A defaultable callable bond pricing model (original) (raw)
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A Defaultable Callable Bond Pricing Model: A 3D Finite Difference Approach
This paper presents a D model for pricing defaultable bonds with embedded call options. The pricing model incorporates three essential ingredients in the pricing of defaultable bonds: stochastic interest rate, stochastic default risk, and call provision. Both the stochastic interest rate and the stochastic default risk are modeled as a square-root diffusion process. The default risk process is allowed to be correlated with the default-free term structure. The call provision is modeled as a constraint on the value of the bond in the finite difference scheme. The numerical example shows that the D model is capable of pricing defaultable bonds with embedded call options adequately. This paper can provide new insight for future research on defaultable bond pricing models. JEL classifications: C00; G13
This paper presents a D model for pricing defaultable bonds with embedded call options. The pricing model incorporates three essential ingredients in the pricing of defaultable bonds: stochastic interest rate, stochastic default risk, and call provision. Both the stochastic interest rate and the stochastic default risk are modeled as a square-root diffusion process. The default risk process is allowed to be correlated with the default-free term structure. The call provision is modeled as a constraint on the value of the bond in the finite difference scheme. This paper can provide new insight for future research on defaultable bond pricing models. JEL classifications: C00; G13
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.
SSRN Electronic Journal, 2003
We develop a model for pricing derivative and hybrid securities whose value may depend on different sources of risk, namely, equity, interest-rate, and default risks. In addition to valuing such securities the framework is also useful for extracting probabilities of default (PD) functions from market data. Our model is not based on the stochastic process for the value of the firm [which is unobservable], but on the stochastic process for interest rates and the equity price, which are observable. The model comprises a risk-neutral setting in which the joint process of interest rates and equity are modeled together with the default conditions for security payoffs. The model is embedded on a recombining lattice which makes implementation of the pricing scheme feasible with polynomial complexity. We present a simple approach to calibration of the model to market observable data. The framework is shown to nest many familiar models as special cases. The model is extensible to handling correlated default risk and may be used to value distressed convertible bonds, debt-equity swaps, and credit portfolio products such as CDOs. We present several numerical and calibration examples to demonstrate the applicability and implementation of our approach.
Semi-analytical pricing of defaultable bonds in a signaling jump-default model
Journal of computational finance, 2003
This paper derives analytical solutions for defaultable bonds when the underlying interest rates follow a mean reverting square-root process. The default event occurs in an expected or unexpected manner when the value of a signaling process representing the credit quality of the issuer reaches a certain lower threshold or at the first jump time of a hazard-rate process, respectively. The hazard rate is dependent on the default-free interest rate. The model generates term structures of credit spreads consistent with empirical observations. 2
SSRN Electronic Journal, 2000
We propose a new model to price defaultable bonds which incorporates features of both structural and reduced-form models of credit risk. In particular we assume that default occurs with certainty when the firm's asset value, which is modeled as a geometric Brownian motion, falls below a fixed threshold level. In addition the default event can also occur as the first jump of a counting process whose intensity is described by a generalized Ornstein-Uhlenbeck stochastic differential equation. In particular the long-run mean of the default intensity is specified as a function of the firm's asset value, while the dynamics of the default intensity around its long-run mean is modeled exogenously, and hence can incorporate the effect of not firm-specific variables.
Empirical Evaluation of Hybrid Defaultable Bond Pricing Models
Applied Mathematical Finance, 2008
We present a four-factor model (the extended model of Schmid and Zagst) for pricing credit risk related instruments such as defaultable bonds or credit derivatives. It is a consequent advancement of our prior threefactor model (see ). In addition to a Þrm-speciÞc credit risk factor we include a new systematic risk factor in form of the GDP growth rates. We set this new model in the context of other hybrid defaultable bond pricing models and empirically compare it to speciÞc representatives. In analogy to we Þnd that a model only based on Þrm-speciÞc variables is unable to capture changes in credit spreads completely. However, consistent to we show that in our model market variables such as GDP growth rates and non-defaultable interest rates and Þrm-speciÞc variables together signiÞcantly inßuence credit spread levels and changes.
The Pricing Of Options On Credit-Sensitive Bonds
2003
We build a three-factor term-structure of interest rates model and use it to price corporate bonds. The first two factors allow the risk-free term structure to shift and tilt. The third factor generates a stochastic credit-risk premium. To implement the model, we apply the Peterson and Stapleton (2002) diffusion approximation methodology. The method approximates a correlated and lagged-dependent lognormal diffusion
Modeling Term Structure of Defaultable Bonds
1997
This article presents convenient reduced-form models of the valuation of contingent claims subject to default risk, focusing on applications to the term structure of interest rates for corporate or sovereign bonds. Examples include the valuation of a credit-spread option. This article presents a new approach to modeling term structures of bonds and other contingent claims that are subject to default risk. As in previous "reduced-form" models, we treat default as an unpredictable event governed by a hazard-rate process. 1 Our approach is distinguished by the parameterization of losses at default in terms of the fractional reduction in market value that occurs at default. Specifically, we fix some contingent claim that, in the event of no default, pays X at time T. We take as given an arbitrage-free setting in which all securities are priced in terms of some short-rate process r and equivalent martingale measure Q [see Harrison and Kreps (1979) and Harrison and Pliska (1981)]. Under this "risk-neutral" probability measure, we let h t denote the hazard rate for default at time t and let L t denote the expected fractional loss in market value if default were to occur at time t, conditional This article is a revised and extended version of the theoretical results from our earlier article "Econometric Modeling of Term Structures of Defaultable Bonds" (June 1994). The empirical results from that article, also revised and extended, are now found in "An Econometric Model of the Term Structure of Interest Rate Swap Yields" (Journal of Finance, October 1997). We are grateful for comments from many, including the anonymous referee, Ravi Jagannathan (the editor),
An Application of New Barrier Options (Edokko Options) for Pricing Bonds with Credit Risk
Hitotsubashi journal of commerce and management, 2002
In order to price bonds with credit risk, we can consider structural models. Basically, default occurs if the value of the firm hits some pre-specified barrier in these models. We extend traditional structural models to put the additional default condition such that the value of the firm remains under some pre-specified level for a long period of time until the maturity after the first time hitting this level. A new framework of barrier options (Edokho Options) allows us to extend default condition. In our approach, the way to describe default time can be applied more precisely to the real world.