For a function of one variable, *f* (*x*), the Taylor Series formula is:*f* (*x* + *Δx*) = *f* (*x*) + *f* ^{′}(*x*)*Δx* + 1/2 *f* ^{′′}(*x*)(*Δx*)^{2} + *. . .* + 1*/n*! *f* ^{(n)}(*x*)(*Δx*)^{n} + *. . . .*
where *f* ^{′}(*x*) is the first derivative, *f* ^{′′}(*x*) the second derivative, *f* ^{(n)} (*x*) the *n*-th derivative, and so on. In practice, we usually just use the first two derivatives, and ignore the effect of the remaining *higher-order* terms:*f* (*x* + *Δx*) - *f* (*x*) = *f* ^{′}(*x*)*Δx* + 1/2 *f* ^{′′}(*x*)(*Δx*)^{2} + Higher Order Terms

For example, considering the Price-Yield formula for bonds, we have:

A similar formula holds for functions of several variables *f* (*x*_{1} *, . . . , x*_{n}). This is usually written as

For example, using Black′s Formula, the expected P&L of an option is usually computed by considering the first-order ...

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