Overview
Model based sensitivity analysis starts with a model that computes the value of a fixed income instrument from a set of underlying parameters. The following shows an example function.
{% value = f(x_1,x_2, ... , x_n) %}
Underlying Factors
Sensitivity
The sensitivity of a security (or portfolio) to factor i is given by
{% sensitivity_i = \frac{\partial f}{\partial x_i} %}
That is, it is just the
partial derivative
of the value function to the given factor. Sometimes the sensitivity is restated as a percentage, in particular to
make it consistent with
duration
and
convexity
are quoted. In this case, we write
{% sensitivity_i = \frac{1}{P} \frac{\partial f}{\partial x_i} %}