本篇論文以Regime Switching Stochastic Volatility（RSV）作為外匯選擇權市場的波動度模型，採用馬可夫鏈蒙地卡羅法（Markov Chain Monte Carlo）中的GibbS Sampling演算法估計RSV模型的參數，並預測外匯選擇權在RSV模型下的價格。 數值結果方面首先對GibbS Sampling參數估計的結果做討論，再對預測出的選擇權價格與Black and Scholes作比較，最後並提出笑狀波幅與隱含波動度平面的結果。 本研究所得到之結論： 1. RSV模型與MCMC模擬法的組合，具備產生笑狀波幅的能力，提供足夠證據顯示，RSV模型與MCMC演算法所計算出來的選擇權價格，確實反應且捕捉到了市場上選擇權價格所應具備的特色。 2. 本模型能有效解釋期限結構 （Term Stucture of Volatility）、笑狀波幅（Volatility Smile）的現象。 關鍵字：馬可夫鏈蒙地卡羅法、外匯選擇權、貝氏選擇權評價、MCMC、Regime switching Regine change、Gibbs Sampling、currency option、Markov Chain Montec Carlo

金融海嘯提供企業以最低成本進行併購的機會，企業藉此達到外部成長的目的，但併購案之綜效價值如何轉化成有意義的數據，幫助主併公司進行併購價格的評估，是許多企業在進行併購時的疑問。 　　本研究的目的為運用企業評價中的現金流量折現法與實質選擇權法，來進行神基科技收購華孚科技之併購價值評估。本研究利用現金流量折現法與實質選擇權評價法相互搭配，將各項決策所創造之彈性價值納入分析，更充分涵蓋併購策略的綜效價值。 　　研究結果顯示，若不考量選擇權彈性價值，則神基科技收購華孚科技所付出之溢價很高，已接近華孚之未來可能價值。加入了選擇權價值之擴充性淨現值比收購價格高出很多，顯示主併公司在評估該收購案時，可能已考量策略彈性價值。 / Financial crisis leads to an opportunity for the enterprise to do mergers and acquisitions at the lower cost. The enterprise could achieve external growth by mergers and acquisitions. However, how to translate the synergy of merger into meaningful data to help companies evaluate the accurate acquisition price during M&A is important and difficult. The objective of this study is to use the evaluation methods of enterprise value during M&A process, including discounted cash flow method (DCF) and real options method, to accurately evaluate the enterprise value of the combined one. The foundation will be based on the evaluation on the two existing companies. Then the assumption of the running situation after merging, and the judgment of the dimension of coordination effects will be the key points.

金融海嘯提供企業以最低成本進行併購的機會，企業藉此達到外部成長的目的，但併購案之綜效價值如何轉化成有意義的數值以幫助主併公司進行併購價格的評估是許多企業在進行併購時的疑問。 　　本研究的目的為運用企業評價中的EVA經濟附加價值法與實質選擇權法，來進行G公司收購N公司之併購價值評估。本研究利用EVA經濟附加價值法與實質選擇權評價法相互搭配，將各項決策所創造之彈性價值納入分析，更充分涵蓋併購策略的綜效價值。 　　研究結果顯示，若不考量選擇權彈性價值，則G公司收購N公司所付出之價格略高於EVA計算出之企業實際價值。加入了選擇權價值之擴充性，淨現值比收購價格高出很多，顯示主併公司在評估該收購案時，可能已考量策略彈性價值。 / Financial crisis leads to an opportunity for the enterprise to do mergers and acquisitions at the lower cost. The enterprise could achieve external growth by mergers and acquisitions. However, how to translate the synergy of merger into meaningful data to help acquiring companies evaluate the accurate acquisition price is a question for many enterprises during M&A. The objective of this study is to use the economic value added (EVA) method and real options method of enterprise evaluation methods to evaluate the acquisition cost of Company G’s acquisition of Company N. This study takes both economic value added (EVA) and real options method, including the analysis the flexibility value and further exploring the synergy of the M&A decision. This study includes that if the flexibility value of options is not considered, the premium paid by Company G acquiring Company N is slightly higher than the real enterprise value by EVA. However, if to include the flexibility of options value, the net present value is much higher than the acquisition cost, which may indicate that the acquiring company has taken flexibility value in to consideration when evaluating such M&A.

