Topic of the master thesis is practice of interest rate models. Literature dedicated to the interest rate models usually presents theory in very general form. Theory presented in general form leads to a gap between theory and practice. Author tries to fill this gap. Thesis describes basic theory and presents practical computations, which are relevant to generating interest rate scenarios. Contribution is given by derivation of formulas and computational methods in form directly applicable for implementation of presented models. It is common practice to validate quality of interest rate scenarios. Author presents several tests and implements them in programming language Python. Tests are implemented as application with graphical user interface.

Thesis (MComm)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: This assignment sets out to address the concept of equity duration, where equity duration is viewed as a measure of the interest rate sensitivity of common stock's market value. The traditional use of standard dividend discount models, results in extremely long duration estimates for equities - in the order of 10 years for income stocks to 25 years and more for growth companies whose cash flows are not expected to materialize until some future period. Leibowitz (1986) identified an alternative approach for assessing equity duration empirically. These empirical estimates of actual stock price sensitivity to underlying changes in interest rates imply that equities behave as if they are much shorter duration instruments. Various attempts have been made to reconcile the difference between theoretical predictions of equity duration and empirical findings. The differences in duration of assets in place and growth opportunities are given as a possible reason for the above mentioned differences. It is argued that investment opportunities are similar to options a company has. These option-like characteristics of growth opportunities may alter the basic relationship between equity valuation and interest rate changes. The option framework suggests that the duration of growth companies may be shorter (not longer) than those of assets in place. The results from option theory can however not be applied directly to growth options, since some of the assumptions may not be valid in the case of growth options. The presence of these growth options makes it virtually impossible to calculate equity duration theoretically. This study empirically tests the relationship between growth opportunities and equity duration by focussing the attention on the interest rate sensitivity of South African growth companies. The following hypotheses regarding equity duration and growth companies are postulated: • There is a significant difference in interest rate sensitivity between growth companies and low-growth companies. • There is a significant difference between duration of growth companies measured using nominal interest rates and duration of growth companies using real interest rates. All non-mining companies on the Johannesburg Securities Exchange SA, for the period 1980 to 2000, were analysed. These companies were sorted into different portfolios that reflected their growth opportunities. Market capitalisation, book-to-market and price-earnings ratios were used as proxies to rank companies according to growth opportunities. The results from univariate regressions suggest positive duration for common equities. The negative relationship between equity returns and changes in nominal interest rates are independent of size, book-to-market or price-earnings ratios of the sampled companies. Including the market factor as an independent variable results in markedly different equity duration. The duration is correlated with size, as both coefficients and t-statistics increase when moving from small companies to larger companies. In addition, the small companies have negative not positive duration, as was the case for simple univariate regressions. There is also some evidence that high growth portfolios, as measured by low book-to-market and high price-earnings ratios, are less sensitive to interest rate changes than low growth portfolios. Employing all three Fama and French's factors, there is no longer a cross-sectional dependence on company size, with the mean duration being close to zero and statistically insignificant in virtually all cases. Also, when dividing changes in the nominal interest rate into changes in real rates and changes in inflation, it does not significantly affect the estimates of equity duration. The author