The Assessment of the Default Risk for the Banks of the Romanian Banking System

International Journal of Economics, Finance and Management Sciences 2015; 3(1): 1-9 Published online January 19, 2015 (http://www.sciencepublishinggroup.com/j/ijefm) doi: 10.11648/j.ijefm.20150301.11 ISSN: 2326-9553 (Print); ISSN: 2326-9561 (Online) The assessment of the default risk for the banks of the Romanian banking system Sorin Mădălin Vlad 1, Gheorghe Ruxanda 2 1The Doctoral School – Economic Cybernetics and Statistics, Bucharest Academy of Economic Studies, Bucharest, Romania 2Department of Economic Cybernetics, Bucharest Academy of Economic Studies, Bucharest, Romania Email address: [email protected] (S. M. Vlad), [email protected] (G. Ruxanda) To cite this article: Sorin Mădălin Vlad, Gheorghe Ruxanda. The Assessment of the Default Risk for the Banks of the Romanian Banking System. International Journal of Economics, Finance and Management Sciences. Vol. 3, No. 1, 2015, pp. 1-9. doi: 10.11648/j.ijefm.20150301.11 Abstract: By the current study we analyze the performance and plausibility of the empirical results provided by the [5] Duffie and Lando (2001) credit risk structural model with asymmetric information. By construction, such a model can allow the endogenous understanding of the default event (typically for a structural model), the plausibility of the default intensity existence (typically for a reduced form model), as well as the tractability of analytical formulas to be used at the estimation of the credit risk parameters. Under this framework we analyze the empirical model results, by the quantitative creditworthiness assessment of the banks from the Romanian banking system, as financial institutions of a low default portfolio. For the model implementation we apply a special calibration approach for the accounting white noise parameter. The empirical study is being conducted by the use of the banks’ financial statement time series over the last Romanian economic cycle, during the period 2002 – 2012. Keywords: Default, Information Asymmetry, Default Probability, Default Intensity, Banks’ Assessment information assumption imbedded, where the corporate debt 1. Introduction investors cannot notice the real value of the firm’s asset value. Compared to the classical structural models ([16] Merton However, not perfectly informed, the corporate debt investors (1974), [3] Black – Cox (1976)), the theoretical and receive the firm’s accounting asset value from the published methodological framework of the default prediction is financial statements at certain moments of time. These missing the information concept and its progressive accounting asset values shall be considered as a benchmark unfolding over time. This kind of structural models have the for the real value of the firm’s asset value over time. Besides, imbedded assumption that the information used at the model to overcome the information incompleteness, the model has calibration and model use is fully available to the corporate the assumption that the default barrier of the firm can be debt investors (respectively, both the corporate debt investors known by the corporate debt investors. and the firm’s shareholders poses the same information level). In the next sections of the article we brief the key concepts By this methodological set up, the model inputs and behind [5] Duffie and Lando (2001) model and we focus in parameters are presumptively known. depth on the understanding of its performance tested with the However, the rational of these models seems to be empirical data of the banks from the Romanian banking system. counterintuitive as far as the reality has been shown us that the firm’s asset value, the asset volatility and asset return are 2. The Model not visible measures. The financial statements that usually contain the proper 2.1. The General Assumptions information to assess the right firm’s distance to default are We present further in this section [5] Duffie and Lando difficult to be interpreted. These issues are furthermore (2001) model, as a methodological instrument in our empirical reflected in the model results which are not fitting in the end study. [5] Duffie and Lando (2001) model assumes that the with the economic sense of the empirical evidence. default barrier of the firm is known to the stakeholders [5] Duffie and Lando (2001) is the first paper approaching (corporate debt investors) of the firm, in the sense that they a credit risk structural model with the asymmetric can infer it using the [11] Leland (1994) model. 