可轉債資產交換定價

Abstract

可轉換公司債為一混合債券和股票性質的證券，標的股票價格位在高處時，持有者可以將手中的可轉債轉換成普通股股票；反之若股票市場表現不如預期，仍可以得到原始債券的固定利息收益，等到合約期結束後拿回本金。台灣市場自1990年第一張可轉債發行開始發展至今，近年每年平均發行金額為2,000億台，為公司籌資的重要工具之一。 可轉債資產交換為將可轉債拆解成固定收益和選擇權兩端，前者形式為利率交換，後者則是一以可轉債為標的之長期美式買權。金管會證期局在西元2000年宣布開放券商承作可轉債資產交換交易，除了可以提供更多元的衍生性金融商品供不同風險偏好的投資人選擇外，亦可提高次級市場的流動性。可轉債資產交換屬於店頭衍生性商品，沒有標準化合約且採取逐筆議價方式交易，其價格由各證券商自行計算，無公開透明揭露之決定方式。再者選擇權端結構複雜，可以視為一種複合型選擇權，影響價格之因素甚多，包含股價、利率、信用貼水等。 本文回顧國內外轉換公司債資產交換選擇權端評價文獻，建構新的定價模型。定價模型使用多因子最小平方蒙地卡羅模擬法，考慮股價和利率的隨機性。股價採用 Heston (1993)的雙因子模型，無風險利率則用 Cox, Ingersoll 和 Ross(1985)提出之單因子模型，配合上使用 TEJ TCRI模型估計之信用風險利率加碼。建模後對模型進行敏感度分析，從眾多影響價值之不確定因素中，找出具有重要影響性之變數，提供給投資人作為風險衡量之基準。

A convertible bond is a cocktail of different risk components, which are a source of potential risk and return. The market risk of convertible can be roughly spilt into two main parts: an equity component and a credit one. The credit part can be associated with the value of bond, and the equity part creates the equity exposure and the convexity. The construction of a convertible asset swap involves an extra counterparty bringing the buyer and seller of the credit together. The seller wants to eliminate the credit risk of convertible, and the transaction between the intermediary and the credit seller covers the ascot. While the transaction between the buyer of the credit and the intermediary is an asset swap. The right to halt or recall the asset swap is held by the credit seller. An ascot is an American option and the buyer can exercise the deal and get the underlying convertible bond, and the early exercise of the option may happen when credit spreads tighten. This kind of product is on the over-the-counter(OTC) market and therefore not very standardized. The ascot belongs to the large family of compound options, which are options on other options and is hard to price the fair value. This study includes the introduction of Taiwan convertible bond market, literature review of various valuation methods, and try to construct a multi-factor model to price an ascot. The numerical method we use here is least-square Monte Carlo simulation, and there are three stochastic factors, such as risk-free rate, volatility and stock. Apart from the assumption of risk-free rate, we also estimate the credit spread amount by the TCRI index, which is released by the database TEJ. After the construction of ascot valuation, we conduct the sensitivity analysis for different risk factors.