Equity Derivatives and Hybrids by Oliver Brockhaus

Author:Oliver Brockhaus
Language: eng
Format: epub
Publisher: Palgrave Macmillan

where . The correlation of (X1,X2) is invariant under positive linear transformations, namely

if α1 > 0,α2 > 0. Generally, if f1 and f2 are increasing and continuous then

9.2.2 Kendall’s Tau

Kendall’s Tau is defined as:

Here is an independent copy of (X1,X2). The intuition is that first a reference point is sampled from the joint distribution. Then an independent second sample is counted as positive if it is in the right upper or left lower quadrant, or negative otherwise.

If f1,f2 are increasing and continuous, then ρK(X1,X2) = ρK(f1(X1),f2(X2)). Hence Kendall’s Tau is a function of the copula. Indeed

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