Rendiconti per gli Studi Economici Quantitativi (original) (raw)
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Optimal default boundary in discrete time models
Rendiconti per gli Studi Economici Quantitativi
In this paper we solve the problem of determining the default time of a firm in such a way as to maximize its total value, which includes bankruptcy costs and tax benefits, with the condition that the value of equity must be nonnegative. By applying dynamic programming in discrete time, we find results which extends those of Merton (1974), and we give an application for the approximation of models driven by a Brownian motion or a Poisson process.
Optimal default boundary in a discrete time setting
… Project, Konstaz, Germany, October 5-7, …, 2001
In this paper we solve the problem of determining the default time of a firm in such a way as to maximize its total value, which includes bankruptcy costs and tax benefits, with the condition that the value of equity must be nonnegative. By applying dynamic programming in discrete time, we find results which extends those of and .
Mathematical Finance, 2000
We first discuss some mathematical tools used to compute the intensity of a single jump process, in its canonical filtration. In the second part, we try to clarify the meaning of default and the links between the default time, the asset's filtration, and the intensity of the default time. We finally discuss some examples. Key Words: default risk, enlargement of filtrations The first part of this work was developed during the visit of M. Jeanblanc to the University of Alberta in August 1998. The support of the Social Sciences and Humanities Research Council and the hospitality of the University of Alberta are gratefully acknowledged. Monique Jeanblanc thanks Marek Rutkowski (Warsaw University) and S. Song (Evry University) for many fruitful discussions. Address correspondence to M. Jeanblanc at Equipe d'analyse et probabilités, Université d'Evry Val d'Essonne, Boulevard François Mitterrand,
The Pricing of Credit Derivatives and Estimation of Default Probability
Under the native-born model of default and the circular model of default, we take the price of credit derivatives into account. It’s supposed that the short-term market interest rates are based on Vasicek model in this article. Firstly, we calculate the price of default-free bonds in zero-coupon bond. Then, we give the default-intensity expressions under the two models. We calculate the prices of default-free bonds under the two default models. For different situations, we estimate the parameters by maximum likelihood estimation method and calculate the default probability of the company. From the analysis of the result, we find that the result conforms to reality. So the models of default intensity we suppose in the bond pricing are reasonable.
What happens after a default: The conditional density approach
Stochastic Processes and their Applications, 2010
We present a general model for default time, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only "before the default". This lack of information is crucial while working in a multi-default setting. In a single default case, the knowledge of the intensity process does not allow to compute the price of defaultable claims, except in the case where immersion property is satisfied. We propose in this paper the density approach for default time. The density process will give a full characterization of the links between the default time and the reference filtration, in particular "after the default time". We also investigate the description of martingales in the full filtration in terms of martingales in the reference filtration, and the impact of Girsanov transformation on the density and intensity processes, and also on the immersion property. * This work has benefited from financial support by La Fondation du Risque et Fédération Bancaire Française.
Valuation and Hedging of Credit Derivatives
2007
In this chapter, we present the so-called structural approach to modeling credit risk, which is also known as the value-of-the-firm approach. This methodology refers directly to economic fundamentals, such as the capital structure of a company, in order to model credit events (a default event, in particular). As we shall see in what follows, the two major driving concepts in the structural modeling are: the total value of the firm's assets and the default triggering barrier. It is worth noting that this was historically the first approach used in this area-it goes back to the fundamental papers by Black and Scholes [17] and Merton [76]. 1.1 Basic Assumptions We fix a finite horizon date T * > 0, and we suppose that the underlying probability space (Ω, F, P), endowed with some (reference) filtration F = (F t) 0≤t≤T * , is sufficiently rich to support the following objects: • The short-term interest rate process r, and thus also a default-free term structure model. • The firm's value process V, which is interpreted as a model for the total value of the firm's assets. • The barrier process v, which will be used in the specification of the default time τ. • The promised contingent claim X representing the firm's liabilities to be redeemed at maturity date T ≤ T *. • The process A, which models the promised dividends, i.e., the liabilities stream that is redeemed continuously or discretely over time to the holder of a defaultable claim.
HAL (Le Centre pour la Communication Scientifique Directe), 2019
The first goal of this article is to identify, for different defaultable claims, the fundamental processes which uniquely determine the pre-default price and therefore require to be modelled. The main message to the reader is that although the use of the default intensity or hazard process is ubiquitous, it may not uniquely characterise the price of some defaultable claims. The second goal is to better consolidate the reduced form approach with the structural approach, by extending the reduced form approach to allow for default times which can occur at stopping times and do not satisfy the immersion property.
On the Determinants of the Implied Default Barrier
SSRN Electronic Journal, 2000
We use the maximum likelihood (ML) estimation approach to estimate the default barriers from market values of equities for a sample of 762 public industrial Canadian firms. The ML approach allows us to estimate the asset instantaneous drift, volatility and barrier level simultaneously, when the firm's equity is priced as a Down-and-Out European call (DOC) option. We find that the estimated barrier is positive and significant in our sample. Moreover, we compare the default prediction accuracy of the DOC framework with the KMV-Merton approach. Using probit estimation, we find that the default probability from the two structural models provides similar in-sample fits, but the barrier option framework achieves better out-of-sample forecasts. Regression analysis shows that leverage is not the only determinant of the default barrier. The implied default threshold is also positively related to financing costs, and negatively to liquidity, asset volatility and firm size. We also find that liquidation costs, renegotiation frictions and equity holders' bargaining power increase the implied default barrier level.
Pricing bonds and bond options with default risk
European Financial …, 1998
The pricing of bonds and bond options with default risk is analyzed in the general equilibrium model of Cox, Ingersoll, and Ross (Cir, 1985). This model is extended by means of an additional parameter in order to deal with financial and credit risk simultaneously. The estimation of such a parameter, which can be considered as the market equivalent of an agencies' bond rating, allows to extract from current quotes the market perceptions of firm's credit risk.