Shokouh Shahbeyk - Department of Statistics, Mathematics, and Computer Science, Allameh Tabataba'i University, Tehran, Iran.
Shokoofe Banihashemi - Department of Statistics, Mathematics, and Computer Science, Allameh Tabataba'i University, Tehran, Iran.

One of the most critical aspects of credit risk management is determining the capital requirement to cover the credit risk in a bank loan portfolio. This paper discusses how the credit risk of a loan portfolio can be obtained by the stochastic recovery rate based on two approaches: beta distribution and short interest rates. The capital required to cover the credit risk is achieved through the Vasicek model. Also, the Black-Scholes Merton model for the European call option is utilized to quantify the Probability of Default (PD). Value at Risk (VaR) and Conditional Value at Risk (CVaR) are used as measures of risk to evaluate the level of risk obtained by the worst-case PD. A stochastic recovery rate calculates VaR related to the underlying intensity default. In addition, the intensity default process is assumed to be linear in the short-term interest rate, driven by a CIR process. The loan portfolio performance is evaluated by considering the relevant characteristics with the Data Envelopment Analysis (DEA) method. This study proposes the losses driven by the stochastic recovery rate and default probability. The empirical investigation uses the Black-Sholes-Merton model to measure the PD of eighth stocks from different industries of the Iran stock exchange market.

Portfolio credit risk, loan portfolio, Data Envelopment Analysis, recovery rate, Default probability, Conditional value at risk