或有可轉換債券的評價

Abstract

或有可轉換債券(CCB)過去被提出作為銀行大到不能倒的一個解決方法，但過去不論或有可轉換債券(CCB)的轉換時點在何時皆以相同的轉換比率進行轉換，但較早進行轉換相較於晚轉換可以賺取些微的利息，因此本文對於或有可轉換債券(CCB)的轉換比率做一些調整，將或有可轉換債券(CCB)在進行轉換時的距離到期時間納入轉換比率的計算。接著本文再對新設計的或有可轉換債券(CCB)進行評價。由於現行利率環境低迷甚至出現負利率，因此本文採用的債券類型為零息債券而不是有息債券，以避免投資者有再投資風險。本文的評價方式為對於或有可轉換債券(CCB)先取風險中立下的期望價值，接著再以無風險利率對風險中立下的期望價值進行折現以取得今日價值。最後再對得到的評價進行敏感度分析以檢驗所得出之模型的合理性，所得到的敏感度分析大致上都很直觀。

Being proposed as a therapy for the too-big-to-fail problem of the banks, however, contingent convertible bonds (CCB) are all converted into same amounts of shares of stock no matter early conversion or late conversion. Early conversion can benefit from the interest compare to late conversion. As a result, this paper modifies the conversion rate of the contingent convertible bonds (CCB) based on time to maturity. Then we evaluate our new design of contingent convertible bonds (CCB). Due to the low interest rates even negative interest rates environment recently, we adopt a zero coupon bond instead of a coupon bond in order to prevent the reinvestment risk. Our evaluation technique is taking the expectation of the contingent convertible bonds (CCB) under risk neutral world, and then we discount this risk neutral expectation by risk free rate in order to get the fair value of contingent convertible bonds today. Last, we do some sensitivity analysis based on our closed-form solution in order to verify our model and most of the sensitivity analyses are intuitive.