Custom Sensitivity Based Risk Measures
Overview
Sensitivity Base Risk Measures
are measures of risk that ask what the effect of a small change in the market has in the value
of an asset or portfolio of assets. This can be useful because
- Large changes can be somewhat extrapolated from the small change
- The underlying risk factors can be effectively hedged by trading the portfolio so that
the change in value becomes zero for a change in the underlying paramter.
Generic Outline
A
{% value = v(x_1, x_2, ..., x_n) %}
{% \Delta value = v(x_1, ... x_i + \delta_i ..., x_n) - v(x_1, x_2, ..., x_n) %}
Fixed Income Risk
{% value = val(contract, curve) %}
where the curve is function of some parameters
{% curve = curve(x_1, x_2, ...) %}
Here, the parameters could be such things as
- Yield at various points along the curve
- Any of the Nelson Siegel Parameters
- Rate volatility
Then one could calculate
{% sensitivity = val(contract, curve(x_1, x_2, ... x_i + \delta_i , ...)) - \\
val(contract, curve(x_1, x_2, ..., x_i, ...))
%}
Note, you need not increment each input separately. For instance, if there are a set of inputs representing
yields at different points along the curve, you can add a delta to each point, with the result being a level
shift up of the curve.