A hedge exists uniquely only when its instrument exposures are independent. A zero determinant detects exact dependence in a square exposure matrix. This note teaches cofactor expansion for small calculations and the pivot method from LU factorisation for larger ones. We then interpret both methods using two instruments that hedge two measured risks.
Learning objectives. By the end of this note you should be able to:
- compute a determinant via cofactor (Laplace) expansion along any row or column;
- compute a determinant as the product of pivots from elimination, tracking sign flips from row exchanges;
- choose the more efficient method for a given matrix's structure;
- state why the pivot method, not cofactor expansion, is the production approach.
In this lesson
- Cofactor expansion
- The pivot method
- Quant example: independent hedge directions
Before you start
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