Abstract
This paper presents the study of reduced-form approach and hybrid model for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return of investment, the most notable being that the yields on bonds correlate strongly to their perceived credit risk. Credit risk embedded in a financial transaction, is the risk that at least one of the parties involved in the transaction will suffer a financial loss due to decline in creditworthiness of the counter-party to the transaction or perhaps of some third party. Reduced-form approach is known as intensity-based approach. This is purely probabilistic in nature and technically speaking it has a lot in common with the reliability theory. Here the value of firm is not modeled but specifically the default risk is related either by a deterministic default intensity function or more general by stochastic intensity. Hybrid model combines the structural and intensity-based approaches. While avoiding their difficulties, it picks the best features of both approaches, the economic and intuitive appeal of the structural approach and the tractability and empirical fit of the intensity-based approach.
Highlights
As stock markets have become more sophisticated, so have their products
We can distinguish between the reduced-form models that are only concerned with the modelling of default time, and that are referred to as the intensity-based models, and the reduced form models with migrations between credit rating classes called the credit migration models
We have in our disposal two models for the valuation of credit risk named the reduced-form model and the hybrid model
Summary
As stock markets have become more sophisticated, so have their products. The simple buy or sell trades of the early markets have been replaced by more complex financial options and derivatives. The first category of credit risk models are the ones based on the original framework developed by Merton [1] They derived an explicit formula for risky bonds which can be used both to estimate the probability of default of a firm and to estimate the yield differential between a risk bond and a default-free bond. Black and Cox [2] introduced the possibility of more complex capital structure with subordinated debts, using the principles of option pricing Black and Scholes [3] In such a framework, the default process of a company is driven by the value of the company’s assets and the risk of a firm’s default is explicitly linked to the variability of the firm’s asset value. Duffie and Singleton [6] followed with a model that when market value at default (recovery rate) is exogenously specified, allows for closed-form solutions for term-structure of credit spreads. In this paper we shall consider reducedform approach and hybrid model for the valuation of credit risk
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