March 2015
Intermediate to advanced
740 pages
23h 17m
English
Content preview from Risk Management and Financial Institutions, 4th Edition
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APPENDIX G Taylor Series Expansions
Consider a function z = F(x). When a small change Δx is made to x, there is a corresponding small change Δz in z. A first approximation to the relationship between Δz and Δx is
(G.1)
This relationship is exact if z is a linear function of x and approximate in other situations. A more accurate approximation is
(G.2)
This relationship is exact if z is a quadratic function of x and approximate in other situations. By adding more terms in the series, we can increase accuracy. The full expansion is
where ! denotes the factorial function: 2! = 2 × 1 = 2$; $3! = 3 × 2 × 1 = 6$; $4! = 4 × 3 × 2 × 1 = 24; and so on.
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