Investment-linked insurance in Taiwan has been listed for almost a decade since 2001. In 2002, after the big sales of the investment-linked insurance, the domestic insurance companies also joined the market. For the investment-linked insurance, the policyholders retain the protection of the life insurance as well as share the earnings of the investment. Since the main investment instruments of the investment-linked insurance are mutual funds, it is important to study how to optimally allocate the portfolio. This research consider the returns of the mutual funds under tree models assumption. The objective is to find the optimal portfolio which has minimum variance and attained a given expected return level. The problem is also known as mean-variance portfolio problem. In the empirical work, we study eleven daily mutual fund price data from Sep. 2007 to Nov. 2008. Using the data of the first 12 months, we first establish initial tree price models, then update the parameters of the tree model by the EWMAmethod. The optimal trading strategies of the mean-variance portfolio are investigated under this model setting. We class the mutual funds into three categories: equity funds, balanced funds and bond funds. Different combination of these three kinds of funds are considered to find the optimal trading strategy respectively. The results showed that the realized returns using this optimal trading strategy in practice is close to the pre-specified expected return level.

This thesis establishes an information system which combines three credit risk models through Service-Oriented Architecture (SOA). The system requires the bank user inputting finance-related data and selecting options to generate a series of credit risk related results, including the probabilities of default, the recovery rates, the expected market value of assets, the volatilities of the expected market value of assets, the default points, the default distances, and four indexes from principal components analyses. In addition to exhibiting the numerical results, graphical results are also available for the user. Three credit risk models joining this system are the Moody¡¦s KMV Model with Default Point Modified, the Risk-Neutral Probability Measure Model, and the Time-Varying Jointly Estimated Model. Several previous researches have demonstrated the validity of these credit risk models, hence the purpose of this study is not to examine the practicability of these models, but to see if these models are capable of connecting each other effectively and eventually establishing a process to evaluate the credit risk of enterprises and industries by the use of testing samples. Testing samples are data from Taiwan Small and Medium Enterprise Credit Guarantee Fund. The finance-related data includes the loan amounts, the book value of assets, the data used to calculate the default point threshold (such as the short-term debt and the long-term debt), and the financial ratios with regard to growth ability (such as the revenue growth rate and the profit growth rate before tax), operation ability (such as the accounts receivable turnover rate and the inventory turnover rate), liability-paying ability (such as the current ratio and the debt ratio), and profitability (such as the return on assets and the return on equity). In addition to inputting the finance-related data, the system also require the user selecting the industrial category, the default point threshold, the way data being weighted, the data period, and the borrowing rates from the option page for every enterprise in order to acquire the results. Among the computing process, user is required to select weighted average method, either weighted by loan amounts or weighted by market value of assets, to obtain ¡§the weighted average probability of default of the industry¡¨ and ¡§the weighted average recovery rate of the industry¡¨ which are both used by the Time-Varying Jointly Estimated Model. This study also makes use of quartiles to simulate the situation when the user is near the bottom and top of the business cycle. Furthermore, the ¡§Supremum Strategy¡¨ and the ¡§Infimum Strategy¡¨ are added to this study to let the user realize the best condition and the worse condition of the ¡§Time-Varying Industrial Marginal Probabilities of Default¡¨.

本論文提出利用機率平賭性質由選擇權市場價格還原風險中立機率測度的雙目標規劃模型。假設對應同一標的資產且不同履約價的選擇權均為歐式選擇權，到期時標的資產的狀態為離散點且個數有限。若市場不存在套利機會時，建構出最小化離差總和及最大化平滑的雙目標規劃模型。將此雙目標規劃模型利用權重法轉換成單一目標之非線性模型，即可還原風險中立機率測度，並利用此風險中立機率測度評價選擇權的公平價格。最後，我們以台指選擇權(TXO)為例，驗證此模型的評價能力。 / This thesis proposes a biobjective nonlinear programming model to derive risk-neutral probability distribution of underlying asset. The method are used to choose probabilities that minimize the deviation between the observed price and the theoretical price as well as maximize the smoothness of the resulting probabilities. A weighting method is used to covert the model into a single objective model. Given a non-arbitrage observed option price, a risk-neutral probability distribution consistent with the observed option can be recovered by the model. This risk-neutral probability is then utilized to evaluate the fair price of options. Finally, an empirical study applying to Taiwan’s market is given to verify the pricing ability of this model.

本論文研究如何由觀測的選擇權市場價格還原風險中立機率測度（等價平賭測度）。首先建構選擇權投資組合的套利模型，其中假設選擇權為單期，到期日時的狀態為離散點且個數有限，並且對應同一標的資產且不同履約價格。若市場不存在套利機會時，可使用拉格朗日乘數法則將選擇權套利模型導出拉格朗日乘子的可行性問題。將可行性問題作為限制式重新建構線性規劃模型以還原風險中立機率測度，並且利用此風險中立機率測度評價選擇權的公正價格。最後，我們以台指選擇權（TXO）為例，驗證此模型的評價能力。 / This thesis investigates how to recover the risk-neutral probability (equivalent martingale measure) from observed market prices of options. It starts with building an arbitrage model of options portfolio in which the options are assumed to be in one-period time, finite discrete-states, and corresponding to the same underlying asset with different strike prices. If there is no arbitrage opportunity in the market, we can use Lagrangian multiplier method to obtain a Lagrangian multiplier feasibility problem from the arbitrage model. We employ the feasibility problem as the constraints to construct a linear programming model to recover the risk-neutral probability, and utilize this risk-neutral probability to evaluate the fair price of options. Finally, we take TXO as an example to verify the pricing ability of this model.