asymmetric volatility
DESCRIPTION
Presentation about Volatility Trading Techniques at London Traders & Investors ClubTRANSCRIPT
Traders and Investors Club
Asymmetric Volatility and Leverage Effect
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
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)
Leverage Effect2)”Volatility of stocks tends to
increase when the price drops” (F. Black)
3)”Negative correlation between past returns and future volatility”(J.P. Bouchaud)
Types of Volatility
Actual Historical
Volatility over a specified period but with the last observation on a date in the past
Types of Volatility
Actual Future
Volatility over a period starting at the current time and ending at a future date
(options’ expiration date)
Types of Volatility
Implied
Volatility observed from historical prices of options
(Black-Scholes model)
Types of Volatility
Stochastic Volatility
Tendency of volatility to revert to some long-run mean value (GARCH family models, Chen model, Heston model, etc)
Proxy for VolatilityTrue 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.
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
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.
Stochastic Volatility
GARCH Model: GARCH (Generalised Autoregressive Conditional Heteroskedasticity) it assumes that the randomness of variance process varies with variance.
Stochastic VolatilityThe 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
Crude Oil Futures Market
.01
.02
.03
.04
.05
.06
.07
07M07 08M01 08M07 09M01 09M07 10M01
Conditional Standard Deviation
News Impact Curve – CL1
.000
.004
.008
.012
.016
.020
.024
-25 -20 -15 -10 -5 0 5 10 15 20 25
Z
SIG
2
Residuals – Crude Oil
0
10
20
30
40
50
60
70
80
90
-2.50 -1.25 0.00 1.25 2.50 3.75
Series: Standardized ResidualsSample 1/03/2007 3/01/2010Observations 795
Mean -0.016696Median -0.009076Maximum 3.618355Minimum -3.375965Std. Dev. 0.998636Skewness -0.079619Kurtosis 3.092973
Jarque-Bera 1.126280Probability 0.569418
Gold Futures Market
.008
.012
.016
.020
.024
.028
07M07 08M01 08M07 09M01 09M07 10M01
Conditional Standard Deviation
News Impact Curve – Gold
.00
.01
.02
.03
.04
.05
-25 -20 -15 -10 -5 0 5 10 15 20 25
Z
SIG
2
Residuals - Gold
0
40
80
120
160
200
-4 -2 0 2 4
Series: Standardized ResidualsSample 1/03/2007 3/01/2010Observations 795
Mean -0.025197Median 0.011170Maximum 4.780058Minimum -5.287299Std. Dev. 1.001487Skewness -0.315884Kurtosis 5.191299
Jarque-Bera 172.2805Probability 0.000000
FTSE 100
.00
.01
.02
.03
.04
.05
.06
07M07 08M01 08M07 09M01 09M07 10M01
Conditional Standard Deviation
News Impact Curve – FTSE100
.000
.004
.008
.012
.016
.020
-25 -20 -15 -10 -5 0 5 10 15 20 25
Z
SIG
2
Residuals – FTSE100
0
10
20
30
40
50
60
70
80
90
-3.75 -2.50 -1.25 0.00 1.25 2.50
Series: Standardized ResidualsSample 1/02/2007 3/01/2010Observations 801
Mean -0.010717Median 0.035188Maximum 3.253203Minimum -4.090106Std. Dev. 0.993679Skewness -0.367643Kurtosis 3.571112
Jarque-Bera 28.92990Probability 0.000001
Euro vs Dollar
.002
.004
.006
.008
.010
.012
.014
.016
07M01 07M07 08M01 08M07 09M01 09M07 10M01
Conditional Standard Deviation
News Impact Curve – Eur vs Dol
.0000
.0001
.0002
.0003
.0004
-25 -20 -15 -10 -5 0 5 10 15 20 25
Z
SIG
2
Residuals – Euro vs Dollar
0
20
40
60
80
100
-3.75 -2.50 -1.25 0.00 1.25 2.50 3.75
Series: Standardized ResidualsSample 1/01/2007 2/26/2010Observations 825
Mean -0.004203Median -0.014799Maximum 4.468386Minimum -3.666132Std. Dev. 0.992727Skewness 0.021811Kurtosis 3.562993
Jarque-Bera 10.96096Probability 0.004167
VIX
1 29 57 85 1131411691972252532813093373653934214494775055335615896176456737017297577850
10
20
30
40
50
60
70
80
90
Series1
Crude Oil 10 years Impact Curve
.000
.001
.002
.003
.004
.005
.006
.007
-25 -20 -15 -10 -5 0 5 10 15 20 25
Z
SIG
2
ConclusionsThe 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)
ConclusionsIn 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