# Piterbarg's Rates Squared - Quadratic Models and Arbitrage

I am trying to follow Piterbarg's formulation in "Rates Squared" paper for QG model. It looks like he is ignoring the third Riccati equation in favour of an arbitrage condition in $T$ forward measure.

It doesn't look like the typical arbitrage condition. Does anybody know if the third equation and his arbitrage equation for $\alpha$ are equivalent? Can it be proved to be equal?

Thanks.

• Can you please be more specific on where he ignored the third equation (i.e., (3))? – Gordon Aug 2 '18 at 13:51