欲透過流動性調整模型來探討流動性風險對或有償權的影響，但本篇研究著重於選擇權的分析。根據Feng (2014)，流動性折現因子由市場流動性與股價對市場流動性敏感度所構成，而且此流動性之動態過程具有均數復歸的特性。根據本篇研究結果，價內選擇權和價平選擇權的評價表現比傳統Black-Scholes好，如果進一步將流動性之跳躍性質引入模型，除了價內選擇權和價平選擇權之外，價外選擇權的評價表現亦呈現大幅度的改善。於探討模型評價表現優劣之餘，本篇文章欲更進一步探究市場不流動性對選擇權避險參數的影響。 / This study uses a liquidity-adjusted pricing model to discuss the impact of the liquidity risk on Contingent Claim. However, we focus on the analysis of option. The liquidity discount factor consists of market liquidity and the sensitivity of stock prices to market illiquidity. The dynamic process of market liquidity possesses mean-reversion. Our empirical results show the liquidity model will improve pricing performance for ITM and ATM options. After incorporating diffusive jumps in liquidity, marked improvements in pricing performance for OTM options are observed. In addition, we discuss the impacts of liquidity risk on hedging parameters.

Brigo與Mercurio提出了三種新的資產價格過程，分別是位移CEV過程、位移對數常態過程與混合對數常態過程。在這三種過程中，資產價格的波動度不再是一個固定的常數，而是時間與資產價格的明確函數。而由這三種過程所推導出來的歐式選擇權評價公式，將會導致隱含波動度曲線呈現傾斜曲線或是微笑曲線，且提供了參數讓我們能夠配適市場的波動度結構。本文利用台指買權來實證Brigo與Mercurio所提出的三種歐式選擇權評價公式，我們發現校準結果以混合對數常態過程優於位移CEV過程，而位移CEV過程則稍優於位移對數常態過程。因此，在實務校準時，我們建議以混合對數常態過程為台指買權的評價模型，以達到較佳的校準結果。 / Brigo and Mercurio proposed three types of asset-price dynamics which are shifted-CEV process, shifted-lognormal process and mixture-of-lognormals process respectively. In these three processes, the volatility of the asset price is no more a constant but a deterministic function of time and asset price. The European option pricing formulas derived from these three processes lead respectively to skew and smile in the term structure of implied volatilities. Also, the pricing formula provides several parameters for fitting the market volatility term structure. The thesis applies Taiwan’s call option to verifying these three pricing formulas proposed by Brigo and Mercurio. We find that the calibration result of mixture-of-lognormals process is better than the result of shifted-CEV process and the calibration result of shifted-CEV process is a little better than the result of shifted-lognormal process. Therefore, we recommend applying the pricing formula derived from mixture-of-lognormals process to getting a better calibration.

