Option Based Default Risk Modeling With Interval Arithmetic

Authors: Altan Arslan, Serdar ÇELEBİ (Istanbul Technical University Informatics Institute, Computational Science and Engineering Department)

Abstract

Default risk is the uncertainty surrounding a firm's ability to service its debts and obligations. Prior to default, there is no way to discriminate unambiguously between firms that will default and those that won't. At best, only probabilistic assessments of the likelihood of default can be done. In this paper, the probability of default had been searched by considering the firm's stock as a call option. With the help of Monte Carlo simulation on stock return values, it is possible to generate various "probable" paths that the stock prices can fallow within the credit maturity period. Then the next step is to calculate at what percentage in these paths, the firm comes to the default position. The interval arithmetic is helpful to work with the real return values of the firm's stock. And also parallel algorithm gives an opportunity to increase the number of Monte Carlo simulations.