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

• Main Authors: Chen-Chiang Fan, 范振強
• Other Authors: Yaw-Huei Wang
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/kduky5

碩士 === 國立臺灣大學 === 財務金融學研究所 === 106 === 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.