Optimal Conversion Strategies and Valuation of Convertible Bonds before Maturity

Abstract

In this chapter, we conduct the corresponding analysis to the previous chapter, but for a conversion date before maturity As the effects at every premature conversion date are basically the same, it is reasonable to employ a two conversion date model to emphasize the basic properties of the conversion strategy and the related asset values. In chapter 7, we will explicitly discuss the differences between the properties at the last and an arbitrary premature conversion date. For the ease of notation, we set the last premature conversion date t _N equal to zero throughout this chapter. Since the total conversion volume before time t = 0, which is denoted by K₀, is zero if only two conversion dates are considered, we can write for the values W₀ (V ^-₀ , r₀, k₀), W ⁺₀ (V ^-₀ , r₀, k₀), S₀ (V ^-₀ , r₀, k₀), and D₀ (V ^-₀ , r₀, k₀) instead of the more sophisticated notation.¹