What is Cross-gamma?

Example 3.14 (The second-order term of the hook)

On the move of 21 October 2022 the book’s ladder gives a first-order loss of exactly USD 3 000 000 (by construction); full revaluation gives $-3\,077\,970$. The gamma matrix, computed by central differences, gives $\tfrac12\,\delta q^\top\Gamma\,\delta q = -78\,189$, which accounts for the difference to within USD 220. The book’s parallel gamma is $-377$ dollars per square basis point: it is short convexity, mostly through its thirty-year payers.