Chen, Chang, Wen and Lin (2013)提出馬可夫調控跳躍過程模型(MMJDM)描述股價指數報酬率，布朗運動項、跳躍項之頻率與市場狀態有關。然而，利率並非常數，本論文以狀態轉換模型配適零息債劵之動態過程，提出狀態轉換下的利率與具跳躍風險的股票報酬之二維模型(MMJDMSI)，並以1999年至2013年的道瓊工業指數與S&P 500指數和同期間之一年期美國國庫劵價格為實證資料，採用EM演算法取得參數估計值。經由概似比檢定結果顯示無論道瓊工業指數還是S&P 500指數，狀態轉換下利率與跳躍風險之股票報酬二維模型更適合描述報酬率。接著，利用Esscher轉換法推導出各模型下的股價指數之歐式買權定價公式，再對MMJDMSI模型進行敏感度分析以評估模型參數發生變動時對於定價公式的影響。最後，以實證資料對各模型進行模型校準及計算隱含波動度，結果顯示MMJDMSI在價內及價外時定價誤差為最小或次小，且此模型亦能呈現出波動度微笑曲線之現象。 / To model asset return, Chen, Chang, Wen and Lin (2013) proposed Markov-Modulated Jump Diffusion Model (MMJDM) assuming that the Brownian motion term and jump frequency are all related to market states. In fact, the interest rate is not constant, Regime-Switching Model is taken to fit the process of the zero-coupon bond price, and a bivariate model for interest rate and stock index return with regime-switching and dependent jump risks (MMJDMSI) is proposed. The empirical data are Dow Jones Industrial Average and S&P 500 Index from 1999 to 2013, together with US 1-Year Treasury Bond over the same period. Model parameters are estimated by the Expectation-Maximization (EM) algorithm. The likelihood ratio test (LRT) is performed to compare nested models, and MMJDMSI is better than the others. Then, European call option pricing formula under each model is derived via Esscher transformation, and sensitivity analysis is conducted to evaluate changes resulted from different parameter values under the MMJDMSI pricing formula. Finally, model calibrations are performed and implied volatilities are computed under each model empirically. In cases of in-the-money and out-the-money, MMJDMSI has either the smallest or the second smallest pricing error. Also, the implied volatilities from MMJDMSI display a volatility smile curve.

台灣不動產投資信託（T-REITs）自2005年發行至今已逾六年，然其市場表現仍不如發行之初所預期。過去國內已有許多研究針對T-REITs市場發展進行探討，然而目前就T-REITs與直接不動產投資市場價格表現間之相關研究尚付之闕如。有鑑於此，本研究藉由共整合與Granger因果關係檢定，檢視REITs與直接不動產市場間之關聯性，了解台灣與美國之REITs市場表現差異及其影響因素，進而作為改進T-REITs運作機制或架構之參考依據。 實證結果發現，美國之REITs與直接不動產市場之間存在共整合關係。此結果表示，長期而言，這兩者可能具有相似之風險分散效益。此外，透過Granger因果關係檢定發現REITs領先於直接不動產，乃因前者市場較具效率。另一方面，台灣之REITs與直接不動產市場之間則不具有共整合以及領先或落後關係，然直接不動產當期價格仍會受到本身與REITs之前期價格影響。 本研究進一步分析台、美兩國實證結果之差異原因如下：資料的樣本期間、REITs市場規模、存在於T-REITs市場之集中性風險以及潛在的代理問題。其中，針對T-REITs潛在代理問題，本研究藉由分析股票與T-REIT報酬率之波動性，發現T-REIT之不動產管理機構若與母集團相關者，則其市場表現較差。因此，我們得出T-REITs市場發展主要是受限於代理問題之結論。本研究成果不僅有助於改善T-REITs市場效率，亦可提供學術與實務之參考。 / The mechanism of Real Estate Investment Trusts in Taiwan (or T-REITs) was launched in 2005, however, T-REITs market did not perform as expected. What caused the limited development of T-REITs market? Current literature on the performance between T-REITs and direct real estate investment is limited. Through the cointegration and Granger causality tests, the purpose of this study is hence to explore the short-term and long-term dynamics between REITs and direct real estate markets in the U.S. and Taiwan, respectively. This study presents evidence of the cointegration relationship between REITs and direct real estate in the U.S. It implies that the diversification properties of these two assets are likely to be similar over the long horizon. According to the Granger causality test, REITs leads direct real estate due to the market information efficiency. These findings are consistent with those of previous studies. On the other hand, we find no cointegration and lead-lag relation between T-REITs and commercial real estate. Moreover, the current commercial transaction price is affected by both its and T-REIT previous price. By comparing the difference between the results of these two countries, there are several possible explanations for the different results between the U.S. and Taiwan, including difference in sample period, market capitalization, concentrated risk, and most importantly, the potential agency problem existing in T-REITs market. Finally, the underperformance of parent-related management T-REIT is verified through the volatilities of stock and T-REIT returns. Therefore, we conclude that the limited development of T-REITs is caused by the agency problem in REITs market. Results of this study may provide T-REITs market for improving its efficiency, as well as for the reference for both academics and real practices.

