Convertible Bond Valuation with Regime Switching

We provide an analytic valuation formula for convertible bonds with regime-switching market conditions. We divide the convertible bond into a coupon-bearing bond component and an American-type exchange option component. We develop a new valuation method of the exchange option component by combining Margrabe (1978)'s exchange option valuation approach and Geske and Johnson (1984)'s pseudo-American option valuation approach. A two-state regime-switching example shows the superiority of our model in both accuracy and computation speed compared to the Monte-Carlo simulation method.