Merton's Credit Risk Model

U ovom radu predstavljeni su strukturni modeli kreditnog rizika. Navedene su pretpostavke Mertonovog modela i opisan je Mertonov model koji je ujedno i začetnik strukturnih modela kreditnog rizika. Mertonov model temelji se na Black Scholesovom modelu nearbitražnog vrednovanja europske put i call opcije. Ideja je modelirati dug i tržišnu vrijednost kapitala tvrtke kao financijske izvedenice na vrijednost imovine. Merton daje formulu za procjenu vjerojatnosti ulaska u default tvrtke u jednoj godini. Prema Mertonu tvrtka će otići u default i kapital će izgubiti na vrijednosti ukoliko imovina vrijedi manje od duga po dospijeću. Merton vjerojatnost ulaska u default modelira pomoću normalne distribucije. Primjenom Mertonovog modela na hrvatske tvrtke: Hrvatski telekom, Adris grupa, Uljanik te Đuro Đaković procjenjena je vjerojatnost ulaska u default za dane tvrtke na temelju povijesnih podataka i bilance tvrtke preuzete sa stranice Zagrebačke burze. Za određivanje vjerojatnosti ulaska u default najprije je potrebno odrediti tržišnu vrijednost imovine i volatilnost imovine. Kako se one ne mogu direktno odrediti postoji nekoliko pristupa za procjenu od kojih su u radu spomenuta dva. S obzirom na restriktivne pretpostavke Mertonovog modela koje je teško zadovoljiti na stvarnom tržištu u realnim uvjetima mnoga istraživanja su dovela do pristupačnijih modela. Jedan od njih je KMV model kojeg su razvili Kealhofer, MeQuow i Vasicek 1984. godine. Poboljšali su formulu udaljenosti do defaulta i izgradili bazu podataka koja uključuje sve tvtke koje su ušle u default do danas. Na temelju spomenute baze podataka odbacili su pretpostavku da se vjerojatnost ulaska u default modelira pomoću normalne distribucije. Oni su kreirali preslikavanje između udaljenosti do defaulta i vjerojatnosti ulaska u defaut. Baza podataka i konačan model nisu u potpunosti poznati javnosti.This thesis will review structural models of credit risk. It will list the assumptions of the Merton’s model and describe Merton’s model which is the foundation of structural models of credit risk. Merton’s model is founded on Black Scholes’ model of no-arbitrage valuation of European put and call option. The idea is to model the debt and the market value as a financial derivative on the value of company’s equity. Merton provides a formula for assessing the corporation’s risk of credit default in a year. According to Merton, the company will default and the equity will lose its value if the assets are less than the debt at the time of maturity. Merton models the probability of default through standard normal distribution. Through application of the Merton model, the paper will assess the probability of default for Croatian companies Croatian Telecom, Adris Group, Uljanik and Duro Dakovi´c using the historic data and company’s balance sheet which were acquired from Zagreb stock market. To determine the probability of default, it is first necessary to determine the market value of the asset and the volatility of the asset. However, they cannot be directly determined and therefore there are several approaches to assessment from which two will be discussed in the paper. Taking into consideration the restrictive assumptions of the Merton model which are hard to achieve in the stock market in realistic conditions, many researches came up with more approachable models. One of them is KMV model which was developed by Kealhofer, MeQuow and Vasicek in 1984. Their approach improved the calculation of the distance to default and created a database which includes every company which defaulted up to date. By using that database, they discarded the assumption that the probability of default is modelled by normal distribution. They introduces a new mapping of finding the probability of default from the given distance to default. The database of default firms and the final model are not fully known to the public