February 6th, 2019, 1:34 pm
Why would anyone think that? I personally would have preferred a simpler SA-CCR -- admittedly probably with bigger flaws -- but with a somewhat flexible approach to its use as a floor. But that's me.
A question about your `3-factor' model: equation (3.11) combined with (3.13). I assume that your [$]dW^i_t[$] are uncorrelated.
Then in [$]t<1[$] there is a singe process active, and:
[$]
dr_t=(\phi(t)-a r_t)dt+\sigma dW_t^1
[$]
In [$]1\le t < 5[$] there are two:
[$]
dr_t=(\phi(t)-a r_t)dt+\sigma \left( \rho_1 dW_t^1 +\sqrt{1-\rho_1^2}dW^2_t \right)
[$]
But of course, the sum of two Brownian motions is another brownian motion, and since that combination is standardized I can introduce the equivalent process:
[$]
dZ_1=\begin{cases}
dW_t^1 & t<1 \\
\rho_1 dW_t^1 +\sqrt{1-\rho_1^2}dW^2_y & 1\le t < 5 \\
\end{cases}
[$]
and recognize that up to [$]t=5[$] the process is just a one factor model with constant parameters in disguise:
[$]
dr_t=(\phi(t)-a r_t)dt+\sigma dZ_t
[$]
(I assume that I could continue this into the next interval, but there is at least one typo in your equation (3.13), so I don't want to get distracted by that.)
I don't see how this model (which appears to be equivalent to a 1-factor model) can lead to the correlation structure you describe. Probably I don't understand something about your construction...