Chapter 2: FAQs 123
Which Numerical Method Should I Use
and When?
Short Answer
The three main numerical methods in common use are
Monte Carlo, finite difference and numerical quadrature.
(I’m including the binomial method as just a simplistic
version of finite differences.) Monte Carlo is great for
complex path dependency and high dimensionality,
and for problems which cannot easily be written in
differential equation form. Finite difference is best for
low dimensions and contracts with decision features
such as early exercise, ones which have a differen-
tial equation formulation. Numerical quadrature is for
when you can write the option value as a multiple
integral.
Example
You want to price a fixed-income contract using the
BGM model. Which numerical method should you use?
BGM is geared up for solution by simulation, so you
would use a Monte Carlo simulation.
You want to price an option which is paid for in instal-
ments, and you can stop paying and lose the option
at any time if you think it’s not worth keeping up the
payments. This may be one for finite-difference methods
since it has a decision feature.
You want to price a European, non path-dependent con-
tract on a basket of equities. This may be recast as a
multiple integral and so you would use a quadrature
method.
