Dominant factors in structural models fol r risky convertibles Issuer's firm value process- volatility 2. Issuer's capital structure- debt/equity ratio 3. Loss given default 4. Terms and conditions of the debt issue 5. Interest rate process 6. Correlation between the interest rate and asset value Difficult to estimate the parameter values when implementing the models
11 Dominant factors in structural models for risky convertibles 1. Issuer’s firm value process - volatility. 2. Issuer’s capital structure – debt/equity ratio. 3. Loss given default. 4. Terms and conditions of the debt issue. 5. Interest rate process. 6. Correlation between the interest rate and asset value. • Difficult to estimate the parameter values when implementing the models
Structural models for pricing convertible bonds Assumptions Non-callable and can be converted only at maturity No transaction costs and no bankruptcy costs Capital structure consists of common shares and non- callable convertibles
12 Structural models for pricing convertible bonds Assumptions • Non-callable and can be converted only at maturity. • No transaction costs and no bankruptcy costs. • Capital structure consists of common shares and noncallable convertibles
N= number of common shares M= number of convertibles f- face value per convertible F- face value of the convertible issue =Mf r= conversion ratio Upon conversion, the convertible holders will possess n fraction of equity, where Mr w+Mr The parameter n is called the dilution factor of the convertible issue
13 N = number of common shares M = number of convertibles f = face value per convertible F = face value of the convertible issue = Mf r = conversion ratio Upon conversion, the convertible holders will possess l fraction of equity, where The parameter l is called the dilution factor of the convertible issue. . N Mr Mr + l =
Let Vr denote the value of the firm at maturity after the last coupon has been paid The holder will convert if and only if 2V>F Value of the convertible bond at maturity vr if V <F F if FV<Fia nV ifV>Fln min(F, vr)+/ max(V-F/n, 0)
14 Let VT denote the value of the firm at maturity after the last coupon has been paid. The holder will convert if and only if Value of the convertible bond at maturity l VT > F min( , ) max( / ,0). if / if / if l l l l l F V V F V V F F F V F V V F T T T T T T T = + - =
payoff to convertible straight bond warrant F F Decomposition into a straight bond plus a units of call with strike F/n and short a put to issuer
15 straight bond payoff to convertible F F/l VT Decomposition into a straight bond plus l units of call with strike F/l and short a put to issuer