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A Merton Model Approach to Assessing the Default Risk: an Application on Selected Companies from BIST1001

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A Merton Model Approach to Assessing the Default Risk: an Application on Selected Companies from BIST1001 IOSR Journal of Economics and Finance (IOSR-JEF) e-ISSN: 2321-5933, p-ISSN: 2321-5925.Volume 8, Issue 6 Ver. I (Nov.- Dec .2017), PP 54-61 www.iosrjournals.org A Merton Model Approach to Assessing the Default Risk: An Application on Selected Companies from BIST1001 Çiğdem ÖZARI2 Abstract: The main objective of this study is to show how the Merton Model approach can be used to estimate the default probabilities of selected BIST100companies. The inputs of the Merton model include stock returns volatility, the company’s total debt, the risk-free interest rate andthe time. They are all known or computable parameters. Instead of the risk-free rate, one-year treasury constant maturity rate obtained from TUIK was used. In addition, distance to default and expected default frequencies of these companies are calculated and their correlation with total debt are examined. Key words: Merton Model, Black& Scholes, Default probability. ----------------------------------------------------------------------------------------------------------------------------- --------- Date of Submission: 13-10-2017 Date of acceptance: 30-11-2017 ----------------------------------------------------------------------------------------------------------------------------- ---------- I. Introduction Credit risk is perceived as the oldest and most important risk of finance and the development of credit- risk modeling can be traced back to Beaver’s (1966) based study, which illustrates significant differences in financial ratios between bankrupt and non-bankrupt companies. In other words, some statistical modelsdivide companies into two groups or clusters such as bankrupt and non-bankrupt. In addition, the prediction of company failure or bankruptcy has been well-researched using developed country data (Beaver 1966; Altman 1968; Deakin 1972; Ohlson 1980; Taffler 1983; Boritz). For instance, Ohlson selected 9 independent variables by thinking that they should be beneficial to forecast the bankruptcy situation, but did not provide a theoretical basis for selection of these variables.Ohlson then chose at least 3 years US stock exchange trading industrial companies for the period of 1970 and 1976.He ended up with 105 failed companies and 2000 non-failed companies. In this study, there were three models that had been estimated. The first model examines the failures within one year. The second examines the failures within two years and the last one examines the failures within one or two years. In these three models, to predict bankruptcyor the probability of failure, he used a logistic function. Another type of credit-risk model is based on the option-pricing model of Black&Scholes (1973). For instance, Merton (1974) has shown that by using an option-pricing model, company’s default probability can be estimated. Vassalou and Xing (2004) showed that using the Merton model, the default likelihood indicator could capture the default risk. In addition, they suggest that company size and book-to-market ratio could be seen as default-related factors. Moreover, Hillegeist, Keating, Cram and Lundstedt (2004) found that the performance of the Merton model was superior to that of accounting models such as Altman's Z-Score and Ohlson's O-score models, while explaining corporate bankruptcies. One can also estimate default probabilities by using historical data, from bond prices and from credit default swap spreads or asset swaps. In this study, we choose the Merton model to calculate the default probabilities of non-failure companies chosen from BIST100. II. Merton Model A model for assessing the credit risk of a company by characterizing the company’s equity as European call option, which is written on its assets, has been proposed by Robert Merton in 1974. Merton Model assumes that a company has a certain amount of zero-coupon debt that will become due at a future time. According to Jones (1984), the default risk for the Merton Model is so low that pricing ability for investment-grade bills is not better than a pure model that assumes no default risk.Afik et all investigates in their study that simplified applications of the Merton model have superior model power compared to more complex and computationalintensive methods (2016) and they recommend to use simple original model. As inputs, Merton’s model requires the current value of the company’s assets (퐴0), the volatility of the 1This article is derived from PhD thesis “Estimating Bankruptcy Probability Using Fuzzy Logic: An Application to a Panel of US and Turkish Sectors”, T.C Kadir Has University, 2012. 