interest rate model

It will be great help if some one explains the differnce betweeen 1 factor int. rate model and 3 factor int. rate model ? What are these “factors”? Thanks in advance …Parket

How about I do 1 factor vs 2 factor and then you figure out 3 factor? A 1-factor interest rate model is a model with 1 source of randomness. Thus, the original interest rate model is the Vasicek 1-factor model where short rates are given by dr[t] = k* (m- r[t])*dt + s*dW[t] So the change in interest rate in some short time interval is some deterministic shift back to its mean m + normal random variable scaled by s. If s is big, it’s volatile. If s is small it’s not. If k is big, it mean-reverts quickly. If k is small, it mean reverts slowly. The problem is that forward rates all have correlation 1 from any such 1-factor model. This is a problem. So we might make a 2-factor model where r[t] = x[t] + y[t] where x[t] and y[t] both follow Vasicek models with their own parameters. In this case, we probably let the two sources of randomness be correlated. This gives us a much broader choice of correlations of forward rates. Of course, we might want an even broader set of possible correlations for forward rates than we can get with the two factor models and that means we might want a 3-factor model… Edit: The factors, then, are sources of randomness but are not usually specifically identified.