運用隨機股價波動度之違約結構模型進行可轉債訂價

A Structural Default Model with Stochastic Volatility Stock Prices for Convertible Bond Pricing

范振強(Chen-Chiang Fan)

指導教授 ： 王耀輝

國立臺灣大學/管理學院/財務金融學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201801650

摘要

在可轉換債券(可轉債)的評價過程中，股票價格、違約風險和資本結構之間的複雜關係無法根據不可觀察的公司價值進行良好建模。在Wang, Dai and Wang (2018)中，將可觀察到的股權價值視為公司價值的下降出局買權，接著應用公司債務狀況來確定出局(違約)邊界，從而確定違約機率，並運用雙因子模型評價。然而，該文獻中公司價值波動度的隨機假設與其定價公式的常數假設相衝突。因此，本研究將該模型的公司價值波動度假設修正為常數，並把股價波動度視為隨機，以三項樹的方式進行可轉債評價。為了融入隨機股價波動的特性在樹中，本文進一步應用Ritchken和Trevor（1999）中的方法調整樹的結構。最後，獲得的違約機率可以恰當地解釋眾所周知的槓桿效應，敏感性分析說明了本模型的穩定性。

關鍵字

可轉債 ； 違約結構模型 ； 隨機股價波動度 ； 二因子評價 ； 三項樹

並列摘要

To evaluate the convertible option embedded in CBs, the complex relationships among the stock price, default risk, and capital structure cannot be well-modeled based on unobservable firm values. In Wang, Dai and Wang (2018), the firm value and its volatility are solved by modeling the evolution of the observable equity value as a down-and-out call option on the firm value; then the information of capital structure is applied to determine default boundaries and thus default probabilities; finally, when evaluating CBs, with their two-factor lattice model, the dilution effect due to CB conversions can be also considered. However, the obtained stochastic volatility of the firm value conflicts with the constant assumption in the down-and-out call option pricing formula utilized by Wang, Dai, and Wang (2018). In this paper, I modify their model to a stochastic stock-price volatility model based on a constant firm value volatility that is solved to reflect the current volatility information of the stock price. The tree-based method in Ritchken and Trevor (1999) is implemented to accommodate the feature of the stochastic stock-price volatility. With the modification, the obtained default probabilities can properly explain the well-known leverage effect. The sensitivity analysis and the empirical examination illustrates the applicability of my model.

並列關鍵字

Convertible Bond ； Structural Default Model ； Stochastic Volatility ； Two-Factor Pricing ； Trinomial Tree

參考文獻

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