Summary

The nature of business requires to be paid or be willing to pay a price for goods and services that will be used in business activities, regardless the core business. Therefore, it is clear that companies need financial resources to enable them to make the payments necessary to carry out their activities. As is well known, there are three main sources of financing: internal resources generated by the same entity, provided by the shareholders of the company and those obtained through the figure of the debt. 
The cost of financing through these sources is determined by applying different models, in the case of equity used equilibrium models, the best known is called the CAPM by its acronym in English (Capital Asset Pricing Model) in the case of debt, there should be an opportunity cost (interest rate) that is attractive to the creditor, which also incorporates the value of money over time, and a premium to cover the probability of default of the organization. In accordance with the rating given by the ratings company or the lender sets, the interest rate should be set on loans to be granted or the yield to maturity that should give the bonus issued by the entity to be finance. Overall, the credit rating determines the opportunity cost of debt, but in the case of Mexican companies, most of them do not have the economic capacity to be characterized by a specialized entity, usually the organizations public or with strong purchasing power that are accessible to be qualified by specialized institutions. This problem is exacerbated when the loans are made between related parties and do not have the credit rating of the issuer of the debt instrument, as in these cases, the transaction might be affected by different economic interests of the parties, taking resulted in the establishment of a credit spread which does not comply with the principle of market value. Due to the above, it is necessary to find a methodology that can be applied widely, so that the cost of debt is directly proportional to the risk of default of the issuing company. 
To resolve this problem, Merton (1974), Leland (1994) and Fan y Sundaresan (2000) developed models that can be used to obtain neutral default probabilities and credit spreads to be added to the base rate. Subsequently, Denzler et al. (2005) proposed two models to convert a default frequency, known by its initials as EDF (Expected Default FrequencyTM) provided by an online system developed by Moody's Investor Service, in a risk-neutral probability of default and turn it into a credit spread. These latter tools have characteristics of both structural models and reduced form. The first is the Brownian Motion Model (BM) and the second is the Power Law Brownian Motion Model (PLBM). Because most of the models mentioned above were calibrated with data from developed economies, this paper decided to try these five models in emerging markets, as is the case of Mexico, considering the debts referenced to a falling base rate to entities listed on the Mexican Stock Exchange during the period from 1998 to 2008. The added value provided by this research is to take information from an emerging market, considering all the challenges involved (inefficient markets, lack of information, relationships between banks and companies, etc.). The following summarizes the main results. 
According to the empirical analysis applied to Mexican data for the period from 1998 to 2008, found that the difference calculated with the Merton model is far from the real value, on average, the Merton (1974) model strongly overestimates the real credit spread. In regard to the Leland model provided the setting is a bit better than that yielded by the Merton model, which is reflected in the statistical value of G, but it remains negative in most years, a exception of fiscal year 2003, while the worst fit occurs in the year 2008. Also, as was done with the Merton model, we compared the actual differential vs. estimated, and in this case the result is mixed, sometimes spreads are underestimated and others are overestimated. Moreover, with respect to the model of Fan y Sundaresan (2000), in the same way as in the investigation conducted by Teixeira (2005), there is an improvement in the adjustment to contrast the results derived from this model with those of Merton (1974) and Leland (1994), however, for the Mexican case, the estimated base points are still far from the actual values, which are underestimated by the model. In accordance with the values of the test statistic G can be inferred that neither the Leland model, or the Fan y Sundaresan (2000) correctly adjusted basis points, but within them the "best" is the Fan y Sundaresan (2000) when bargaining power between creditors and shareholders are balanced (? = 0.5) or slightly biased towards shareholders (? = 0.6).
Once it was found that the results offered by the structural models were not satisfactory, mixed models were tested, and in accordance with estimates made with the Mexican market information (an emerging economy), it was exactly the same conclusion reached by Denzler et al. (2005) (who applied their models in bonds issued in USA and Europe) that approximates the model further the real credit spread is the PLBM. So in summary, this latest model is recomended in this work to companies not listed on public exchanges or do not have a credit rating issued by a rating agency. Just as Teixeira did, we analyzed the residues of the observed and estimated spreads derived from the models closer into actual credit spreads: BM and PLBM, for it is the recovery rate calculated by the equation 118, and looked for variables that could account for suboptimal values of the statistic G. 
In order to conduct a short analysis only for the year 2008, we performed a regression between the residues from these models as the dependent variable and as independent variables the sector of the company (taking the rating given by the Mexican Market Exchange), the leverage ratio, etc. According to these results, it was observed that the regression model does not explain properly to the errors of the BM model. However, when running the regression of the residuals of PLBM with all independent variables were significant level of leverage (borrowing), but only measured by long-term debts, as well as performance in the stock price , the type of industry, with significant that organizations belonging to the communications and transportation or service, as not belonging to various sectors.
Moreover, because in Mexico there is not a public database that can be consulted to establish recovery rates on loans, once the entities fall into default, and recognizing that this variable was of vital importance in adjustment of the models used to predict credit spreads, sought various ways to estimate this variable.
We modeled the rate of recovery in several ways: simple regression, transformations on the recovery rate, multiple regression and implied recovery rates and default contained in the binomial model adapted to determine the market value of equity. 
The best results were obtained using the logistic model, taking as independent variable intensity of default calculated using the formula 118, segregating the data by credit rating and taking complete time series. 
Derived from this analysis concluded that R is not constant, however it is a random variable that depends on the characteristics of the instrument (senior or junior) as well as the probability of default. It was also noted that the best fit is obtained by applying a logistic regression on these data, which private companies can approximate its recovery rate.