

NelsonSiegel Yield Curve Model »download NEW: Nelson & Siegel with Svensson 1994 extension
The Excel model does not just illustrate the model
but, as an illustrative example, fits a term structure of spot rates
References:
 
NelsonSiegel Yield Curve Model with Svensson 1994 Extension »download
References:  
OneFactor Interest Rate Models »downloadError in calculation of A (missing
brackets) in CIR model fixed 26/10/05. Hint from Rafael Nicolas Fermin from
the Richard Ivey School of Business, University of Western Ontario The pictures below show how rates will be distributed in the very longrun, i.e. their probability distribution after the effect of the initial spot rate r at t=0 has vanished. Both distributions have a mean of b (the longterm equilibrium). Yet under Vasicek they are normally distributed and so there is a probability for them being negative. For the CIR model this density function has the property of a Gamma distribution, not allowing for negative interest rates. 
Model parameters for above distributions: a = 0.15, b = 6%, s =0.02 (Vasicek)/0.05(CIR)
References:
Vasicek, O. 1977 "An Equilibrium Characterization of the term structure." Journal of Financial Economics 5: 177188.
Cox, Ingersoll, and Ross. "A Theory of the Term Structure of Interest Rates". Econometrica, 53 (1985). 385407.
Hull, John C., Options, Futures & Other Derivatives. Fourth edition (2000). PrenticeHall. P. 567f
Interest
Rate Trinomial Tree  Hull & White Method »download

This model presents the general treebuilding procedure as proposed by Hull and White for a more general group of onefactor models.
It handles spot interest rate processes that follow of the following general form:
With constants a (pullback factor of mean reversion process) and s the volatility parameter of Wiener process dz for f(r) = r and f(r) = ln(r) At time t the process reverts to a level q(t)/a. q(t) is set to fit the current term structure of interest. It is a property of these models that they can be fitted to any term structure of interest.
Normal Model
Lognormal Model
Below is a screenshot of the Excel/VBA model. Note the threshold factor 0.184 which was proposed by Hull & White to avoid unnecessary sampling of unlikely interest rate scenarios. It basically determines the maximum number of interest rate steps in the grid. Obviously the model as it stands now has limited practical use but it can now easily be extended to price interest rate sensitive instruments like bonds and interest rate options. This is done by rolling the payoff of the instrument back trough the tree, discounting at the interest rates determined at each node. To understand the basic idea, refer to Cox, Ross & Rubinstein Binomial Tree in this website for an example of equity option valuation in a binomial tree.
Reference:
Adapted from Hull, John C., Options, Futures & Other Derivatives. Fourth edition (2000). PrenticeHall. p. 580.
Literature:
Hull, J. White, A. "Numerical Procedures for Implementing Term Structure Models I: Single factor models", Journal of Derivatives 2, 1 (1994), 716.
Hull, J. White, A. "Using HullWhite Interest Rate Trees", Journal of Derivatives, (Spring 1996), 2636.f
