**4. Calculation of ČEZ, a.s.**

The ČEZ Group is the largest energy group operating in Central and Southeastern Europe. Besides the headquarters in Bohemia, it has representation in most of the countries in the region, including Slovakia. To date, ČEZ ranks among the top 10 European energy companies in terms of market capitalization and is the largest company among the new European Union countries. The activities of the ČEZ Group include, in addition to the sale

and production of electricity, also telecommunications, informatics, nuclear research, design, construction and maintenance of energy equipment, extraction of raw materials, and processing of various secondary energy intermediates and products. ČEZ is the most profitable and also the least indebted energy company in the region, which reflects its high credit rating. Its stable growth is also achieved due to a balanced portfolio of resources.

The first step is the construction of yield curves for ČEZ, a.s. For the 3, 6, 9, and 12 months horizon, we use the interbank interest rates PRIBOR and for horizons from 2 to 20 years, we use known values of government bonds of Czech Republic. Subsequently, we use the Nelson-Siegel-Svensson method. We construct the yield curves for each year of the prediction, as is shown in **Figure 1**.

Yield curves do not have a traditional shape, except the curve constructed for 2011. The most specific shape is in the case of curve for 2014. In this case, short-term interest rates were higher than government bond rates over 1 year. Changes and natural growth in interest rates occur only in the fifth year. However, the interest rates described by this yield curve follow very low values. Similarly, the low values are also observable in the case of curve constructed for 2015.

In order to determine the market value of assets, we have to stabilize the timeline first, by weighing down the yield on the shares. Consequently, we calculate the market value of assets using the iterative procedures based on Black-Scholes formula [7]. From **Figure 2**, we can see that the shares value of ČEZ, a.s. has a long-lasting character. Shares as the main input of market valuation of assets reflect market reactions to published annual reports and hence

**Figure 1.** Yield curves for ČEZ a.s.

**Figure 2.** Value of equity for ČEZ, a.s.

reaction to company results. Moody's rating has a worsening tendency just like the value of assets, which has always deteriorated in the past 2 years due to the expected debt growth in the coming years.

**Figure 3** shows the development of the equity volatility between 2010 and 2015. We chose the moving average method for the volatility calculation, EWMA, and GARCH (1.1) methods. The highest volatility levels in each of observed periods were the ones generated by GARCH (1.1) model. **Table 1** shows the input data for the calculation of each model. The book value of assets is higher than their market value in the first 3 years of the forecast, which means that the company's assets are underestimated. In the last 2 years, the situation has changed and the market value is higher than the accounting value.

**Figure 3.** Volatility of shares for ČEZ, a.s.


**Table 1.** Input data for ČEZ, a.s.

reaction to company results. Moody's rating has a worsening tendency just like the value of assets, which has always deteriorated in the past 2 years due to the expected debt growth in

**Figure 3** shows the development of the equity volatility between 2010 and 2015. We chose the moving average method for the volatility calculation, EWMA, and GARCH (1.1) methods. The highest volatility levels in each of observed periods were the ones generated by GARCH (1.1) model. **Table 1** shows the input data for the calculation of each model. The book value of assets is higher than their market value in the first 3 years of the forecast, which means that the company's assets are underestimated. In the last 2 years, the situation has changed and the

the coming years.

**Figure 2.** Value of equity for ČEZ, a.s.

**Figure 1.** Yield curves for ČEZ a.s.

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market value is higher than the accounting value.

We will work with a 20-year time horizon, which is identical to how the individual yield curves were constructed. In the case of the Credit Grades model, we will also need an average rate of return on all debts. Here, we will use the value that the studies and the Credit Grades technical document recommend, and we will work withΛ¯¯ = 0.5 [8]. We also choose the volatility of the barrier on the basis of these sources at λ = 0.3.

**Figure 4** shows the probability of default in all models for all calculated volatility types by the end of 2015. The KMV model achieves a significantly lower probabilities of default. In the first half of the predicted time horizon, the probability of default is approaching zero. In short time horizons, the probability of defaults is at minimum values close to zero. This is due to fact

**Figure 4.** Probability of default in all models for 2015.

that ČEZ a.s. had relatively low volatility of shares during the observed period. The highest Merton probabilities were generated by original Merton model (**Figures 5**–**12**).

Default curves of ČEZ, a.s. have similar pattern in all models. However, the predicted probability values differ considerably. In a time horizon of up to 1 year, predictions in each of the selected models are close to zero. In the forecast for 2013, there is a sharp increase in the probability of default. This is particularly influenced by the volatility and value of leverage in 2013, which is high in that year in comparison with the other monitored years. In the Black-Cox model, there is an interesting situation when the curves representing the first three seasons are nearing zero. In the long run, they have the highest probability of default in all models for the years 2014 and 2015, which is also influenced by the shape of the yield curves for 2014 and 2015, based on very low interest rates.

