Forecasting Volatility in Financial Markets

1
Forecasting Volatility in Financial Markets

• ---- Survey on concepts, motivation, techniques
  and future work

2
Outline

• Preliminaries
• risk, std, volatility
• Motivation
• why to model and forecast volatility?
• Stylized facts in volatility
• Models used in volatility forecasting
• HISVOL, GARCH, ISD, SV and their comparison
• Go where in future?
• Conclusion

3
Preliminaries

• Volatility
• Integrated volatility
• Realized volatility
• Implied volatility derived from the option price
• Other measures of risk
• Volatility is different from risk
• Mean absolute return, inter-quantile range,
  semi-variance

4
Why model forecast volatility?

• Hard to model and forecast return (price) (ACF)
• Financial market uncertainty public confidence
• determine option price, barometer for
  vulnerability
• Stylized facts about volatility
• Volatility clustering, asymmetry and mean
  reversion
• Forecast volatility
• In-sample forecast out-of-sample forecast

5
ACF of return, squared return, and absolute return
6
Forecast evaluation

• Measuring forecast errors
• Mean error (ME), mean square error (MSE), root
  mean square error (RMSE), mean absolute error
  (MSE), mean absolute percent error (MAPE), mean
  logarithm of absolute errors (MLAE). Theil-U,
  LINEX.
• Comparing different models
• Considering serial correlation in errors and
  uncertainty in parameters
• Test error to general loss function
• Judged on measures of economics significance
• Bias prediction power

7
Models for volatility forecast
8
Predictions based on past Stds

• HISVOL historical volatility models
• Random walk, historical averages of squared
  (absolute) returns time series models based on
  historical volatility using moving average,
  exponential weights, autoregressive models,
  fractionally integrated autoregressive absolute
  returns (Appendix A1)
• Omitting the goodness of fit the return
  distribution

9
ARCH class models (1)

• Do not make use of sample std, but formulate
  conditional variance ht via ML.
• one-step ahead forecast available More than one
  step ahead formulated iteratively.
• ARCH(q) ht is a function of q past squared
  returns.
• GARCH(p,q) additional dependencies on p lags of
  past ht.

10
ARCH class models (2)

• Variations
• EGARCH no need to impose estimation constraints,
  asymmetrical dependency
• TGARCH asymmetrical dependency
• Nonlinear GARCH
• IGARCH/FIGARCH introduce I(d) process, allow for
  slow decay (long memory) of ht
• Regime switching GARCH

11
Stochastic volatility model

• Parameter-driven Volatility depends not on post
  observations, but on some (stochastic) latent
  structure. Log-normal SV model
• greater flexibility in modelling volatility
• Substantially harder estimation

12
Regime switching (RS) models

• Market reacts to large and small shocks
  differently. Volatility adjustment in high and
  low volatility follows twin-speed process.
• RS ARCH with leverage effect gt asymmetry version
  of GARCH

13
Extreme value outlier

• ARCH models fail to capture
• Large kurtosis of residuals
• ARCH effect sensitive to large shock
• Volatility persistence artifact of extremes or
  outliers?
• Removed or trimmed or impact separately handled?
• Relation between tails, extremes and outliers
• Residuals scaled by volume approximately
  Gaussian, thick tails removed.

14
Long memory (LM) models

• Some short memory models (e.g. extreme value,
  RS) can also produce long memory
• LM models FIGARCH, FIEGARCH
• Despite lower data frequency, implied outperforms
  LM

15
Right forecast with wrong model?

• Time series models approximate a deeper
  time-varying volatility construction
• Forecast well or not depending on fluctuations in
  the underlying driving variables
• Nelson 92, 95 Misspecified models provide right
  forecast with high frequency.

16
Implied volatility (1)

• Preliminary Black-Schols model, option pricing
  and implied volatility
• Assumption
• constant volatility, no transaction cost or
  taxes, divisible securities, no dividend before
  maturity, no arbitrage, constant risk-free
  interest rate
• More (different) information than other models
  option price
• Forecasting power of option ISD depends on
• Option market efficiency
• Correct option pricing model

17
Implied volatility (2)

• Volatility smile Nonlinear shapes of implied
  volatility against strike price
• Reason
• Distributional assumption
• Stochastic volatility (volatility risk)
• Application in different assets (different
  measurement errors and liquidity)
• individual stocks, stock market index, exchange
  rate
• ATM or weighted implied?
• Different weighting strategy for better
  performance

18
Go where in future?

• Forecast evaluation combining different models
• New information extracted? Accuracy improved?
• Volume-volatility research
• Price-volatility research (guess)
• Forecast return or price with new information?
  (guess)

19
Summary conclusion

• Volatility is forecastable.
• Comparison ?
• Volatility forecasting not violate market
  efficiency?