found no evidence to support the stated hypotheses, when employing the Fama and French's three factor model. This may mean that the relationships are subsumed in the Fama and French risk factors. / AFRIKAANSE OPSOMMING: Hierdie werkstuk bestudeer die konsep van die duur van gewone aandele (equity duration), waar die duur van 'n gewone aandeel gedefinieer word as 'n maatstaf van die rentekoerssensitiwiteit van die markwaarde van die aandeel. Die tradisionele gebruik van standaard dividend verdiskonterings modelle, lei tot uiters lang duur beramings vir gewone aandele - in die orde van 10 jaar vir inkomste aandele tot 25 jaar en meer vir groei ondernemings wie se kontantvloei nie verwag word om te materialiseer voor 'n sekere toekomstige datum nie. Leibowitz (1986) identifiseer 'n alternatiewe empiriese benadering vir die beraming van gewone aandeel duur. Hierdie empiriese bepaling van die sensitiwiteit van die werklike aandeelprys tot onderliggende veranderings in rentekoerse, impliseer dat gewone aandele reageer asof hulle baie korter duur instrumente is. Verskeie pogings is aangewend om die verskille tussen teoretiese voorspellings van gewone aandeel-duur en empiriese bevindings te rekonsilieer. Die verskille tussen duur van bates in plek en groei-geleenthede word aangevoer as 'n moontlike rede vir bogenoemde verskille. Dit word geargumenteer dat investeringsgeleenthede soortgelyk is aan die opsies wat 'n onderneming het. Hierdie opsie-soortgelyke eienskappe van groei-geleenthede kan die basiese verhouding tussen gewone aandeel waardasie en rentekoers verandering wysig. Die opsie raamwerk dui daarop dat die duur van groei-ondernemings korter kan wees (en nie langer nie) as die van bates in plek. Die resultate van opsie teorie kan egter nie direk toegepas word op groei-opsies nie, aangesien sekere van die aannames nie geldig mag wees in die geval van groei-opsies nie. Die teenwoordigheid van hierdie groei-opsies het tot gevolg dat dit feitlik onmoontlik is om gewone aandeel-duur teoreties te bereken. Die studie toets empiries die verhouding tussen groei-geleenthede en gewone aandeel-duur deur te fokus op die rentekoers sensitiwiteit van Suid Afrikaanse groei-ondernemings. Die volgende hipoteses met betrekking tot die gewone aandele duur en groei-ondernemings word gestel: • Daar is 'n betekenisvolle verskil in rentekoers sensitiwiteit tussen groei-ondernemings en lae groei-ondernemings. • Daar is 'n betekenisvolle verskil tussen duur van groei-ondernemings gemeet deur gebruik te maak van nominale rentekoerse en duur van groei-ondernemings deur gebruik te maak van reële rentekoerse. Alle nie-myn ondernemings op die Johannesburg Sekuriteite Beurs SA, vir die periode 1980 tot 2000, is ontleed. Hierdie ondernemings is gesorteer in verskillende portefeuljes wat hulle groei geleenthede reflekteer. Markkapitalisasie, boek-tot-markwaarde en prysverdienste verhoudings is gebruik as maatstawwe om ondernemings te rangskik volgens groeigeleenthede. Die resultate van enkel veranderlike regressies dui positiewe duur aan vir gewone aandele. Die negatiewe verhouding tussen aandeelopbrengs en verandering in nominale rentekoerse is onafhanklik van grootte, boek-tot-markwaarde of prysverdienste verhoudings vir die getoetste ondernemings. Indien die markfaktor ingesluit word, as 'n onafhanklike veranderlike, lei dit tot opvallend verskillende gewone aandeel-duur. Die duur is gekorreleer met grootte, met beide koëffisiënte en t-statistieke wat styg wanneer beweeg word van klein ondernemings tot groter ondernemings. Addisioneel, die klein ondernemings het negatiewe, nie positiewe duur, anders as in die geval van eenvoudige enkel veranderlike regressies. Daar is ook bewyse dat hoë groei portefeuljes, soos gemeet deur lae boek-tot-markwaarde en hoë prysverdienste verhoudings, minder sensitief is vir rentekoers veranderings as lae groei portefeuljes. Met die aanwending van al drie Fama en French se faktore is daar nie meer kruis-selektiewe afhanklikheid (cross-selectional dependence) op ondernemingsgrootte aanwesig nie, met die gemiddelde duur wat naby nul is en statisties onbedeidend in feitlik all gevalle is. Wanneer die verandering in die nominale rentekoers verdeel word in veranderings in reële koerse en veranderings in inflasie, beïnvloed dit ook nie betekenisvol die bepaalde gewone aandeel duur nie. Die outeur het met die gebruik van die Fama & French drie faktor model geen bewyse gevind wat die vermelde hipoteses staaf nie. Dit mag beteken dat die rente-risiko verwantskappe in die Fama en French risiko faktore vervat is.

