH to Predict VIX

India VIX vs. SPX VIX

The VIX index is considered a gauge of fear in the markets. A high VIX entails high option implied volatility and occurs when traders bid up options. Given the recent market turbulence where pretty much all asset classes and equity markets across the board tanked, we wanted to check if VIX indices across markets had any relationship with each other.

VIX since 2009

The India VIX index was introduced only in 2009. Let’s start by plotting it vs. the S&P 500 (SPX) Vix to see if it passes a visual sniff test.

vix.historical

We can see at least five instances where India Vix popped without a corresponding move by SPX VIX.

Distribution

The problem with trying to nail down a relationship between the two indices is that, as one would expect, India VIX is way more dispersed than its SPX counterpart. Here’s the density plot.

india vix - spx vix density plot

India vs. spx vix density plot by year.

They might share the same suffix, but they are two completely different beasts.

Cross-correlation

The plots above look at VIX levels. Maybe we should check if the changes in VIX are related. Here’s the cross-correlation plot.

india vix and spx vix cross-correlation plot

India vix and spx vix cross correlation by year.

Conclusion

We cannot really use the two Vix indices to predict each other’s moves.

ARMA + GARCH to Predict VIX

GARCH(1,1)

GARCH(1,1) is a common approach for modeling volatility. They were developed by Robert Engle to deal with the problem of auto-correlated residuals (which occurs when you have volatility clustering, for example) in time-series regression.

What we did:

  1. Picked the best fit ARIMA(p,d,q) model for historical VIX over different look back periods
  2. Created a GARCH(1,1) model based on ARMA(p,q)
  3. Predicted t+1 VIX

500-day lookback

We found that modeling based on the previous 500-day VIX closing levels gave us the least prediction errors. The appendix has the charts for other lookback periods.

Prediction vs. Actual

VIX.prediction.500

Note how in some periods, the predicted value (red) is just the previous value.

Prediction error

VIX.prediction.pctError.500

Values less than zero implies that the model prediction overshoots the actual VIX level the next day.

Prediction vs. Actual Density Plot

VIX.prediction.density.500

The model bias towards higher estimation of VIX is made explicit here.

Next steps

We will integrate this model to our morning ‘Options Daily’ posts so that we get an idea of both the current state of VIX and the expected modeled behavior.

Caveats:

  1. The 500-day lookback is purely empirical. Maybe some other look-back period that we have not tested would have been ideal to model. We will never know.
  2. Only the known history can be modeled. The outputs should be used along with market determined proxies of expected volatility.
  3. There is always a probability distribution around a predicted value. We will publish this in our daily posts.

Appendix

VIX.pacf

VIX.acf

VIX Model vs. Actual across various lookback periods. (pdf)

quant.stackexchange

Volatility Forecasting I: GARCH Models, Rob Reider (pdf)