![]() ![]() ![]() As the formula indicates, the higher the Z-score value, the lower the probability of bank failure \(i\). \[E = V\mathcal\) is the standard deviation of \(ROA\) of bank \(i\) in period \(t\). If the value of the assets is insufficient to cover the firm’s obligations, then shareholders with a call option do not exercise their option and leave the firm to their creditors. In this case, the exercise price of the option equals the book value of the firm’s obligations. A call option on the underlying assets has the same properties as a caller has, namely, a demand on the assets after reaching the strike price of the option. The Merton model uses the Black and Scholes (1973) model of options in which the firm’s equity value follows the stipulated process of Black and Scholes (1973) for call options. The beauty of structural models is that they allow us to use option pricing formulas such as Black. They are called structural models as default is based on the company’s balance sheet structure. A concise explanation of the theory behind the calculator can be found here. Where \(V\) is the total value of the firm’s assets (random variable), \(\mu\) is the expected continuous return of \(V\), \(\sigma_V\) is the firm value volatility, and \(dW\) is the standard process of Gauss–Wiener. The probability of default is endogenous as default normally occurs when the value of the firm’s assets hits a barrier representing default. The cumulative probability of default for n coupon periods is given by 1-(1-p)n. In the Merton model, it is assumed that the total value of the firm follows a geometric Brownian motion process. The Merton (1974) model aims to find the values of assets and their volatilities in a dynamic process following Black and Scholes (1973). Note that the assembled panel is unbalanced, containing 155,775 observations. The analysis period covers the first quarter of 2000 until the third quarter of 2016 with a periodicity of 67 quarters in 2,325 banks and 92 countries. In the foreground, we use the values extracted from the balance of payments, then we use the financial statements, and lastly, we use the stock price history of world banks listed on the stock exchange, all extracted from the database of Bloomberg. The data used in the study are utilized in three stages. (2013), which is an adaptation of the Altman (1968) model. In particular, this post considers the Merton (1974) probability of default method, also known as the Merton model, the default model KMV from Moody’s, and the Z-score model of Lown et al. ![]() In this post, I intruduce the calculation measures of default banking. ![]()
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