Thesis (MComm (Business Management))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: This study focuses on banking book interest rate risk management, more specifically shortterm interest rate risk management problems. This type of risk is induced by the inflation targeting policy of the South African Reserve Bank. As a result, inflation leads to an uncertain interest rate cycle and a period of uncertain interest rate levels as it relates to lending and borrowing products in the South African commercial banking sector. The lending rates of most South African commercial banks are tied to the prime overdraft rate. The borrowing rates are linked to the money market rates such as the Johannesburg Interbank Agreed Rate (JIBAR) which is indirectly affected by the prime overdraft rate. Hence, lending and borrowing rates are related to the repo-rate. Furthermore, a fixed relationship exists between the prime overdraft rate and the repo-rate. The monetary policy committee meets every two months during the year to make inflation and repo-rate adjustments, as stipulated in the inflation targeting policy. A subject portfolio containing fixed-rate loans, advances and floating-rate deposits is exposed to the change of the repo-rate. This short-term banking book interest rate risk is defined based on the fact that the repo-rate adjustment occurs every two months, the banking book risk management is short term focused, and hedging instruments against interest rate risk are short term dated contracts. Such a short term risk may have a negative impact on the bank’s profitability. The study starts with a review of the bank risk management processes, and then discusses the enterprise risk management framework that guides the formation of the risk management processes and systems. In order to benchmark against international risk management practices, a comparative analysis is carried out to evaluate the risk management tendencies of bank risk management in South Africa and globally. The empirical findings reveal that most banks (i.e. eighty per cent of all local banks) manage the short-term interest rate risk by following the same process as the interest rate risk in general. The key elements (risk identification, measurement, mitigation and monitoring and reporting) of the banking book interest rate risk management are not linked together as a systematic process. This is not in line with the Basel II Accord to manage market risks through a process approach. The study also proposes a generic short-term interest rate risk management framework and in doing so, addresses some of the weaknesses of current risk management practices. Based on this framework, the South African banks may develop their own processes to manage such short-term banking book interest rate risk exposure. Some of the problems of bank risk management that come to light from the empirical findings, are summarised in the last chapter and may be considered for future research. / AFRIKAANSE OPSOMMING: Hierdie studie fokus op die probleme van die bankboek rentekoersrisikobestuur, meer spesifiek die korttermyn rentekoers risikobbestuursprobleme. Hierdie tipe risiko word deur die inflasieteikenraamwerk beleid van die Suid-Afrikaanse Reserwebank veroorsaak. Dit veroorsaak ‘n tydperk van onsekere rentekoersvlakke veral sover dit uitleen- en leenprodukte in die Suid-Afrikaanse kommersiële banksektor aangaan. Die uitleenkoerse van die meeste Suid-Afrikaanse kommersiële banke is aan die prima bankoortrekkingskoers gekoppel. Die leningstariewe is aan die geldmarkkoerse soos die Johannesburgse Interbank Ooreengekome Koers (JIBOK) gekoppel wat indirek geraak word deur die prima bankoortrekkingskoers. Uitleen- en leenkoerse is redelik afhanklik van die repo-koers waar laasgenoemde ‘n redelike vaste verwantskap met die prima bankoortrekkingskoers het. Die monetêre beleidkomitee vergader elke twee maande van die jaar om inflasie en repokoers aanpassings te maak, ooreenkomstig die inflasieteiken beleid. 