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For an equity-linked insurance, the death benefit is linked to the performance of the company’s investment portfolio. Hence, both mortality risk and equity return shall be considered for pricing such insurance. Several studies have found some dependence between mortality improvement and economy growth. In this thesis, we showed that American mortality rate and Dow Jones Industrial Average (DJIA) index price are negatively dependent by using several copulas to define the joint distribution. Then, we used these copulas to forecast mortality rates and index prices, and calculated the payoffs of a 10-year term equity-linked insurance. We showed that the predicted insurance payoffs will be smaller if dependence between mortality and index price is taken into account. / October 2016

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This thesis explores board nationality diversity, focusing on foreign non-executive directors and their relationship with CEO compensation, firm performance, and crash risk for a sample of UK firms from 2002 to 2015. First, we examine the changes in board composition over the years and find an increase in foreign non-executive directors and in the number of foreign CEOs managing UK firms. We discover boards have become smaller, more independent and CEOs occupying dual roles have considerably reduced. Next, we analyse the relationship between foreign non executive directors and CEO compensation and note that firms with more foreign non executive directors pay less to their CEO. Moreover, European and other international non-executive directors are particularly effective at limiting CEO compensation. Then we examine the impact of foreign non-executive directors on firm performance and show that foreign non-executive directors positively impact firm value. CEO and executive directors’ equity-like compensation and share ownership also positively influences firm performance. Our findings suggest that European and American non executive directors are more effective in improving corporate performance. Finally, we analyse the relationship between foreign non-executive directors, CEO compensation and crash risk. Foreign non-executive directors monitor the board and mitigate the impact of CEO equity-linked pay on stock price crash risk. Our analysis reveals that leverage increases crash risk, but that foreign non-executive directors, of high leverage firms lower crash risk. Overall, foreign non-executive directors serve as effective monitors and advisors to moderate executive pay, improve firm performance and reduce stock price crash risk.

近年來，衍生性金融商品不停的推陳出新，不論是金融機構、企業或個人，絕大多數皆可能從事過金融商品交易。此外，為了滿足投資人與發行者各式各樣的需求，以及因應不同的經濟環境背景，金融商品不停推陳出新。 2003年，證期會核准14家國內券商可發行新台幣結構性債券（Structure Notes），2004年證期會更擴大國內券商連結標的可為國外標的，雖然目前稅法問題尚未解決，但預估未來將有千億元以上的投資額。結構性債券利用財務工程及金融創新，將債券和選擇權相結合，依據景氣及投資人的需要設計，不但可擴大券商的業務範圍及增添獲利空間，又可使投資人或企業得到多樣化的投資及避險管道。舉凡債券、保單、共同基金、銀行存款…等，都是連動的對象，甚至通貨膨脹率、原物料價格連動，可搭配出的商品變化很多。目前國內股價連動商品發展日趨重要，因此，結構式債券商品的理論價格衡量存在其必要性。 本論文的目的，針對兩種股價連動債券商品進行評價，本研究目的可歸結為以下數點： 1.介紹雙收益連動債券與高收益鎖定配息債券之產品特色，並加以評價與分析。 2.探討雙收益連動債券與高收益鎖定配息債券之發行商與投資人的利潤分析。 3.進行雙收益連動債券與高收益鎖定配息債券之避險交易策略。 4.闡述本研究之結論與心得，並提出改進之處以供後續研究參考。

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

Magister Scientiae - MSc / The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant. / South Africa

有鑑於附有最低保證給付投資型保險期末現金流量與選擇權如出一轍，是以應用平賭訂價理論(The Martingale Pricing Method)嵌入HJM利率模型，對隨機利率下附有最低保證給付投資型保險進行評價。並對繳費方式與利率型態兩議題所構成四種類型附有最低保證給付投資型保險作實地數據模擬與評價，以及敏感度分析。 研究結果可以歸納為四點結論。 (1) 單就附有最低保證給付投資型保險簡化版（忽略期中死亡理賠與期滿生存機率）而言： 可視為是最低保證給付折現與以之為履約價的買權組合。因此，當影響因子僅與買權有相關性時，附有最低保證給付投資型保險與理論買權的敏感度分析結果，如出一轍。連動標的期初價格與波動度變動於附有最低保證給付投資型保險影響便是實證。 (2) 延續上點論述衍生： 當影響因子同時對買權與附有最低保證給付折現具有相關性時，由於買權佔整個保險價值比重過低，是以主要影響力皆來自附有最低保證給付的變動。附有最低保證給付與固定利率折現因子變動對於保險價值影響，即反應此結果。 (3) 分別就繳費方式不同下，投保年齡與投保期限變動對於附有最低保證給付投資保險的影響而言： 躉繳型繳費方式下，由第二點結論可得，投保期限越長保費越低，是以當投保年齡越大，期中死亡率提高，且期間短的保費較高的情況下，投保年齡變動對於附有最低保證給付投資型保險影響為正向；分期繳型繳費方式下，由於條款設定不同，無法與躉繳型一概而論，反映在投保期間越長保單價值與保費皆增加，但若是比較其增加的幅度（二階條件小於零）逐漸減少，倒是與躉繳型投資保險投保期間與保費關係意思相同，只是呈現方式不同。分期繳型投資型保險保單價值與投保年齡關係，從投保期限與保費關係以及高年齡層死亡率較高，可以得知，隨著投保年齡的增加，分期繳型投資保險中因為死亡理賠的現金流量產生機會提高，而此部分期間短保單價值較低，是以投保年齡與保單價值呈現反比關係，但是保單價值平準化後的保費，源於平準因子每期存活率因投保年齡增加而減少，造成投保年齡越高，保費也越高。 (4) 就性別而言： 躉繳型附有最低保證給付投資保險，由於女性相較於男性死亡率較低，容易取得期間較長的期滿保證金，而此部分價值較低，是以女生保費較男生便宜；分期繳型附有最低保證給付投資保險，則是相反的表現，由於此部分價值較高，是以女性的保險價值高於男性，同時因女性平準因子中的存活率也比男性高，是以每期所要繳交的保費也比男性低廉。 (5) 就利率型態而言： 隨機利率下躉繳型投資型保險與固定利率下躉繳型投資保險相較，便宜許多，主要是因為利率型態為隨機，且期初利率期間結構打破水平狀態的假設，真實反應正常期初利率期間結構(Normal Interest Rate Term Structure)，是以評價出的保費較固定利率型態下的保費低廉，甚至於分期繳型附有最低保證給付投資保險，在隨機利率下，隨著投保期限增加，保費反而下降。