2Assistant Professor, Istanbul Aydın University, Department of Economics and Administrative Sciences, Istanbul - Turkey [email protected] DOI: 10.9790/5933-0806015461 www.iosrjournals.org 54 | Page A Merton Model Approach to Assessing the Default Risk: An Application on Selected Companies .. company’s assets (휎퐴), the outstanding debt, and the debt to maturity. One way to implement the Merton model is to use the approach proposed by Jones et al. (1984) to calculate the present value of the company assets and the volatility of the asset from the market value of the company's own equity and the instant volatility of equity. A debt maturity date is selected and debt payments are matched to a single payment on the same date in some way. To sum up, Merton model generates the probability of default (PD) for each company in the sample at any given point in time. In this study, we use following notation, which is defined for variables that we did not mentioned before, that we use to construct Merton Model. At : Value of company’s assets at time t DT : Debt repayment due at time T E0 : Value of company’s equity today ET : Value of company’s equity at time T σE : Instantaneous volatility of equity If the value of company’s assets is worth less than the promised debt repayment at time T, the company defaults. In other words, model assumes that the company promises to pay DT to the bondholders at maturity T. If this payment is not met, that is, if the value of the company’s assets at maturity is less than DT , the bondholders take over the company and shareholders receive nothing. The equity of the company can be seen asa European call option on the assets of the company with maturity T and strike price can be seen equal to the face value of the debt. Notice that default can be triggered only at T maturity and this happens only when AT < D .In other words, the payoff of equity holders is equivalent to European call option on the assets of the company with a strike price DT and maturity T. T ET = max(AT D ,0 ) The payoff of debt holdersis equivalent to a portfolio, which consists of a European put option and debt. The strike price of the European put option is DT with maturity T and written on the assets of the company. So, its T T T value at time T is min(AT ,D ) , which is equal to D max(D AT ,0 ) and Table 1 summarizes this situation and illustrates the value of portfolio at maturity. Table 1:The Value of Portfolio At Time T At Time 0 T T D > AT D AT Equityholders European Call Option Not Exercised T AT - D T Debtholders European Put Option+Debt DT AT Not Exercised + D The model assumes that the underlying value of each company follows a geometric brownian motion and that each company has issued just one zero-coupon bond. TheBlack & Scholes pricing modeland also Merton model assumes that there are no transaction costs, no taxes, no dividends, the risk-free interest rate is constant and same for all maturities. The remaining assumption of the model is that security trading is continuous function. At the end, the price follows a geometric brownian motion with constant drift parameter and volatility.One of the important assumptions and weakness of the model that the company can default only at time T. Merton's approach should be avoided if the debt can be recovered in the case of a debt, if the value of the company falls to a minimum level before the maturity of debt. To cope with this difficulty the problem can be handled by constructing the model on barrier option. 2.1 Forecasting Default Probabilities with KMV Merton Model The KMV-Merton model adapts Merton’ study in 1974, in which the equity of the company is a European call option on the underlying value of the company with a strike price equal to the face value of the company’s debt. The model recognizes that the volatility of the company and its underlying value can not be directly observed. According to the model’s assumptions both of these values can be subtracted from equity value, the volatility of equity and other observable variables by solving two nonlinear simultaneous equations. After these values are calculated, the model indicates that the PD is the normal cumulative density function of a Z-score based on the underlying value of the company, volatility of the company and the face value of the company’s debt. The Merton model has two important assumptions. The first is that the total value of a company is assumed to follow geometric brownian motion, DOI: 10.9790/5933-0806015461 www.iosrjournals.org 55 | Page A Merton Model Approach to Assessing the Default Risk: An Application on Selected Companies .. 푑푉 = 휇푉푑푡 + 휎푉푉푑푊 where, 푉: the total value of the company. 휎푉: the volatility of the company value. 휇: the expected return on V. 푑푊 : standard Weiner Process. The second assumption of the Merton model is that the company has exported a discount bond maturing during the T period. Under these assumptions, the company's equity is a call option on the company's underlying value with a strike price equal to the face value of the company's debt and time to maturity T.
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