Bankruptcy Risk Analysis and Estimation of Healthy and Distressed Stocks Using Extended Black-Scholes Model

Ram Daniel Andrian Vernando, Rudianto Artiono

Abstract


The classical Black-Scholes model assumes that stock prices follow a Geometric Brownian Motion (GBM) process, in which stock prices remain strictly positive throughout time. However, this assumption restricts the model’s capability to represent firms experiencing financial distress, where stock prices may gradually approach zero as bankruptcy risk increases. This study employs the Extended Black-Scholes Model (EBSM), which introduces a stoppingtime mechanism that enables stock prices to reach the bankruptcy boundary, to analyze and compare bankruptcy risk characteristics between financially healthy and distressed stocks. Historical adjusted closing price data from Microsoft Corporation (MSFT.US) and Bed Bath & Beyond Inc. (BBBY.US) were utilized, with model parameters estimated using quadratic variation and Maximum Likelihood Estimation (MLE) methods. The estimation results revealed different stochastic characteristics between the two stocks, where MSFT.US generated a positive drift parameter of 0.216682, whereas BBBY.US generated a negative drift parameter of −0.248385 along with higher volatility. The bankruptcy risk analysis demonstrated that MSFT.US produced infinite Expected Bankruptcy Time (EBT) and Conditional Expected Bankruptcy Time (CEBT) values, while BBBY.US yielded a finite EBT of 5.113633 years, with CEBT values updated according to the observed stock price conditions. These results suggest that the EBSM framework can effectively differentiate bankruptcy risk characteristics by combining stochastic stock price dynamics with time-to-bankruptcy measures.

Keywords


Extended Black-Scholes Model; Bankruptcy Risk; Expected Bankruptcy Time; Conditional Expected Bankruptcy Time; Stochastic Stock Price Dynamics.

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DOI: https://doi.org/10.18860/cauchy.v11i2.44791

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