This paper studies the short-time behavior of the optimal conversion boundary of convertible bonds using singular perturbation technique. The fundamental result is the analytic prediction of the optimal conversion price close to maturity. Even though the asymptotic expansion is valid for a short time interval, it complements the conventional approaches to evaluate this financial instrument at times that are not close to expiry. The analysis presented here is applicable to a wide range of nonlinear derivatives pricing problems.
Mathematics Subject Classification: 91G20; 91G30; 91G80
Keywords: Convertible bonds; singular perturbation; Black-Scholes model