此研究主要研究壽險業的系統性風險與違約風險之評價，基於投資組合的波動度去建立隨機過程模型。特別是那些隱含無法被多角化的財務風險、系統性風險，透過研究，使用Heston(1993)模型去描述標的資產的隨機波動程度比以往使用Black-Scholes(1973)模型描述股價的波動變化更能反映實際的風險狀況，並透過CIR過程來表示瞬間的波動程度。在這個模型之中，把過去以平賭測度決定違約選擇權的方法延伸。此外透過探討違約價值之敏感度，根據不同的情境測試對於壽險公司負債的影響。最後透過數值的結果與敏感度分析隨機波動模型與確定性的模型之差異。 當資本準備增加時，資產與負債比提高，因負債仍固定承諾予保戶之利率增長，而資產因應系統性風險的發生而減損仍能支付負債，致使違約風險降低，進而使得評價時點的違約金額降低。當系統風險發生時，風險值上升，違約價值為右偏分布，代表在極端條件下有可能有極大的損失；反之，當整個金融體系經濟情勢良好，公司擁有足夠的經濟資本時，風險值下降，滿足VaR75與CTE65的法規限制，此時公司的清償能力足以反映系統性風險。 / This paper considers the problem of valuating the default option of the life insurers that are subject to systematic financial risk in the sense that the volatility of the investment portfolio is modeled through stochastic processes. In particular, this implies that the financial risk cannot be eliminated through diversifying the asset portfolio. In our work, Heston (1993) model is employed in describing the evolution of the volatility of an underlying asset, while the instantaneous variance is a CIR process. Within this model, we study a general set of equivalent martingale measures, and determine the default option by applying these measures. In addition, we investigate the sensitivity of the default values given regulatory forbearance for the life insurance liabilities considered. Numerical examples are included, and the use of the stochastic volatility model is compared with deterministic models. As reserve of capital is increasing, asset-liability ratio is also increasing. The liability grew up with promised interest rate, and it could be covered by the asset when the systematic risk events happened. Therefore, the default risk was decreasing, that caused the default value decreasing. When the systematic risk events happened, the value of risk was increasing, and the default value was positive skew distribution. That means the maximum loss will be coming in the extreme case. On the other hand, when prosperity economy occurred, the value of risk was decreasing, which in compliance with the law of VaR75&CTE65 rules, and the insurance company had enough capital to face the systematic risk events.

本文利用分量迴歸方法探討經濟成長和經濟波動間的關係，使用亞洲10個主要經濟體的實質GDP季資料來進行分析。從實證結果發現，大部分國家在大多數分量下產出波動對實質GDP成長率有正向影響，唯有在某些國家當經濟成長率低時產出波動對經濟成長會有負面影響。另外，進一步考慮了產出波動結構性改變因素之後，基本上仍然不會改變波動性對經濟成長率的影響，產出波動變數同樣在大多數國家的大部分分量對GDP成長率有顯著影響，其中高所得國家在高低分量皆為正相關；中低所得國家在低分量下為負相關，高分量下為正相關。此結果顯示，即使在同一個國家資料中，經濟波動的影響也會隨著經濟成長率的高低而有所不同；此外，因為不同國家有不同所得水準，所受到的正、反向影響也會不一樣。 / This thesis employs the quantile regression model to investigate the link between economic growth and its volatility, using quarterly real GDP data for ten main Asian economies. Our empirical results show that the output growth volatility positively affects real GDP growth rate at most quantiles for most nations. Only when some countries are at a period of low economic growth, does output volatility negatively affect economic growth. In addition, after considering possible structural breaks in the GDP growth volatility, the relation between volatility and output growth rate stays qualitatively the same. That is, the output volatility still has significant impact on real GDP growth rate at most quantiles for most nations. For high income countries, volatility and economic growth are positively correlated at higher and lower quantiles; while for low and middle income countries, these two factors are negatively correlated at lower quantiles, and positively correlated at higher quantiles. Our empirical evidence indicates that even in the same country, the impact of volatility varies according to the country’s economic growth rate. Besides, due to different income levels, the volatility impact on economic growth rate will differ in different countries.

