基於最小平方蒙地卡羅模擬法評價可轉債：以中國大陸市場為例

Evaluation of Convertible Bonds Based on the Least Square Monte Carlo Simulation: Take Mainland China Market as an Example

崔璨(Cui Can)

指導教授 ： 林士貴 ； 張興華

國立政治大學/商學院/金融學系/碩士(2020年)

https://doi.org/10.6814/NCCU202001794

摘要

可轉債是一種可以按照約定的價格轉換成股票的公司債券，融合了股票及債券特性，是中國資本市場的重要組成部分。目前，隨著越來越多的機構及個人投資者加入可轉債的市場，需要一個合理的評價模型，讓市場參與者可以有一個公允的參考價值。
本文首先介紹了可轉債的定義，以及可轉債定價理論的研究現狀，然後圍繞可轉債定價存在的問題進行研究，主要內容包括分析影響可轉債的因素、各可轉債條款的影響。接著，介紹了BS 定價模型、二項樹模型（BT）以及最小平方蒙地卡羅模型（LSM）在評價可轉債時的理論及優缺點。
本文選擇對仍上市流通、交易量較高、條款設置合理的39 只可轉債進行分析。選取了各可轉債在2019 年的12 個節點進行了模擬，比較2019 年的交易價格和模擬出的理論價格差異。通過實證分析，可以看出無論是單個時間節點，還是整體的誤差率，LSM 模型都比BT 模型更貼近可轉債的實際價格，但仍與實際價格有一些偏差，並且中國可轉債價值存在被市場低估的現象。

關鍵字

可轉債 ； 蒙地卡羅模擬 ； 二項樹模擬

並列摘要

Convertible bond is a kind of corporate bond that can be converted into stock according to the agreed price. It integrates the characteristics of stock and bond, and is an important part of China's capital market. At present, with more and more institutional and individual investors joining the convertible bond market, a reasonable evaluation model is needed so that market participants can have a fair reference value.
This paper first introduces the definition of convertible bonds, and the research status of the pricing theory of convertible bonds, and then studies the problems existing in the pricing of convertible bonds. The main content includes the analysis of the factors affecting convertible bonds and the impact of the terms of convertible bonds. Then, it introduces the theory, advantages and disadvantages of BS pricing model, binomial tree model (BT) and least square Monte Carlo model (LSM) in evaluating convertible bonds.
This paper chooses 39 convertible bonds in China which are still on the market, with high trading volume and reasonable terms. The paper selects 12 nodes of each convertible bond in 2019 to simulate, and compares the trading price in 2019 with the theoretical price. Through the empirical analysis, it can be seen that the LSM model is closer to the actual price of convertible bonds than the BT model, whether it is a single time node or the overall error rate, but there are still some deviations from the actual price, and the value of convertible bonds in China is underestimated by the market.

並列關鍵字

Convertible Bond ； Monte Carlo Simulation ； Binomial Tree Simulation

參考文獻

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