使用雙因子樹狀模型評價可轉換公司債資產交換選擇權端價值

隨著台灣金融市場的活絡，能符合不同市場需求的可轉換公司債資產交換越來越受投資人歡迎，所以針對此商品的定價就變成一個重要的課題。一般來講，評價方法是將可轉換公司債資產交換拆解為利率交換及選擇權兩個部份分別評價，但因為具有可提前贖回、賣回及轉換權利等，使得選擇權端的評價變得困難。先前的文獻主要是假設股價服從幾何布朗運動、利率服從均衡模型，再使用蒙地卡羅最小平方法來模擬未來的股價及利率的路徑，從而計算可轉換公司債資產交換選擇權端的價值。但均衡模型無法配適目前的利率期間結構，因此本文假設利率服從無套利模型並考慮股價與利率間的相關係數，以雙因子樹狀模型來計算可轉換公司債資產交換選擇權端的價值。數值結果顯示，在本文的模型假設下使用雙因子樹狀模型，不僅能夠符合實際上市場的利率期限結構，亦可以得到與先前文獻類似的結果。

關鍵字

可轉換公司債；可轉換公司債資產交換；可轉換公司債選擇權；雙因子模型；樹狀模型

並列摘要

As the development of Taiwan financial market, the convertible bond asset swap (CBAS) that corresponds to the needs of different market is increasingly welcomed by investors, so pricing for this derivative has become an important issue. In the general pricing method, the value of CBAS can be split into two parts: an interest rate swap and a call on convertible bond. However, it difficult to pricing a CBAS due to the properties of callable, putable and convertible. Previous literatures assume that stock price follows geometric Brownian motion and interest rate follows equilibrium model, and then use Monte Carlo least square method to simulate the path of future stock price and interest rate, thereby gaining the value of CBAS option. But the equilibrium model cannot match the current interest rate term structure. Therefore, this paper assumes that the interest rate obeys the no-arbitrage model and considers the correlation coefficient between stock price and interest rate, and uses the two-factor tree model to calculate the value of the CBAS option. The numerical results show that using the two-factor tree model under our model of this paper can not only match the interest rate term structure, but also obtain similar results as the previous literature.