A Simple Novel Approach to Valuing Risky Zero Coupon Bond in a Markov Regime Switching Economy

Abstract

We have addressed the problem of pricing risky zero coupon bond in the framework of Longstaff and Schwartz structural type model by pricing it as a Down-and-Out European Barrier Call option on the company’s asset-debt ratio assuming Markov regime switching economy. The growth rate and the volatility of the stochastic asset debt ratio is driven by a continuous time Markov chain which signifies state of the economy. Regime Switching renders market incomplete and selection of a Equivalent martingale measure (EMM) becomes a subtle issue. We price the zero coupon risky bond utilizing the powerful technique of Risk Minimizing hedging of the underlying Barrier option under the so called “Risk Minimal” martingale measure via computing the bond default probability.