Hi, I have 2 questions on this topic: 1) Why "Single factor short-rate models mean that all maturities behave in the same way - there is no independence"? 2) On page 32 of the CMP, it states that by the state price deflator approach, r(t) = - \mu_A(t). Is there a way to intuitively understand this formula? Or how to derive it formally? Would appreciate any thoughts on this. Thanks!
1) The single factor models are driven by a single standard Brownian motion engine, and so there just isn't enough flexibility to generate yield curves that can twist - all maturities behave in the same way (ie they either all move up or all move down). A two-factor model, using two standard Brownian motions, can be constructed to overcome this limitation, but it's a lot harder to deal with. 2) The state-price deflator content hasn't been in this chapter for some years (it was removed in 2022). Check to make sure you're using the most up-to-date version of the course.
