Integrals of Higher Binary Options and Defaultable Bond with Discrete Default Information
In this article, we study the problem of pricing defaultable bond with discrete default intensity and barrier under constant risk free short rate using higher order binary options and their integrals. In our credit risk model, the risk free short rate is a constant and the default event occurs in an expected manner when the firm value reaches a given default barrier at predetermined discrete announcing dates or in an unexpected manner at the first jump time of a Poisson process with given default intensity given by a step function of time variable, respectively. We consider both endogenous and exogenous default recovery. Our pricing problem is derived to a solving problem of inhomogeneous or homogeneous Black-Scholes PDEs with different coefficients and terminal value of binary type in every subinterval between the two adjacent announcing dates. In order to deal with the difference of coefficients in subintervals we use a relation between prices of higher order binaries with different coefficients. In our model, due to the inhomogenous term related to endogenous recovery, our pricing formulae are represented by not only the prices of higher binary options but also the integrals of them. So we consider a special binary option called integral of i-th binary or nothing and then we obtain the pricing formulae of our defaultable corporate bond by using the pricing formulae of higher binary options and integrals of them.
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- Marco Realdon, 2007. "Credit risk pricing with both expected and unexpected default," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 3(4), pages 225-230.
- Hyong-Chol O & Ning Wan, 2013. "Analytical Pricing of Defaultable Bond with Stochastic Default Intensity," Papers 1303.1298, arXiv.org, revised Apr 2013.
- Lara Cathcart & Lina El-Jahel, 2006. "Pricing defaultable bonds: a middle-way approach between structural and reduced-form models," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 243-253.
- Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
- Hyong-Chol O & Jong-Jun Jo & Chol-Ho Kim, 2013. "Pricing Corporate Defaultable Bond using Declared Firm Value," Papers 1302.3654, arXiv.org, revised Jul 2013.
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