本篇論文的目的在驗證台股期貨報酬率與其波動度之間的相對應關係是由槓桿效果或是波動度回饋效果之因果關係所驅動，並且分別以日資料以及高頻率日內資料進行實證。實證結果發現在高頻率日內資料的應用下，能夠比日資料揭露出更詳細的波動度資訊，將報酬率與波動度間的對應關係描繪得更加明瞭。且在大多數資料期間內，同期下，台股期貨報酬率與其波動度之間會呈現負相關性，而負相關的程度會隨著報酬率遞延期數越長而逐漸遞減，因此可以發現報酬率與其波動度間呈現一個經由報酬率進而影響波動度的對應關係，與槓桿效果的因果關係雷同。最後，本文亦採用了常見的波動度預測模型，歷史模擬法、GARCH(1,1)模型、EGARCH(1,1)模型以及GJR-GARCH(1,1)模型，觀察這些波動度模型所預測出之波動度是否含有上述驗證的資訊意涵，並比較各波動度模型的預測能力，結果發現GJR-GARCH模型於樣本外期間所預測之波動度，其與報酬率之間不但具有槓桿效果的因果關係，且預測能力亦於四個波動度模型中表現最佳。

We investigate the spillover of industry effect in Taiwan stock market. Using a generalized vector autoregressive where forecast-error variance decompositions are invariant to variable ordering, we objectively propose measures of both total and directional spillovers on return and volatility daily data. In full-sample analysis, there is a heavy spillover effect in the interaction between stock market and industries. The stock market acts as a receiver from the information diffused from the industries, but the industries could not be confirmed as spillover outputer or inputer. The rolling-sample findings also pinpoint the high spillovers during the financial events. Finally, conducting the robustness test, we divide the sample periods into subperiods and switch the daily data toward weekly and monthly data, then obtaining the consistent results with prior inference.

受2008年金融海嘯影響，人壽保險業因資本及信用市場之系統性風險而導致帳列資產價值大幅減損，進一步影響壽險公司清償能力，而主管機關為兼顧審慎監理與市場穩定原則，而採行資本監理寬容措施，卻使得資本不足之保險公司缺口擴大。另外，保險安定基金以保費為基礎徵收單一費率，加劇保險公司間交叉補貼之情形。因此，如何透過以責任準備金為基礎，計算公平合理之風險差別費率，以避免產生影響其他保險公司正常經營之系統性風險，抑或引發保險公司道德風險，為本文研究之主要議題。 本文與過去文獻主要之差異為：(1) 資產模型依資產配置方式，使用蒙地卡羅模擬詳盡現金流路徑，著重於描述壽險業之情境；(2) 股票型風險性資產加入跳躍過程 (Jump) 與隨機波動兩種情境，以表達壽險業資產端承受資本市場變動加劇之風險；(3) 考慮政府監理寬容措施，以描述主管機關對於壽險業監理態度。 依蒙地卡羅模擬法試算保險安定基金公平費率，研究結果發現：(1)監理寬容期限增加時，安定基金公平費率增加；(2)監理標準提高，安定基金公平費率有先降後升之效果；(3)保險公司財務槓桿比例增加時，安定基金公平費率上升。 / Due to the global financial crisis in 2008 that resulted in systematic risks in the equity and credit market, it creates significant deprecation in the life insurers’ balance sheet which affect insurers’ solvency. In order to retain prudent supervision and market stability, the authority has announced capital temporal relief plan that may make insolvency insurer worse. Recent occurrences of financial distress to some insurers have raised questions about whether the current guaranty system that charge a flat levy rate in premium-based is adequate to protect policyholders. A risk-weighted levy rate in reserve-based has been proposed to establish reasonable contribution method which can avoid high risk insurers’ moral hazard and protect the other insurers from further systematic risks. A brief summary of the advantages of this paper is listed below：(1) By Monte Carol simulation method, detailed cash flow of insurer’s asset allocation can be used to describe the risk preference of life insurer. (2) Our stock model incorporates jump diffusion and stochastic volatility in order to reflect that life insurers face increasing volatility in capital market. (3) Consider regulatory forbearance to represent government’s attitude to life insurers. We calculate fair guaranty premium through Monte Carol simulation method. We find that： (1) Fair premium increases as extending the period of regulatory forbearance. (2) As regulatory criterion raises fair premium decreases at first, but increases if regulatory criterion reaches certain level. (3) Increasing leverage ratio of the insurer results in increasing fair premium.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20063号 / 工博第4251号 / 新制||工||1658(附属図書館) / 京都大学大学院工学研究科建築学専攻 / (主査)教授 川瀬 博, 教授 林 康裕, 教授 松島 信一 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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.

