Journal of Mathematics and Modeling in Finance

Credit Risk Management Of Portfolio And Distance To Default Estimation Based On Firm Equity Approach

Document Type : Research Article

Author

Saba Yaghobipour

Department of Mathematics and Computer Science, Lorestan University, Lorestan, Iran.

10.22054/jmmf.2026.91229.1256
Abstract
In this paper, the credit risk of investment is managed by a new structural mean-reverting model. For this purpose, the utility maximization problem is expressed as an optimization problem with an expected logarithmic objective function and a mean-reverting constraint. The existence of a solution to the expressed problem is proved in a lemma. Moreover, one theorem for facilitating the optimal strategy design algorithm is proved. In this way, the optimal strategy is obtained for hedging the credit risk of investing in stocks of companies. Finally, the distance to default of investment is calculated by using the Black-Scholes formula for call options on wealth values obtained by optimal portfolio selection based on the proposed the optimal strategy. ‎Also, ‎the ‎stability ‎of ‎the ‎proposed ‎method ‎is ‎proved ‎in ‎the ‎second ‎theorem.‎ ‎For demonstrating the applicable results, the portfolio allocation problem is simulated by using the proposed method and compared with the non-mean-reverting equity approach. According to the simulation result, the portfolio values don’t fall and default doesn’t occur during the investment period [0, T], approximately. Also, distance to default tends to zero. ‎period [0, T], approximately. Also, distance to default tends to zero.

Keywords

Credit risk
Mean-reverting model
Utility maximization
[1] H. Chau, D. Nguyen, and T. Nguyen, Continuous-time optimal investment with portfolio constraints: A reinforcement learning approach, European Journal of Operational Research, Vol.328, (3), (2026), pp:1068-1092.
[2] G. DI. Nunno, and S. Sjursen. International Journal of Theoretical and Applied Finance, Vol.17, (08), (2014), 1450050.
[3] M. J. Capiński, and E. Kopp, Portfolio Theory and Risk Management, Cambridge University Press (2014).
[4] G. C. Heywood, J. R. Marsland, and GM. Morrison, Practical Risk Management for Equity Portfolio Managers, British Actuarial Journal; Vol.9, (5), (2003), pp:1061-1123. doi:10.1017/S1357321700004463.
[5] D. Lamberton, B.Lapeyre, Introduction to Stochastic Calculus Applied to Finance (2nd ed.), Chapman and Hall/CRC, (2007), https://doi.org/10.1201/9781420009941.
[6] A. Ahmad Dar, and N. Anuradha, Probability Default in Black Scholes Formula: A Qualitative Study, Journal of Business and Economic Development, Vol.2, (2), (2017), pp:99-106. doi:10.11648/j.jbed.20170202.15
[7] Z. Yanling, K. Wang, and Y.Ren. Dynamics of a mean-reverting stochastic volatility equation with regime switching, Communications in Nonlinear Science and Numerical Simulation, Vol.83, (2020) pp: 105110. https://doi.org/10.1016/j.cnsns.2019.105110.
[8] P. J. Crosbie, and J. R. Bohn, Modelling Default Risk, Working Paper, KMV Corporation, (2003).
[9] A. Ahmad Dar, and N. Anuradha, Probability Default in Black Scholes Formula: A Qualitative Study, Journal of Business and Economic Development, Vol.2,(2) (2017) pp:99 106, doi:10.11648/j.jbed.20170202.15.
[10] A. L. Lewis, Option Valuation Under Stochastic Volatility, Finance Press, (2000).
[11] S. Hwang, A Mean-Reverting Model of Exchange Rate Risk Premium Using Ornstein-Uhlenbeck Dynamics, arXiv:2504.06028v1[q-fin.CP], (2025).
[12] M. Capiński, and E. Kopp, Discrete Models of Financial Markets, Cambridge University Press, (2012).
Journal of Mathematics and Modeling in Finance
Volume 6, Issue 2
July 2026
Pages 241-252

  • Receive Date 30 January 2026
  • Revise Date 27 June 2026
  • Accept Date 28 June 2026

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