Pricing Of Callable Convertible Bonds With Conversion Warning Time

This desertation is based on Black-Scholse option pricing model. Under the assumption of no-arbitrage , we establish the mathematical model callable convertible bonds with conversion warning time requirement by hedging principle, which is a free boundary problem. The main results as followes:First, we prove the existence and uniqueness of solutions of the free boundary problem, with the technique of penalty function, Schauder fixed point theorem and the maximum principle.Second, We discuss the impact of parameter on the convertible bonds price. And we also prove that the price of convertible bonds increases with stock price and time , decreases with interest rate.Third, we study the properties of optimal conversion boundary . As results the optimal conversion boundary are continous and monotonic increasing with time, and intersect calling boundary at t₀∈(0, T).We determine t₀∈(0, T]:(1) If c≥rK(?),then t₀ = T .The strategy of bondholder is : Ifstock price is less than optimal conversion price ,and then bondholder continues to keep his bonds in hands, and if stock price is more than optimal conversion price, then bondholder converts his bonds to the stock of the firm.(2) Ifc0∈(0, T). When t≤t₀ ,the strategy of bondholder is: If stock price is less than optimal conversionprice ,and then bondholder continues to keep his bonds in hands, and if stock price is more than optimal conversion price, then bondholder converts his bonds to the stock of the firm. When t > t₀ , The strategy of bondholder is: If S < (?), then bondholder continues to keep his bonds in hand, and If S = (?), then bondholder converts his bonds to the stock of the firm.Fourth , We study that the impact of warning time on bondholder's optimal conversionpolicies and convertible bonds price.we obtain that the warning time will lead to accerlation of the convertible bonds price with stock decreasing and convertible bonds price increasing. The warning time has no influence on the relation convertible bonds price with interest rates,the time for the intersection of conversion and calling boundary.