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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.

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