1. Traders and Investors Club
Asymmetric Volatility and Leverage Effect

2. Introduction
1)THEORY AND DEFINITIONS
2) VOLATILITY PROXY AND LOG-RETURNS
3) STOCHASTIC VOLATILITY
3A) STOCHASTIC VOLATILITY CHARTS: GOLD,CRUDE OIL,FTSE and EURO vs DOLLAR
3. Leverage Effect
1) Negative returns seemed to be more important predictors of volatility than positive returns. Large prices declines forecast greater volatility than similarly large prices increases (R. Engle)
4. Leverage Effect
2)Volatility of stocks tends to increase when the price drops (F. Black)
3)Negative correlation between past returns and future volatility(J.P. Bouchaud)
5. Types of Volatility
Actual Historical
Volatility over a specified period but with the last observation on a date in the past
6. Types of Volatility
Actual Future
Volatility over a period starting at the current time and ending at a future date (options expiration date)
7. Types of Volatility
Implied
Volatility observed from historical prices of options
(Black-Scholes model)
8. Types of Volatility
Stochastic Volatility
Tendency of volatility to revert to some long-run mean value (GARCH family models, Chen model, Heston model, etc)
9. Proxy for Volatility
True volatility cannot be observed because it is very difficult to separate:
- market-wide factors (systematic variables)

stock-specific factors (idiosyncratic variables).

Therefore, log-normal returns are usually employed as a proxy for the true volatility.
10. Log-Normal Returns
The log-normally distribution of data allows for a more accurate estimation of the return sensitivity for a given change in the information set available in the market for any given time period
11. Log-Normal Returns
Rt = ln (Pt / Pt-1)
Where Rt denotes the log - return at time t for the assetprice , Pt denotes the price at time t whilst Pt-1 represents the price at timet-1.
12. Stochastic Volatility
GARCH Model: GARCH (Generalised Autoregressive Conditional Heteroskedasticity) it assumes that the randomness of variance process varies with variance.
13. Stochastic Volatility
The GARCH variance is a weighted average of 3 different variables:
1) Long run average volatility
2) Forecasted volatility values calculated in previous period
3) New information not available when the previous forecast was made
14. Crude Oil Futures Market
15. News Impact Curve CL1
16. Residuals Crude Oil
17. Gold Futures Market
18. News Impact Curve Gold
19. Residuals - Gold
20. FTSE 100
21. News Impact Curve FTSE100
22. Residuals FTSE100
23. Euro vs Dollar
24. News Impact Curve EurvsDol
25. Residuals Euro vs Dollar
26. VIX
27. Crude Oil 10 years Impact Curve
28. Conclusions
The analysed markets present strong evidence of leverage effect processes
The financial crises re-shaped many markets that were usually considered NOTTO BE LEVERAGED (Currency markets, Crude Oil , Gold, commodity markets)
29. Conclusions
In leveraged markets returns drop much more quickly than normal markets
Asymmetric volatility can be used to scale trades and re-enforce short or long positions
Asymmetric volatility is often used in options and futures strategies both for speculating and hedging purposes