# Learning Center

SAFE TOOLBOXES® comes with many types of models to deal with interest rates. They are presented in the table below:

Model Objective

Vasicek

Models the evolution of short-term interest rates.

CIR (Cox–Ingersoll–Ross)

Models the evolution of short-term interest rates.

Svensson

Models the full yield curve from market data.

Nelson and Siegel

Models the full yield curve from market data.

HJM (Heath-Jarrow-Morton)

Models the full yield curve from market data and its evolution over time.

Cubic spline

Interpolate over some set of yield nodes already calculated using any yield curve construction method.

Flat forward

Interpolate over some set of yield nodes already calculated using any yield curve construction method.

All above functions follow a very convenient syntax in their name definitions. They all begin with “sInterestRates_” followed by the name of the model and an end that has the following meaning:

• FIT: Get the parameters of the model from data.
• RAND: Returns a random yield or random curve.
• SpotYield: Returns the yield that discounts the cash flow at time t to the present time.
• PriceZeroCouponBond: Returns the discounting factor the cash flow at time t to the present time.
• PRICES: Returns the prices of a list of fixed income instruments.

Let’s illustrate all these functionalities using the Vasicek model as an example. The fitting inputs for this model is a list of historical short-term interest rates, as the ones shown below:

 A B C D 1 Historical short term interest rates 2 3 Time Rate 4 0 0.055 5 0.01 0.054649 6 0.02 0.052634 7 0.03 0.052038 8 0.04 0.050721 9 0.05 0.051034 10 0.06 0.050217 11 0.07 0.050458 12 0.08 0.050591 13 0.09 0.049645 14 0.1 0.052252 ... ... ... ... ... 223 2.19 0.090403 224 2.2 0.09004 225 2.21 0.089473 226 2.22 0.090949 227 2.23 0.094295 228 2.24 0.096013 229 2.25 0.09709 230 2.26 0.097574 231 2.27 0.09818 232 2.28 0.098084 233 2.29 0.095937 234 2.3 0.092375 235 2.31 0.091961 236 2.32 0.092919 237

To fit the model, at the Financial Toolbox tab select the option “Interest rate models” in the “Market” group. Then fill the fields as following:

After confirming, a new sheet will appear with the fitted parameters for the model and some sample applications that you can quickly adapt to calculate something that you want.