一般Levy过程下带违约风险的可转换债券定价模型

对可转换债券的相应标的股价S_t=S_0exp(r-q)t+X_t],在X_t是Levy过程的假设下,运用傅立叶变换和残数定理,得出了带有赎回和回售条款的可转换债券的定价公式;同时,结合Duffie关于衍生产品带违约风险的定价方法,给出了带违约风险的可转换债券定价公式.

Pricing model of convertible bonds with default risk in a generic Levy process

Based on the underlying stock price S_t=S₀exp(r-q)t+X_t], where X_t is a generic Levy process, this thesis has established a pricing model of convertible bonds, making use of residue theorem and Fourier transform. Further more, on the assumption that the default time τ is a stopping time of F_t, t≥0 under the equivalent martingale measure Q, and the average intensity of τ on t,T] is λ^*, the pricing model of convertible bonds with default risk is obtained. The pricing formula is more veracious, because the redemption provisions and the put provisions are taken into account all the while.