Advances in Risk Management

RICCARDO BRAMANTE AND GIAMPAOLO GABBI 231

Table 12.2 Regression equation of higher correlation EUR–USD changes
explained by volatility differences

Variable Coefficient Std. error t-statistic Prob.

C 0.256095 0.058295 4.393106 0.0001
DEURV3 3.887041 0.978974 3.970526 0.0002

DUSDV1 3.251217 0.572326 5.680705 0.0000
DUSDV3 −2.514702 0.769123 −3.269570 0.0019

DUSDV8 −2.420236 1.361542 −1.777570 0.0814

R-squared 0.500639 Mean dependent var 0.321851

AdjustedR-squared 0.461473 S.D. dependent var 0.199156
S.E. of regression 0.146150 Akaike info criterion −0.923327
Sum squared residuals 1.089344 Schwarz criterion −0.742492

Log likelihood 30.85316 F-statistic 12.78261
Durbin–Watson stat. 2.262736 Prob(F-statistic) 0.000000

Notes: The dependent variable; differences of exponential correlations between the equity euro mar-
ket and the equity US market. Explanatory variables are DEURV3: equity euro market exponential
volatility differences with 3 days lag; DUSDV1: equity US market exponential volatility differences with
1 day lag; DUSDV3: equity US market exponential volatility differences with 3 days lag; and DUSDV8:
equity US market exponential volatility differences with 8 days lag. C: constant in regression. Number
of observations=bigger 56 daily changes.

0.6

0.4

0.2

0.0

5 10152025303540455055

0.2

0.4

RESID

Number of observations  56 daily changes

Spread between actual and estimated

dependent variable

No. of observations

Figure 12.5Plot of residuals of correlation EUR–USD higher changes

explained by volatility differences

the Euro market 7 days before, and the variation of the volatility measured
in the Japanese market 7 days before (Table 12.4).
Very similar outcomes are found for the US and Japanese market corre-
lations. When we estimate the correlation breakdowns, we obtain a lower