An Empirical Econometric Model for the Mexican Target Rate and its application to determine the Interest Rate Curve

The term structure of interest rates is an extremely important subject in Finance. The rates’ value influences the pricing of practically any asset, and it is also important to determine the value of several liabilities. Its study has been a field of intense research, both from the theoretical point of view as well as from the purely applied point of view. In this work, we review the different approaches that have been taken to describe it with the idea of better understand the reasons subjacent to its assessment. We also propose, for the Mexican case, a novel approach to model empirically the Target Rate that Banco de México (Banxico) sets as part of their monetary policy. We propose a model based on the difference of two Poisson distributions in terms of public data: the monetary decisions taken by the Federal Reserve, the exchange rate, the inflation rate and its expectation, and the economic growth results and expectations. The addition of the expectations, which come from surveys made from Banxico as well, improved the results in a significant manner, showing the relevant value of “soft” data in this type of analysis. Our model also determines the probability of a rise or of a lower of the rate and the amount of this movement as shown in an example of application. Since the Target Rate serves as basis for the other interest rates, modeling it is of extreme importance. After the modelling of this rate was completed, we used this rate as the one-day rate to determine the prices of short-term rate bonds to estimate the given prices with excellent statistical significance. However, for medium-term rates we noticed that this approach was not enough. So, after a deeper analysis of the rate curve, we used our rate together with some macroeconomic variables (namely, public spending without financial costs as a proportion of GDP.) Incorporating this, we established the corresponding behavior of mid-term rates with a very good statistical significance as well.