Presentation about Asymmetric Volatility at the London Traders & Investors Club

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)

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 asset price , Pt denotes the price at time t whilst Pt-1 represents the price at time t-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 NOT TO 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