Abstract
In this paper we present a new model to assess the firm value and the default probability by using a bivariate contingent claim analysis and copula theory. First we discuss an unfeasible case, given the current derivative market on corporate bonds, which involves univariate digital options to compute the risk neutral probabilities. We then discuss a feasible model, which considers risky interest rates, instead. Moreover, we develop in this framework a new methodology to extract default probabilities from stock prices, only, going beyond the standard KMV-Merton model. Besides, the non-observability of the Merton model’s state variable requires numerical methods, but the results can be unstable with noisy risky data. We show how the null price can be used as a useful barrier to separate an operative firm from a defaulted one, and to estimate its default probability. We then present an empirical application with both operative and defaulted firms to show the advantages of our approach.
Similar content being viewed by others
References
Bharath, S. T., & Shumway, T. (2006). Forecasting default with the KMV-Merton model. AFA 2006 Boston Meeting Papers.
Biais B., Glosten L., Spatt C. (2005). Market microstructure: A survey of microfoundations, empirical results and policy implications. Journal of Financial Markets 8(2): 217–264
Bielecki T.R., Rutkowski M. (2002). Credit risk: Modeling, valuation and hedging. Berlin- Heidelberg, Springer-Verlag
Black F., Scholes M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81: 637–659
Cherubini U., Luciano E., Vecchiato W. (2004). Copula methods in finance. NY, John Wiley
Dionne, G., Laajimi, S., Mejri, S., & Petrescu, M. (2006). Estimation of the default risk of publicly traded Canadian companies. Bank of Canada Working Paper 2006–28.
Glosten L.R., Jaganathan R., Runkle D. (1993). On the relation between the expected value and the volatility of the normal excess return on stocks. Journal of Finance 48, 1779–1801
Hao, H. (2006). Is the structural approach more accurate than the statistical approach in bankruptcy prediction? Queen’s School of Business Working Paper, May-2006.
Hansbrouck, J. (2007). Empirical market microstructure. Oxford University Press.
Höeffding W. (1940). Masstabinvariante Korrelationstheorie. Schriften des Mathematischen Instituts und des Instituts für Angewandte Mathematik der Universitat Berlin 5, 179–233
Ingersoll, J.E., Jr. (1987). Theory of financial decision making. Rowman & Littlefield.
Joe H. (1997). Multivariate models and dependence concepts. London, Chapman Hall
Ketz E.J. (2003). Hidden financial risk. Understanding off-balance sheet accounting. NJ, John Whiley
Mason, S., & Merton, R. C. (1985). The role of contingent claims analysis in corporate finance. In E. Altman & M. Ubrahmanyam (Eds.), Recent advances in corporate finance. Homewood, Ill: R.D. Irwin.
Merton, R.C. (1970). A dynamic general equilibrium model of the asset market and its application to the pricing of the capital structure of the firm. A.P. Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Ma. (reprinted on Merton, R. C. (1990). Continuous time finance. Blackwell, ch.11).
Merton R.C. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449–470
Merton R.C. (1977). On the pricing of contingent claims and the Modigliani-Miller theorem. Journal of Financial Economics 15(2): 241–250
Miller M.H., Modigliani F. (1958). The cost of capital, corporation finance and the theory of investment. American Economic Review 48, 261–297
Miller M.H., Modigliani F. (1961). Dividend policy, growth, and the valuation of shares. Journal of Business 34, 411–433
Nelsen, R. B. (1999). An introduction to copulas. Lecture Notes in Statistics 139. NY: Springer.
Pulito, L. (2002). L’alleanza Fiat-Gm e la fusione Daimler-Chrysler nella prospettiva della globalizzazione dei mercati e il ruolo dell’informazione, LUISS–CERADI.
Ronn E.I., Verma A.K. (1986). Pricing risk-adjusted deposit insurance: An option-based model. The Journal of Finance 4, 871–895
SEC. (2005). Annual Report GM, Cost of Change in Assets, 16-Mar-2005, Form 10-K.
Sklar A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris 8, 229–231
Wong, H. Y., & Li, K. L. (2004). On bias of testing Merton’s model. Proceedings of the conference in Financial Engineering and Applications. M.I.T., USA.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
De Giuli, M.E., Fantazzini, D. & Maggi, M.A. A New Approach for Firm Value and Default Probability Estimation beyond Merton Models. Comput Econ 31, 161–180 (2008). https://doi.org/10.1007/s10614-007-9112-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10614-007-9112-4