使用L&eacute;vy隨機過程下之可轉債定價－以鴻海一為實證分析

本研究主要目的是採用利維過程(Lévy Process)中的兩個分配(Normal Inverse Gaussian and Variance Gamma，分別簡稱為NIG與VG)所建構的股價隨機模型和LongStaff and Schwartz (2001)所提出的最小平方蒙地卡羅法(Least Square Monte Carlo Simulation)來求解可轉換公司債的理論價格。一般化的定價模型都是建立在報酬為常態分配假設下，此與Garvin(2000)在新興市場報酬率的分配經常存在有厚尾的特性不符，因此，建立在常態分配假設下的隨機過程，並無法捕抓到資產報酬厚尾的情形，而導致訂價偏誤的產生。採用利維過程所建構的資產報酬的隨機過程，可以藉由將資產報酬的峰態與偏態的情況列入模型的考量當中，進而可以更精確的捕抓到資產厚尾的情況，而改善定價偏誤的情況。文中以鴻海所發行的可轉債為例來作數值分析，比較兩個利維過程所建構的股價模型與傳統GBM股價模型在可轉換公司債訂價誤差的比率。

關鍵字

利維過程(L&eacute ； vy Process) ； Normal Inverse Gaussian ； Variance Gamma ；最小平方蒙地卡羅法

並列摘要

This paper investigates the valuation of the convertible bonds whose value depends on the stock price and the clauses set by the issuing companies. First, assuming that underlying stock price process is driven by the Lévy process and we use the Normal Inverse Gaussian (NIG) and the Variance Gamma (VG) distribution to model the stochastic process of stock price. Second, we adopt the QQ-plot, Kolmogorove-Smirnov and Anderson and Darling test to test the goodness of fitness of the model to the empirical data. Third, we use the Least-squared Monte Carlo Simulation (LSM) proposed by LongStaff and Schwartz (2001) to deal with the early-exercised problem of the convertible bonds. Fourth, we compare the performance of the models (GBM, NIG and VG models). At last, we find the performance of using Lévy process in pricing the convertible bonds is better than the Weiner Process.

並列關鍵字

Convertible bonds ； L&eacute ； vy process ； Normal Inverse Gaussian ； Vairance Gamma ； QQ-plot ； Kolmogorove-Smirnov test ； Anderson and Darling test ； LSM