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1.
本文利用传染模型研究了可违约债券和含有对手风险的信用违约互换的定价。我们在约化模型中引入具有违约相关性的传染模型,该模型假设违约过程的强度依赖于由随机微分方程驱动的随机利率过程和交易对手的违约过程.本文模型可视为Jarrow和Yu(2001)及Hao和Ye(2011)中模型的推广.进一步地,我们利用随机指数的性质导出了可违约债券和含有对手风险的信用违约互换的定价公式并进行了数值分析.  相似文献   

2.
Pricing formulae for defaultable corporate bonds with discrete coupons (under consideration of the government taxes) in the united two-factor model of structural and reduced form models are provided. The aim of this paper is to generalize the two-factor structural model for defaultable corporate discrete coupon bonds (considered in [1]) into the unified model of structural and reduced form models. In our model the bond holders receive the stochastic coupon (which is the discounted value of a predetermined value at the maturity) at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered. The expected default event occurs when the equity value is not sufficient to pay coupon or debt at the coupon dates or maturity and the unexpected default event can occur at the first jump time of a Poisson process with the given default intensity provided by a step function of time variable. We provide the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons and consider its duration.  相似文献   

3.
In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a subfiltration structure. The Euler–Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical scheme for pricing. Finally, the antithetic variable technique is used to reduce the variance of credit default swap option prices.  相似文献   

4.
We use Lévy random fields to model the term structure of forward default intensity, which allows to describe the contagion risks. We consider the pricing of credit derivatives, notably of defaultable bonds in our model. The main result is to prove the pricing kernel as the unique solution of a parabolic integro-differential equation by constructing a suitable contractible operator and then considering the limit case for an unbounded terminal condition. Finally, we illustrate the impact of contagious jump risks on the defaultable bond price by numerical examples.  相似文献   

5.
In this paper a generalized defaultable bond pricing formula is derived by assuming that there exists a defaultable forward rate term structure and that firms in the economy interact when default occurs. Generally,The risk-neutral default intensity χ^Q is not equal to the empirical or actual default intensity λ,. This paper proves that multiple default intensities are invari-ant under equivalent martingale transformation,given a well-diversified portfolio corresponding to the defaultable bond. Thus one can directly apply default intensities and fractional losses empirically estimated to the evaluation of defaultable bonds or contingent claims.  相似文献   

6.
In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R.A. Jarrow and F.Yu (2001), S.Y.Leung and Y.K.Kwok (2005), A.Wang and Z.Ye (2011)). By using the method of change of measure and the technology (H. S.Park (2008), R.Hao and Z.Ye (2011)) of dealing with jump diffusion processes, we obtain the analytic pricing formulas of defaultable zero-coupon bonds. Moreover, by the “total hazard construction”, we give the analytic pricing formulas of credit default swap (CDS).  相似文献   

7.
We study the pricing of defaultable derivatives, such as bonds, bond options, and credit default swaps in the reduced form framework of intensity‐based models. We use regular and singular perturbation expansions on the intensity of default from which we derive approximations for the pricing functions of these derivatives. In particular, we assume an Ornstein‐Uhlenbeck process for the interest rate, and a two‐factor diffusion model for the intensity of default. The approximation allows for computational efficiency in calibrating the model. Finally, empirical evidence on the existence of multiple scales is presented by the calibration of the model on corporate yield curves.  相似文献   

8.
This paper studies the problem of pricing and trading of defaultable claims among investors with heterogeneous risk preferences and market views. Based on the utility-indifference pricing methodology, we construct the bid-ask spreads for risk-averse buyers and sellers, and show that the spreads widen as risk aversion or trading volume increases. Moreover, we analyze the buyer’s optimal static trading position under various market settings, including (i) when the market pricing rule is linear, and (ii) when the counterparty—single or multiple sellers—may have different nonlinear pricing rules generated by risk aversion and belief heterogeneity. For defaultable bonds and credit default swaps, we provide explicit formulas for the optimal trading positions, and examine the combined effect of risk aversions and beliefs. In particular, we find that belief heterogeneity, rather than the difference in risk aversion, is crucial to trigger a trade.  相似文献   

9.
ABSTRACT

The jump threshold framework for credit risk modelling developed by Garreau and Kercheval enjoys the advantages of both structural- and reduced-form models. In their article, the focus is on multidimensional default dependence, under the assumptions that stock prices follow an exponential Lévy process (i.i.d. log returns) and that interest rates and stock volatility are constant. Explicit formulas for default time distributions and basket credit default swap (CDS) prices are obtained when the default threshold is deterministic, but only in terms of expectations when the default threshold is stochastic. In this article, we restrict attention to the one-dimensional, single-name case in order to obtain explicit closed-form solutions for the default time distribution when the default threshold, interest rate and volatility are all stochastic. When the interest rate and volatility processes are affine diffusions and the stochastic default threshold is properly chosen, we provide explicit formulas for the default time distribution, prices of defaultable bonds and CDS premia. The main idea is to make use of the Duffie–Pan–Singleton method of evaluating expectations of exponential integrals of affine diffusions.  相似文献   

10.
In this Note we are concerned with backward stochastic differential equations with random default time. The equations are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. We show that these equations have unique solutions and a comparison theorem for their solutions. As an application, we get a saddle-point strategy for the related zero-sum stochastic differential game problem.  相似文献   

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