本文考量波動度不對稱效果(Volatility Asymmetric Effect)與均數回歸(Mean Reverting)兩個特性，並考量台股市場特性，嘗試建立一個適合台灣市場的波動度交易策略。利用GARCH(1,1)波動度與VIX指標建構第一個交易訊號，並建立當日沖銷部位。以賺取日內行情為出發點，利用時間序列模型捕捉波動度的高估或低估且搭配純跨式(Pure Straddle)策略或根據Delta調整後的跨式(Adjusted Straddle)策略。第二個交易訊號則是利用市場敏感指標，觀察外資與自營商在交易部位與未平倉部位的變化，找出對於波動度的影響。建立由選擇權與期貨組成的Delta-Hedged部位，藉由觀察市場上主力籌碼的變化，動態調整部位契約，尋找波段之間的獲利機會。 實証部分以期交所公布的每日交易資料與VIX日資料，利用2007至2008兩年的歷史資料，估計參數與測試交易訊號。樣本外期間為2009年1月開始至3月結束共55個交易日。考量交易成本後，兩個不同型態的交易訊號，仍然能夠藉由本研究的策略，獲得正的報酬。本文認為台灣為一個淺碟市場，過度反應資訊的特性，讓波動度策略出現獲利的機會。藉由這個波動度交易系統的研究，除了讓資金豐沛的機構投資人使用外，也能夠讓一般投資大眾建立自己的波動度交易策略 關鍵字:波動度交易，選擇權交易策略，GARCH(1,1)，VIX，市場情緒指標 / Trying to apply a preliminary study of volatility trading strategies in Taiwan derivative market is the topic of this dissertation. Capturing the market movement or even the dynamic of underlying asset is a Pandora’s Box for academic researchers and industry participants. Mean-reverting and asymmetrical effects are the two special characteristics of volatility for us to design our trading system according to the previous empirical studies. In our study, we use different type of volatility signal to capture the trading opportunities. Use the new released information form TAIFEX including VIX and Position Structure of Institutional Traders to design our signal. We apply the idea to use pure option position and delta-hedged position as our trading tools in this volatility trading system and look for the opportunities between realized volatility and implied volatility. An over-reaction may rises the uncertainty and also lead the market volatility change coherently. We use history data from 2007 to 2008 test our trading signal and parameters. The out sample period is from 2009 January to 2009 March which has 55 trading days to simulate our strategies. In the end, we see a positive result in both trading signals which earns positive return after considering the trading cost. Key words: Volatility Trading, Market Sentiment Indices, Option Strategies, VIX, GARCH(1,1)

