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## Wednesday, October 29, 2014

### hazard rate - my first lesson

Imagine credit default is caused only by a natural disaster (say hurricane or tsunami). For a brief duration ΔT (measured in Years), we assume the chance of disaster hitting is λ*ΔT, with a constant [1] λ .

Pr(no hit during    A N Y   5-year period)
= Pr (surviving 5 years)
= Pr (no default for the next 5 years from now)
= Pr (T > 5) = exp(-5λ) , denoted V(5) on P522 [[Hull]]

, where T :=  # of years from now to next hit.

This is an exponential distribution. This λ is called the hazard rate, to be estimated from market data. Therefore it has a term structure, just like the term structure of vol.

More generally,  λ could be assumed a function of t, i.e. time-varying variable, but a slow-moving variable, just like the instantaneous vol. In a noisegen, λ  and vol function as configurable parameters.

In http://www.financial-risk-manager.com/risks/credit/edf.html, λ is denoted "h", which is assumed constant over each 12-month interval.

"Hazard rate" is the standard terminology, and also known as "default intensity" or "failure rate".

I feel hazard rate is perhaps the #1 or among top 3 applications of
conditional probability,
conditional distribution,
conditional expectation

So the big effort in studying the conditional probability is largely to help understand credit risk.