我國勞工退休金新制自2005年7月1日開始實施，由過去的確定給付制改為具有確定提撥特色的「個人帳戶制」。對於勞工而言，確定提撥制和過去確定給付制不同之處在於承擔退休金投資風險的責任將由雇主轉由個人承擔。如何透過退休機制的設計以降低退休金的投資風險是近年來的重要議題，因此本文主要從個人偏好與風險的觀點探討保證投資收益率制度與制度轉換選擇權等兩個降低確定提撥制投資風險的重要配套措施。 在本論文的第一篇研究中發現，資產配置與國際投資對保證成本的影響頗大，在個人可選擇資產配置的情況下，高投資風險的資產選擇將造成政府未來龐大的或有負債。為了解決政府保證成本過高造成代內與代間的財富移轉，本文從使用者付費與個人效用的觀點探討保證投資收益率制度的設計，發現藉由設立保證投資收益上限可提升風險趨避者、損失趨避者與後悔趨避者等偏好下的預期效用，且能降低個人管理下方風險所需的提撥成本與退休計畫參加者所需繳交的保證費用，故建議政府可將投資收益率上限納入保證投資收益率制度，供退休計畫參加者選擇合於本身偏好的保證收益率上限。 在近來許多國家的公、民營退休體系由過去以確定給付制改為確定提撥制，為了降低在確定提撥制下的退休金投資風險，在美國的佛羅里達州之公務人員退休體系中，存在著可供個人選擇是否轉換到確定給付制的機制。在我國勞退新制中除了從過去的確定給付制改為確定提撥制外，亦輔以「年金保險制」供勞工選擇與轉換，若年金保險制具有確定給付制的特徵，則勞工等於是擁有一個從確定提撥轉換轉到確定給付制的選擇權，因此制度選擇權的探討對我國而言亦是相當地重要。在本論文的第二篇研究中發現，當風險趨避程度越高則轉換至確定給付制的機率越高，轉換到確定給付制的高峰期會出現在開始工作的初期與屆臨退休之際等兩段期間。隨著工作期間的延長，個人轉換到確定給付制的機率越低，但仍可有效地提升退休金的所得替代率與達到降低退休金下方風險的效果，在加入退休制度初期不得轉換的限制之後，會降低轉換到確定給付制的機率。 / The Labor Retirement Pension Act enacted in 2005 introduced defined contribution (DC) pension plan for substituting the traditional defined benefit (DB) pension plan. In the defined contribution pension plan, the investment risk is transferred to the participants. However, the design of rate of return guarantee makes the investment risk less severe for participants. In the first essay, we find that the asset allocation and foreign investment have large impact on the guarantee cost: the high risky investment may result in large potential liability of the government in the future if participants have the investment portfolio choice. This study develops a framework to analyze design of rate of return guarantee from the financial engineering and user paid principle view. We find that the cap of investment return guarantee not only increases the expected utility of risk aversion, loss aversion and regret aversion, but also decreases the contribution cost to participant associated with managing the downside risk. Around the world, the defined contribution (DC) plans have been the primary trend of pension reform in the both public and private sector. In an attempt to decrease the investment risk associated with DC plan, the public employees are provided with an option to buy back DB plan in the Florida State of U.S.A. In the second essay, we find that the higher level of risk aversion is, the higher probability to buy back DB plan is. During the employee’s early years of service and as the employees near retirement, the probability to exercise the option is the highest. The probability to exercise the option is decreasing with the years of service being increasing; the option also increase the pension replacement rate as well as decrease the downside risk of pension. The probability to exercise the option is lower, when the option to buy back the DB plan is prohibited during the employee’s early years of service.

本論文提出線性規劃的方法以還原隱藏於選擇權市場價格中的風險中立機率測度，並利用該機率測度計算選擇權的合理價格。模型中假設選擇權對應同一標的資產與到期日，資產價格於到期日的狀態為離散點且個數有限，當市場不具任何套利機會時，以極小化市場價格與合理價格之離差總和作為挑選風險中立機率測度的準則。最後，以臺指選擇權(TXO)的交易資料做為實證對象。實證中發現，加入平滑限制式與離差權重之線性規劃模型在評價歐式選擇權合理價格的效能最為優異。 / The thesis proposes a liner programming to recover the risk-neutral probability distribution of an underlying asset price from its associated market option prices, and we evaluate the fair prices of options via the resulting risk-neutral probability distribution. Assume that we face a series of European options with different exercise prices on the same maturity and underlying asset in this linear programming model. The criterion of choosing a risk-neutral probability distribution is minimizing the sum of total deviations subject to requiring that the fair prices of options are consistent with observed market option prices. Finally, we take the trading data of TXO as an empirical study. The empirical study indicates that the model with smooth constraints and weighted deviations has the best performance in pricing the rational price of European options.