Financial curiosity

[Matt Agajanian]

Hi all.

No got an MBA. Just a casual question. I’ve noticed most financial calculations use natural logarithms (base e). Most notably, the Exponential Curve Fit. What is it about Natural Logarithm that it is applied so frequently?

Thanks.

[ijabbott]

Continuous compounding of interest uses the natural anti-log.

[Valentin Albillo]

(03-09-2022 11:13 PM)Matt Agajanian Wrote:  I’ve noticed most financial calculations use natural logarithms (base e). Most notably, the Exponential Curve Fit.

It doesn't matter what base (e or 10, say) is used for an Exponential Curve Fit   y = a*e^bx, because the term b would simply absorb the conversion factor between the bases, i.e.,

        y = 3*e^{5 x} = 3*10^{(0.43429*5*x)} = 3*10^{2.17147 x}

so using one base or another is just a matter of taste or convenience if you lack some of the functions. Mathematically, there's no difference.

V.

[Frido Bohn]

I think that the algorithms used for computation produce natural logarithms. The decadic logarithm (base 10) is then calculated as log(x)=ln(x)/ln(10), where ln(10) is implemented as a constant.
The use of the natural logarithms thus spares an additional calculation step, i.e., is more efficient.

[Albert Chan]

Compounding effect involve use of powers, and powers can easily transformed into ln/exp pairs

(1+r/n)^(n*t) - 1 = exp((n*t)*ln(1+r/n)) - 1 = expm1((n*t)*log1p(r/n))

This term pop out in financial calculations many times.
Evaluate it via log1p/expm1 is more accurate.