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wor
king
pap
er
An Investor’s Perspective on
Volatility as an Asset Class:
Evidence from the European
Stock Market
Reinhold HafnerMartin Wallmeier
Mai 2005
risklab germany GmbH
Nymphenburger Str. 112-116
80636 München
Tel. +49.89.1220 7750
wp 05-02
0.8 0.9 1.0 1.1 1.2
0.14
0.16
0.18
0.20
0.22
0.24
0.26
Strike price / Index level
Impl
ied
vola
tility
0.0
0.1
0.2
0.3
0.4
Var
ianc
e sw
ap ra
te
1996 1998 2000 2002 2004
DAXESX
Asian crisis
Russian crisis
W TC attack
Financial crisis
Iraq war0.
00.
10.
20.
30.
4
Var
ianc
e sw
ap ra
te
1996 1998 2000 2002 2004
DAXESX
Asian crisis
Russian crisis
W TC attack
Financial crisis
Iraq war
020
4060
8010
0
Spr
ead
Sw
ap ra
te o
ver A
TM im
plie
d va
rianc
e (in
%)
1996 1998 2000 2002 2004
DAXESX
0.007590.00781
0.001840.00371
0.00278
0.00117 0.00159 0.00122
0.00670
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
DAX 95-04 DAX 00-04 ESX 00-04
AsymmetryCurvatureSlope
01
23
4D AX
Dis
cret
e re
turn
1 9 9 6 1 9 9 8 2 0 0 0 2 0 0 2 2 0 0 4
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
E S X
Dis
cret
e re
turn
2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5
L o g re turn va r ia nc e s w a p D A X
Den
sity
-1 .5 -1 .0 -0 .5 0 .0 0 .5 1 .0 1 .5
0.0
0.2
0.4
0.6
0.8
1.0
L o g re turn va ria nc e s w a p E S XD
ensi
ty-1 .5 -1 .0 -0 .5 0 .0 0 .5 1 .0
0.0
0.2
0.4
0.6
0.8
1.0
-1.5 -1.0 -0.5 0.0 0.5 1.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
Log return variance swap DAX
Log
retu
rn v
aria
nce
swap
ES
X
-0.4 -0.3 -0.2 -0.1 0.0
-1.0
-0.5
0.0
0.5
1.0
1.5
Log return DAX
Log
retu
rn v
aria
nce
swap
DA
X
0.00 0.05 0.10 0.15 0.20 0.25-1
.5-1
.0-0
.50.
00.
5
Log return DAX
Log
retu
rn v
aria
nce
swap
DA
X
-0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00
-1.5
-1.0
-0.5
0.0
0.5
1.0
Log return ESX
Log
retu
rn v
aria
nce
swap
ES
X
0.00 0.05 0.10 0.15 0.20
-1.5
-1.0
-0.5
0.0
0.5
Log return ESX
Log
retu
rn v
aria
nce
swap
ES
X
0.02 0.01 0.01 0.02
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Return volatility
DAXVar Swap
1
2
3
4
5
Expected excess return