已實現投資報酬率與無風險利率之差、被稱為超額報酬，而股票的預期報酬率超過無風險利率的部份則為股票風險溢酬，是許多資產評價模型的重要依據，例如資本資產定價模型。有不同的理論架構解釋說明風險溢酬值，例如；股票風險溢酬的迷思、短期損失的憎惡、生還存留因素和回歸與偏離平均值等等。 研究台灣股市的超額報酬與股票風險溢酬，有助投資大眾和企業理性面對股市的預期報酬和風險，對台股才有合理的期望報酬值。分析1967年迄2003年的台灣金融市場，計算過去37年長期的幾何平均年報酬率，以臺灣證券交易所發行量加權股價指數為台股市場報酬率，已實現台股實質年報酬率為6.71%。無風險報酬率使用第一銀行的一年期定期存款利率，實質台幣存款年利率為3.07%，消費者物價指數年增率則為4.80%。以年資料計算的台股實質超額報酬，算術和幾何值分別為12.48%和3.63%(年)，計算月資料算術平均和幾何平均值分別為0.77%和0.25%(月)。過去37年長期的台股超額報酬現象未較歐美市場的情況更加明顯，也比一般市場的預期報酬率低。 因資料取得的限制、台股的理論超額報酬方面，1991年迄2003年的近十三年來，經固定股利成長模式和盈餘成長模式的兩種計算方式，台股的實質超額報酬分別為 0.6%和-4.3%，此時期台股的投資報酬率比起台幣存款並不突出、且是低超額報酬。同期的已實現的實質超額報酬值；算術平均1.69%和幾何平均-3.35%。評估目前台股風險溢酬，將十分接近過去37年長期歷史資料得到的超額報酬數值，算術年均值為12.48%(年)和0.77%(月)，幾何平均分別為3.63%(年)和0.25%(月)，低風險溢酬是當前台灣股票市場的一般現象。 / The difference between the observed historical investment return and the risk-free interest rate is the excess return. The equity risk premium, ERP is the expected rate of return on the aggregate stock market in excess of the rate of risk-free security. ERP is one of important factor of many asset-pricing models, including Capital Asset Pricing Model, CAPM. There were many theories and factors to explain the equity risk premium; equity premium puzzle, myopic loss aversion, survivorship bias, mean reversion & aversion and etc. Studying the value of Taiwan equity excess return and risk premium is fundamental for investors and institutions evaluating the expected market investment return and risk. Analyzing the data from year 1967 to 2003 for thirty-seven years long holding period, Taiwan Stock Exchange Capitalization Weighted Stock Index as Taiwan stock market return, the realized real return was 6.71%. One-year bank time deposit rate as NT dollars risk-free asset rate and real interest rate was 3.07% and consumer price index, CPI annual growth rate was 4.80%. The historical real yearly excess return was 12.45% for arithmetic mean and 3.63% geometric mean; the historical real monthly excess return was 0.77% for arithmetic mean and 0.25% geometric mean. Taiwan realized equity excess returns were not higher than the returns in the developed countries and were also lower than the market's expectation. Due to the limits of available data, the theoretical equity excess returns that were calculated on two theoretical models; Constant Growth Dividend Discount Model (dividend yield model) and earnings yield model were 0.6% and -4.3% from year 1991 to year 2003. Comparing the same period of historical realized excess returns of 1.69% for arithmetic mean and -3.35% geometric mean, Taiwan stock market returns were not spectacular. The current equity risk premium of Taiwan stock market is low and should be near the level of the long historical realized equity excess return.