Opuscula Math. 24, no. 1 (2004), 57-69
Pricing of a defaultable coupon bond in an extended Merton's model
Abstract. Three alternative approaches to the valuation of a defaultable coupon bond in an extended Merton's model are given. Probabilistic approach yields a closed-form expression for the arbitrage price of this bond. A boundary value problem method is based on the concept of an CD-extended generator for Markov processes. The third approach relies on a recursive procedure method in which at every step a suitable Cauchy problem is solved.
Keywords: arbitrage valuation, Markov processes, contraction semigroup, generators.
Mathematics Subject Classification: 60J25, 60J35, 91B70.