216 Frequently Asked Questions In Quantitative Finance
What is Asymptotic Analysis and How
is It Used in Financial Modelling?
Short Answer
Asymptotic analysis is about exploiting a large or small
parameter in a problem to find simple(r) equations or
even solutions. You may have a complicated integral
that is much nicer if you approximate it. Or a par-
tial differential equation that can be solved if you can
throw away some of the less important terms. Some-
times these are called approximate solutions. But the
word ‘approximate’ does not carry the same technical
requirements as ‘asymptotic.’
Example
The SABR model is a famous model for a forward rate
and its volatility that exploits low volatility of volatility
in order for closed-form solutions for option prices to
be found. Without that parameter being small we would
have to solve the problem numerically.
Long Answer
Asymptotic analysis is about exploiting a large or small
parameter to find simple(r) solutions/expressions. Out-
side finance asymptotic analysis is extremely common,
and useful. For example almost all problems in fluid
mechanics use it to make problems more tractable. In
fluid mechanics there is a very important non-dimensional
parameter called the Reynolds number. This quantity is
given by
Re=
ρUL
μ
,
whereρis the density of the fluid,Uis a typical velocity
in the flow,Lis a typical lengthscale, andμis the fluid’s
