On the Pricing of Corporate Bonds: Non-Diversifiable Risk and Mean-Variance Hedging

Abstract

Given a defaultable corporate liability in an incomplete market, we derive a new pricing model by incorporating the value of an optimal-replication portfolio and a certain reduction due to the "non-diversifiable risk". We solve the mean-variance hedging problem: finding a self-financing trading strategy that most closely approximates the payoff of the contingent claim at maturity. By applying stochastic dynamic programming to the minimization of a mean-squared error loss function under Markov-state dynamics, we derive a system of partial differential equations. In the application to evaluate a simple zero-coupon corporate bond, we solve the system of PDEs explicitly and implement the model by simulations. The results show that the yield spreads in our proposed model have comparative features with those in the Merton model. Moreover, we prove that the proposed pricing model is arbitrage-free by choosing the "non-diversifiable risk premium parameter" to be small enough.