Multidimensional Diffusion Models - Computational Methods for Quantitative Finance - page 192

Fig. 13.4 Eigenvalue
spectrum (normalized by s 1 )
of the realized volatility
covariance matrix of the
constituents of the Dow Jones
index over a period of 252
days ( top ) and recovery ratio
η d , d =

1 ,...,d ( bottom )

Table 13.3 First eigenvalues

d

s 2
d

s d η d

s 2

d , d = 1 ,..., 5, of the Dow
Jones realized volatility
covariance matrix Q and
recovery ratio η d

1 0.2052 0.0421 0.5307

2 0.0990 0.0098 0.6542

3 0.0940 0.0088 0.7655

4 0.0791 0.0062 0.8443

5 0.0459 0.0021 0.8708

respectively, and

f(e y ) = f(e y 1 ,...,e y d ,e y d + 1 + λ d + 1 T ,...,e y d + λ d T )

max ( 0 ,e

+

i

+ λ i T

1 α i

y i

1

y i

= − K).

=

i = d +