## Hazard Rates

The relationship between the hazard rate , survival probability and the forward hazard rate is

Where represents the risk-neutral expectation conditional on information at time and .

Initial survival probabilities are represented as a log survival probability curve defined as where and for .

## HWHazardRateModel

The Hull-White instantaneous hazard rate process is modeled as:

All symbols defined as per Hull White 1 factor for interest rates. The final form of the model is

Where:

- ,