Study On The Optimal Call Policy For Convertible Bonds

In this paper, I focus on the optimal call policy for convertible bondsand the numerical method of solving the optimal call policy.By the aid of no-arbitrage theory, I derive that for a convertible bondit is optimal to call when the bond’s conversion value is equal to itseffective call price. Based on the Black-Scholes equation, I derive theequation which convertible bond price should follow. Taking properties ofconvertible bonds into consideration, I can specify the boundary conditionsfor this equation. Using the finite difference method, I further illustratecalculation procedures to obtain a numerical solution of the optimal callpolicy for convertible bonds.Real call strategies that companies follow are usually different fromthe theoretical optimal call policy for convertible bonds. In this paper, Itake advantage of the combination of equilibrium theory and corporatefinancial crisis cost theory in order to explain that this kind difference existbecause companies want to make sure the call strategies will success.