Stochastic Volatility Modeling

Multi-asset stochastic volatility 431

ρ(bσ

2

T

, S

1

)/ρ(bσ

2

T

, S

2

)

over several maturities. Likewise, for the determination

of

χ

σσ

, two values are obtained by averaging either

ρ(bσ

1

T

, bσ

2

T

0

)/ρ(bσ

1

T

, bσ

1

T

0

)

or

ρ(bσ

1

T

, bσ

2

T

0

)/ρ(bσ

2

T

, bσ

2

T

0

), for all (T, T

0

) couples.

Note that it is important to use asynchronous estimators – lest we underestimate

correlations; see [12].

S&P500 Stoxx50 S&P500 Stoxx50 NIKKEI S&P500 Stoxx50 S&P500 Stoxx50 NIKKEI

Stoxx50 FTSE NIKKEI NIKKEI KOSPI Stoxx50 FTSE NI KKEI NIKKEI KOSPI

83% 89% 55% 60% 67% 71% 86% 45% 59% 66%

87% 95% 59% 63% 85% 78% 89% 56% 61% 108%

86% 93% 71% 78% 78% 75% 91% 53% 77% 65%

84% 92% 54% 60% 72% 72% 85% 31% 40%