CT 8 INTEREST RATE MODELS

How can one ascertain whether a particular interest model is arbitrage free or not? and why a interest rate model in which interest rates are assumed to be constant cant be regarded as a arbitrage free model ? in the course notes its mentioned that -

"An arbitrage-free model of the term structure is one that generates arbitrage-free bond prices. "

so any model will have assumptions about the future interest rates, so according to that model the bond prices are arbitrage free , then why not constant interest models are arbitrage free ? please help.

 

I'm not sure you're interpreting that statement correctly. It's really just saying that if the bond prices generated by a particular model are arbitrage-free, then we call the model an arbitrage-free model.

You're correct that constant interest rate models (ie a flat yield curve) are not arbitrage-free, as the associated bond prices aren't arbitrage-free. This is effectively the negative of the statement quoted.

To be honest, it's difficult to know whether a given interest rate model is arbitrage-free or not. We're told in Section 4 of Chapter 17, that using the method outlined gives arbitrage-free bond prices, although this is not proved for us, so I'd advise taking that at face value. The three models we go on to study (Vasicek, CIR, HW) are arbitrage-free, but I can't recall an exam question where you've needed to do anything other than state that.

 

Okay ,thanks for the reply sir