Journal of Business and Economic Development

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Probability Default in Black Scholes Formula: A Qualitative Study

Received: 08 November 2016    Accepted: 26 December 2016    Published: 24 January 2017
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Abstract

A default risk is the risk that a person or an organization will fail to make a payment that they have promised. There are many models that help us to analyze credit risk, such as Default Probability, Loss Given Default, and Migration Risk. All these models are important for evaluating credit risk, but the most important factor is the Probability of Default that is mentioned in this paper. This paper uses the Black Scholes formula for European call option to find the probability default of a firm. How d2 in Black schools model became the probability default of a Merton model. Merton model is the structural model because it is using firm’s value to inform the probability of firms default and here we are going to show the relationship between Black Scholes European call option and the probability of default of a firm. The main aim of this paper is to describe the factor that affects the default probability default using Black Scholes model for European Call option by the help of some examples.

DOI 10.11648/j.jbed.20170202.15
Published in Journal of Business and Economic Development (Volume 2, Issue 2, May 2017)
Page(s) 99-106
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Black Scholes Model, Merton Model, Probability Default, Probability Distance

References
[1] Black, F. & Cox,. C (1976). Valuing Corporate Securities: Some Effects Of Bond Indenture Provisions, Journal of Finance, 31 (2), pp. 351-367.
[2] Bohn J. R. (2000). A Survey Of Contingent-Claims Approaches To Risky Debt Valuation, The Journal of Risk Finance, Spring 2000, 53-70.
[3] Bohn, J, Arora N & I Korablev, (2005). Power And Level Validation Of The EDF Credit Measure In The U.S. Market, Moody’s KMV Working Paper.
[4] Black, F. and Scholes M. (1973). The Pricing Of Options And Corporate Liabilities, Journal of Political Economy, No 81, pp. 637-659.
[5] Bose, S & Coondoo, D. (2003). A Study Of The Indian Corporate Bond Market, Money & Finance, Vol. 2, No. 12, January-March 2003.
[6] Crosbie, P. J. & Bohn, J. R.(2003). Modelling Default Risk, Working Paper, KMV Corporation.
[7] Duffee, Darrell. & Wang, Ke. (2004). Multi-Period Corporate Failure Prediction With Stochastic Covariates, Working Paper, Stanford University.
[8] Emilia Matei. Black scholes-mertn model approach-merits and shortcomings, EC372 Term paper.
[9] Farmen, E. S., Westgaard, S., Fleten, S. & Wijst, N. (2003). Default Risk And Its Greeks Under An Objective Probability Measure, Paper presented at Stockholm School of Economics - Department of Finance seminar series November 2003.
[10] Hull, J. C. (2009). Options, Futures And Other Derivatives, 7th Ed, First Indian Reprint, Pearson Education, pp 277-300.
[11] Jigish Amit and Alok. How good is merton model at assessing credit risk.
[12] Merton, R. C. (1974). On The Pricing Of Corporate Debt: The Risk Structure Of Interest Rates, Journal of Finance, 29, 449-470.
[13] Stein, Roger. (2002). Benchmarking Default Prediction Models: Pitfalls and Remedies in Model Validation, Moody’s Risk Management Services, Technical Report no. 020305.
[14] Varma, J. R. and Raghunathan, V. (2000). Modelling Credit Risk In Indian Bond Markets, ICFAI Journal of Applied Finance, 6 (3): 53-67.
[15] Yu Wang (2009). Structural credit risk modelling, society of actuaries’ issue 16.
Author Information
  • Department of Mathematics and Actuarial Science, B. S Abdur Rahman Uinversity, Chennai, India

  • Department of Management Science, B. S Abdur Rahman Uinversity, Chennai, India

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  • APA Style

    Amir Ahmad Dar, N. Anuradha. (2017). Probability Default in Black Scholes Formula: A Qualitative Study. Journal of Business and Economic Development, 2(2), 99-106. https://doi.org/10.11648/j.jbed.20170202.15

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    Amir Ahmad Dar; N. Anuradha. Probability Default in Black Scholes Formula: A Qualitative Study. J. Bus. Econ. Dev. 2017, 2(2), 99-106. doi: 10.11648/j.jbed.20170202.15

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    AMA Style

    Amir Ahmad Dar, N. Anuradha. Probability Default in Black Scholes Formula: A Qualitative Study. J Bus Econ Dev. 2017;2(2):99-106. doi: 10.11648/j.jbed.20170202.15

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  • @article{10.11648/j.jbed.20170202.15,
      author = {Amir Ahmad Dar and N. Anuradha},
      title = {Probability Default in Black Scholes Formula: A Qualitative Study},
      journal = {Journal of Business and Economic Development},
      volume = {2},
      number = {2},
      pages = {99-106},
      doi = {10.11648/j.jbed.20170202.15},
      url = {https://doi.org/10.11648/j.jbed.20170202.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.jbed.20170202.15},
      abstract = {A default risk is the risk that a person or an organization will fail to make a payment that they have promised. There are many models that help us to analyze credit risk, such as Default Probability, Loss Given Default, and Migration Risk. All these models are important for evaluating credit risk, but the most important factor is the Probability of Default that is mentioned in this paper. This paper uses the Black Scholes formula for European call option to find the probability default of a firm. How d2 in Black schools model became the probability default of a Merton model. Merton model is the structural model because it is using firm’s value to inform the probability of firms default and here we are going to show the relationship between Black Scholes European call option and the probability of default of a firm. The main aim of this paper is to describe the factor that affects the default probability default using Black Scholes model for European Call option by the help of some examples.},
     year = {2017}
    }
    

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    AB  - A default risk is the risk that a person or an organization will fail to make a payment that they have promised. There are many models that help us to analyze credit risk, such as Default Probability, Loss Given Default, and Migration Risk. All these models are important for evaluating credit risk, but the most important factor is the Probability of Default that is mentioned in this paper. This paper uses the Black Scholes formula for European call option to find the probability default of a firm. How d2 in Black schools model became the probability default of a Merton model. Merton model is the structural model because it is using firm’s value to inform the probability of firms default and here we are going to show the relationship between Black Scholes European call option and the probability of default of a firm. The main aim of this paper is to describe the factor that affects the default probability default using Black Scholes model for European Call option by the help of some examples.
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