The Credit Grades model generates interesting types of curves. Within a short horizon of up to 1 year, the company is virtually safe for all applied models. In the long run, the forecasts vary considerably from 5 to 33%. This is due to both the different design and the ability of models to sensitively react to changes in the input parameters in such a long horizon. Interesting in terms of progress is 2013, which is close to zero in most models, with the exception of the Credit Grades model. The model works with a stochastic barrier, but even then, none of the applied models were able to generate curves with decreasing character. This may be due to the nonrepresentativeness of the sample size.

Credit spreads generated by each model have very similar patterns in all cases. In other applications of these models, we obtained results with negative spreads in the case of KMV model, but not this time. Looking at the reason why this effect does not occur in this case, it is necessary to note the probability of defaults. Over a longer time horizon at higher probability of defaults, the pattern tends to show negative spreads. Therefore, it is better to apply this model to predictions with a shorter time horizon. Another weakness in all three Merton based models is low spreads in short time horizons within 1 year. Highest credit spreads again were however generated by Credit Grades model, because of stochastic barrier.

Modeling Default Probability via Structural Models of Credit Risk in Context of Emerging… http://dx.doi.org/10.5772/intechopen.71021 119

**Figure 5.** Probability of default for ČEZ, a.s. between years 2011 and 2015—Merton model.

that ČEZ a.s. had relatively low volatility of shares during the observed period. The highest

Default curves of ČEZ, a.s. have similar pattern in all models. However, the predicted probability values differ considerably. In a time horizon of up to 1 year, predictions in each of the selected models are close to zero. In the forecast for 2013, there is a sharp increase in the probability of default. This is particularly influenced by the volatility and value of leverage in 2013, which is high in that year in comparison with the other monitored years. In the Black-Cox model, there is an interesting situation when the curves representing the first three seasons are nearing zero. In the long run, they have the highest probability of default in all models for the years 2014 and 2015, which is also influenced by the shape of the yield curves for 2014 and 2015, based on very low interest rates.

The Credit Grades model generates interesting types of curves. Within a short horizon of up to 1 year, the company is virtually safe for all applied models. In the long run, the forecasts vary considerably from 5 to 33%. This is due to both the different design and the ability of models to sensitively react to changes in the input parameters in such a long horizon. Interesting in terms of progress is 2013, which is close to zero in most models, with the exception of the Credit Grades model. The model works with a stochastic barrier, but even then, none of the applied models were able to generate curves with decreasing character. This may be due to

Credit spreads generated by each model have very similar patterns in all cases. In other applications of these models, we obtained results with negative spreads in the case of KMV model, but not this time. Looking at the reason why this effect does not occur in this case, it is necessary to note the probability of defaults. Over a longer time horizon at higher probability of defaults, the pattern tends to show negative spreads. Therefore, it is better to apply this model to predictions with a shorter time horizon. Another weakness in all three Merton based models is low spreads in short time horizons within 1 year. Highest credit spreads again were

however generated by Credit Grades model, because of stochastic barrier.

Merton probabilities were generated by original Merton model (**Figures 5**–**12**).

the nonrepresentativeness of the sample size.

**Figure 4.** Probability of default in all models for 2015.

118 Financial Management from an Emerging Market Perspective

**Figure 6.** Probability of default for ČEZ, a.s. between years 2011 and 2015—KMV model.

**Figure 7.** Probability of default for ČEZ, a.s. between years 2011 and 2015—Black-Cox model.

**Figure 8.** Probability of default for ČEZ, a.s. between years 2011 and 2015—Credit Grades model.

**Figure 9.** Credit spreads for ČEZ, a.s. between years 2011 and 2015—Merton model.

**Figure 10.** Credit spreads for ČEZ, a.s. between years 2011 and 2015—KMV model.

**Figure 11.** Credit spreads for ČEZ, a.s. between years 2011 and 2015—Black-Cox model.

**Figure 8.** Probability of default for ČEZ, a.s. between years 2011 and 2015—Credit Grades model.

120 Financial Management from an Emerging Market Perspective

**Figure 9.** Credit spreads for ČEZ, a.s. between years 2011 and 2015—Merton model.

**Figure 10.** Credit spreads for ČEZ, a.s. between years 2011 and 2015—KMV model.

**Figure 12.** Credit spreads for ČEZ, a.s. between years 2011 and 2015—Credit Grades model.