Black and Scholes (1973)對於報酬率提出以B-S模型配適，但B-S模型無法有效解釋報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性的性質。Merton (1976)認為不尋常的訊息來臨會影響股價不連續跳躍，因此發展B-S模型加入不連續跳躍風險項的跳躍擴散模型，該模型可同時描述報酬率不對稱高狹峰和波動度微笑兩性質。Charles, Fuh and Lin (2011)加以考慮市場狀態提出狀態轉換跳躍模型，除了保留跳躍擴散模型可描述報酬率不對稱高狹峰和波動度微笑，更可以敘述報酬率的波動度叢聚和長記憶性。本文進一步拓展狀態轉換跳躍模型，考慮不連續跳躍風險項的帄均數與市場狀態相關，提出狀態轉換跳躍相關模型。並以道瓊工業指數與S&P 500指數1999年至2010年股價指數資料，採用EM和SEM分別估計參數與估計參數共變異數矩陣。使用概似比檢定結果顯示狀態轉換跳躍相關模型比狀態轉換跳躍獨立模型更適合描述股價指數報酬率。並驗證狀態轉換跳躍相關模型也可同時描述報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性。最後利用Esscher轉換法計算股價指數選擇權定價公式，以敏感度分析模型參數對於定價結果的影響，並且市場驗證顯示狀態轉換跳躍相關模型會有最小的定價誤差。 / Black and Scholes (1973) proposed B-S model to fit asset return, but B-S model can’t effectively explain some asset return properties, such as leptokurtic, volatility smile, volatility clustering and long memory. Merton (1976) develop jump diffusion model (JDM) that consider abnormal information of market will affect the stock price, and this model can explain leptokurtic and volatility smile of asset return at the same time. Charles, Fuh and Lin (2011) extended the JDM and proposed regime-switching jump independent model (RSJIM) that consider jump rate is related to market states. RSJIM not only retains JDM properties but describes volatility clustering and long memory. In this paper, we extend RSJIM to regime-switching jump dependent model (RSJDM) which consider jump size and jump rate are both related to market states. We use EM and SEM algorithm to estimate parameters and covariance matrix, and use LR test to compare RSJIM and RSJDM. By using 1999 to 2010 Dow-Jones industrial average index and S&P 500 index as empirical evidence, RSJDM can explain index return properties said before. Finally, we calculate index option price formulation by Esscher transformation and do sensitivity analysis and market validation which give the smallest error of option prices by RSJDM.

本研究探討選擇權交易量之大小對於波動度預測之效率性所造成之對偶效果(dual effect)，驗證〝正常的高交易量〞與〝異常的高交易量〞對於波動度預測能力是否有不同的影響。本研究採用panel data之資料型態，以LIFFE上市的個股買權為對象，資料長度為三年左右。主要欲探討之假說為： 1.一般而言，交易量大的選擇權，其波動度估計誤差較交易量小的選擇權來得小。 2.相對於平日水準而言，某日交易量異常高的選擇權將有較大的波動度估計誤差。 本研究所使用的波動度預測模型為隱含波動度(ISD)，採用的是最接近到期月份及最接近價平的合約。實證以組合迴歸、固定效果模型、隨機效果模型分別估計之，加以比較。結果發現固定效果模型為較佳之解釋模型，然而結果顯示交易量的對偶效果並不明確影響波動度預測誤差，故推測有某種影響公司間差異的因素，即公司間之異質性，比相對交易量更容易影響波動度預測之誤差。另外，透過組間與組內效果之分析，發現不論是長期還是短期，由於公司間的異質性存在，使得相對交易量對於波動度預測誤差均無明顯影響。 / The purpose of this research is to study the dual effect on the efficiency of volatility forecasting which is caused by the volume of option market, with the intent to test whether〝normal high volume〞and〝abcdrmal high volume〞cause different results on the ability of volatility forecasting. The data used is in the form of panel data. It is drawn from LIFFE, and has a length of about three years. The hypotheses to be examined in this study are：1. High-average-volume options have smaller volatility forecasting errors than low-average-volume options; 2. Options have larger volatility forecasting errors on abcdrmally-high-volume days than on normal-volume days. In this research, volatility is forecasted by implied standard deviation (ISD) which is implied in the at-the-money and the nearest expiry month options. Pooled regression、fixed effect model、and random effect model methods were applied. The results show that the fixed effect model made the best analysis amongst the three models. However, the result does not support the hypotheses made above, which means that volume does not have much influence on volatility forecasting error. It is inferred that there exists some other factors which could cause the difference between firms, namely heterogeneity, and these factors have much more powerful influence over volatility forecasting error than volume. Finally, it was found that no matter for long run or short run, because of the existence of heterogeneity, relative volume doesn’t have obvious influence on volatility forecasting errors when analyzing the difference between the between-individual effect and the within-individual effect.