Overview
Also known as the zero volatility spread, it is the spread that when added to the entire rate curve (typically the risk free or Treasury curve), would yield the bond price when its cash flows are discounted by the new curve.
When using continuous compounding , the discounted value of a cash flow is
{% PV = exp(-rT)\times Value %}
Adding a static spread to the above discounting formula yields
{% PV = exp(-(r + \lambda)T)\times Value %}
This effectively means that a static spread effectively multiplies each cash flow by a factor that can be
written as
{% exp(-\lambda T) %}
The static spread thus ties to the
Poisson Model
of
credit risk.