Frequently Asked Questions In Quantitative Finance

Chapter 2: FAQs 65

(A multiplicative factor has been ignored here.) I.e.

−

N

σ

+

1

σ^3

∑N

i= 1

φi^2 = 0.

Therefore our best guess forσis given by

σ^2 =

1

N

∑N

i= 1

φi^2.

You should recognize this as a measure of the variance.

Quants’ salaries In the figure are the results of a 2004
survey onwww.wilmott.comconcerning the salaries of
quants using the Forum (or rather, those answering the
question!).

This distribution looks vaguely lognormal, with distribu-
tion

1

√

2 πσE

exp

(

−

(lnE−lnE 0 )^2

2 σ^2

)

,

whereEis annual earnings,σis the standard deviation
andE 0 the mean. We can use MLE findσandE 0.

It turns out that the meanE 0 =$133,284, withσ= 0 .833.

Figure 2-4:Distribution of quants’ salaries.