2 Sorin Mădălin Vlad and Gheorghe Ruxanda: The Assessment of the Default Risk for the Banks of the Romanian Banking System [11] Leland (1994) model provides a consistent approach of value, that is normal distributed and independent of Z() t (the the estimation of the default barrier, this being thought as the assumption of independence is fulfilled without loss of ˆ result of the optimal capital structure allocation by the generality, given that the normal law of lnVt and lnVt ). shareholders at the firm set up. The principle of the optimal Moreover at each time t ∈[0,∞ ) the corporate debt investors capital structure is consistent with the shareholders incentive notice if the shareholders have already declared the firm’s ( ) that the limited capital amount shall cover the firm’s losses up insolvency. This means that the information filtration Gt to a certain maximum level. This loss level is achieved by the available to the corporate debt investors is defined by the decrease of the firm’s asset value below the debt value, up to following expression: the cross of the default barrier. Consequently, the default = ∨σ ≤ = σ ≤ ≤ barrier is estimated such as at default time the firm’s capital Gt At (Ns, s t) ({Y ( t1),...,Y( tn ),1{τ ≤s} 0: s t}) (1) value to cover all its losses. With other words, when the asset ≤ * value is equal to the default barrier, the shareholders would for the highest n such that tn t , where: τ = τ() υ is the ( ) rather declare the firm insolvency instead of bringing default time, At is the information filtration of the asset = additional money for covering higher losses. process, and N s 1{τ ≤s} is the pure jump process (with jump For simplicity in the estimation of the optimal capital step of 1) that signals the default time appearance. structure it is considered that the firm’s asset process is time For simplicity, it is assumed that the firm’s capital is not homogenous (the parameters of diffusion process shall not publically traded (there is no public equity subscription) and depend of the time passing therefore), this approach being the firm’s managers are not allowed for public trading the argued by other authors such as [10] Fischer, Heinkel and firm’s debt on the stock exchange, because of the regulations Zechner (1989); [11], [12] Leland (1994, 1998); [1] Anderson, regarding the forbiddance of the debt trading by the firm’s Pan and Sundaresan (1992); [2] Anderson and Sundareson internal staff. (1996); [13] Leland and Toft (1996); [14] Mella-Barral and These assumptions allow for the simplicity of the model’s ( ) Perraudin (1997); [17] Uhrig (1998); [15] Mella – Barral information filtration Gt (defined by the expression (1)) (1999); [9] Fan and Sundareson (2000), also. from the secondary market, and avoid a complex approach Using the default barrier estimated with [11] Leland (1994) with rational expectations and asymmetric information. model, [5] Duffie and Lando (2001) model provides then estimates related to: the conditional distribution of the firm’s 2.3. The Model Outputs asset value given the incomplete observation of their real Furthermore, [5] Duffie and Lando (2001) model provides values, the associated default probabilities, the default the analytical formulas for the probability of default, as intensity and the credit risk spreads. presented below: Z = z b(. Y , z , t ) Z 2.2. The Incomplete Information about the Firm’s Asset Let it be 0 0 , the density t 0 of the t process τ = ≤υ Value inf{t: Zt } (with Z t process stopping at the default time − , υ = ln(υ* V ) We pay attention further on the capabilities of the corporate − 0 ) conditioned by the unfolding of the accounting credit risk assessment from the corporate debt investors’ side, = + asset value information Yt Zt U t as of time t , is being who act on a bond or over-the-counter market. Consequently, after the corporate bond/ loan is issued/ granted, the corporate defined by the following expression: debt investors are not fully informed about the firm’s ψ(z −υ,x −υ, σ t )(φ Y − x)()φ x creditworthiness. However they understand that under the 0 − − U t Z b( xY,,) z t = (2) t 0 φ framework of the optimal capital structure, the firm’s Y()Y t shareholders will declare the firm’s insolvency procedure only when its asset value will decrease to the optimal default barrier −2zx * φ level υ . Thus, even if the corporate debt investors cannot where 2 and is the standard normal (σ t ) understand directly the firm’s real asset value V, they receive Ψ(,,z x σ t )= 1 − e < density. at certain times t1, t 2,..., with ti t i+1 , the firm’s financial statements. Let’s consider that at each selected time, there is Consequently, the firm’s survival probability conditioned provided a new financial statement with new information by the unfolding of the accounting asset value information Yt about the firm’s accounting asset value, denoted here by the as of time t , is being defined by the following expression: ˆ ˆ lnV process Vt , where lnVt and t are normal distributed. The +∞ = Zt firm’s real asset value is defined by Vt V0 e , with τ > = P{ t Yt } ∫ b( z Yt ,,) z0 t dz (3) = + + σ Zt Z 0 mt Wt and follows a diffusion process which is υ defined by a standard Brownian motion W , with asset ∈ −∞ ∞ volatility parameter σ > 0 and drift m (,) .

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