Empirical evaluation of the market price of risk using the CIR model

We describe a simple but effective method for the estimation of the market price of risk. The basic idea is to compare the results obtained by following two different approaches in the application of the Cox–Ingersoll–Ross (CIR) model. In the first case, we apply the non-linear least squares method to cross sectional data (i.e., all rates of a single day). In the second case, we consider the short rate obtained by means of the first procedure as a proxy of the real market short rate. Starting from this new proxy, we evaluate the parameters of the CIR model by means of martingale estimation techniques. The estimate of the market price of risk is provided by comparing results obtained with these two techniques, since this approach makes possible to isolate the market price of risk and evaluate, under the Local Expectations Hypothesis, the risk premium given by the market for different maturities. As a test case, we apply the method to data of the European Fixed Income Market.