Table 1

	Hull-White*	AD&Co two-factor Gaussian
Zero-coupon rate distribution	Normal	Normal
Input set	Yield curve + ATM swaption matrix	Yield curve + ATM swaption matrix + correlations of 2 long rates with the short rate
Calibration to yield curve	Analytical, exact	Analytical, exact
Calibration to ATM swaption volatility matrix	Analytical, using very accurate approximation	Analytical, using very accurate approximation
Correlations between rates	100%	User-controlled, constant
Volatility specification	Time-dependent or constant	Time-dependent or constant
Mean reversion(s)	Constant	Two constants
Path sampling	Over pre-built lattice	Lattice-free, analytical

* AD&Co implementation

Here are the main features of our two-factor model:

Transparent mathematical definition. The short rate is defined as the sum of two correlated single-factor (Orstein-Ulenbeck) processes, r(t) = q(t) + x₁(t) + x₂(t) where q(t) is the rate calibrating function. Processes x₁(t) and x₂(t) are normal, zero-centered, with constant mean reversions and either constant or time-varying volatilities. Note that every two-factor Guassian model with real eigen-values can be defined (or redefined) this way.

 

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