'n Bepaalde portefeulje met vasterente lenings, voorskotte en vlottende koers deposito’s is blootgestel aan die verandering in die repokoers. Hierdie korttermyn rentekoersrisiko van die bankboek word gedefinieer op grond van die feit dat die repo-koers aanpassing elke twee maande gebeur. Die bankboek risikobestuur het ‘n korttermyn fokus, en verskansingsinstrumente teen rentekoersrisiko is korttermyn kontrakte. So 'n korttermyn risiko kan 'n negatiewe impak op die bank se winsgewendheid hê. In hierdie studie word bankrisikobestuur prosesse beskou. Die risikobestuursraamwerk wat die basis vorm van die risikobestuursprosesse en stelsels word aangespreek. Om 'n idee te vorm van die huidige internasionale risikobestuurspraktyke of tendense by banke, word die state van internasionale en oorsese banke kortliks beskou. Die empiriese bevindinge uit die opname dui daarop dat die meeste banke (d.w.s tagtig persent van alle plaaslike banke) die korttermyn rentekoersrisiko nie afsonderlik van rentekoersrisikobestuur in die algemeen bestuur nie. Die sleutelelemente van die risikobestuursproses (risiko identifisering, mitigasie, implementering, monitering en verslagdoening) kom wel voor maar die bankboek rentekoersrisikobestuur is nie gekoppel as 'n sistemastiese proses nie. Dit blyk dat hierdie situasie na alle waarskynlikheid nie in lyn is met die Basel II akkoord om markrisiko's deur 'n prosesbenadering, te bestuur nie. Die studie stel ook ‘n generiese raamwerk voor vir die bestuur van korttermyn rentekoersrisiko wat dan ook van die swakhede van die huidige risikobestuurspraktyke aanspreek. Op grond van hierdie raamwerk, kan die Suid-Afrikaanse banke dit oorweeg om hul eie prosesse te ontwikkel vir die bestuur van bankboek rentekoersrisiko blootstelling. Sommige navorsingsprobleme van bank risikobestuur wat uit die empiriese bevindinge aan die lig gekom het, word in die laaste hoofstuk opgesom en kan vir verdere navorsing in die toekoms oorweeg word.

本篇研究旨在探討利率政策對所得分佈不均的關係，利用 Azzimonti, De Francisco, and Quadrini (2014) 的模型加以延伸擴展，並加入土地或資產的價格變動，從而進一步探討中央銀行的低利率政策對企業主與受薪階層的影響。 模型假設簡單將市場參與者分成2大類，分別是企業家與受薪的勞工，藉由此2大類分別的終生效用函數對利率的變動來說明利率政策對所得分配的影響。Joseph E. Stiglitz (2015b) 提及在低利率政策之下將導致信用的膨脹，進而使土地或資產的價值提高，而土地或資產之價格不斷上漲為造成所得分佈不均之重要原因之一，故本篇論文將土地價格變動納入模型加以延伸，並觀察台灣近幾年之現況。 此篇研究發現，在中央銀行的低利率政策之下，有產階層的企業家之財富條件將會愈來愈好，而與之相對的受薪階層的勞工之財富條件將會愈來愈差；而台灣近幾年之數據亦顯示當利率降低之際，代表所得分佈不均的GINI指數隨之上升，與本篇之研究結果相符。 / The objective of this thesis is to testify the relation between interest rate policy and income inequality. We develop a model based on Azzimonti, De Francisco, and Quadrini (2014) and expand the model by considering the change of the land or asset price so as to analyze the impact of low interest rate on the welfare of entrepreneurs and workers, respectively. The model simply divides the agents into two groups, entrepreneurs and workers, and uses their lifetime utility to explain the impact of interest rate policy on income inequality. Joseph E. Stiglitz (2015b) mentioned that low interest rate would expand the credit availability and drive up the land or asset price. The continuous upward trend of land or asset price is one of the important reason causing income inequality. After taking into account the land or asset price on the sensibility of income inequality toward interest rate, this thesis is able to provide a theoretical underpinning of Taiwan’s empirical observation in recent years. We find out that with low interest rate policy, entrepreneurs’ wealth condition is doing better and better while the workers’ wealth is getting worse. Taiwan’s data in the recent years also shows that once the central bank lowering the interest rate GINI index, which represent the income inequality distribution, will rise immediately. This situation is in accord with the thesis.

In this thesis we establish a relationship between the Potential Approach to interest rates and the Market Models. This relationship allows us to derive the dynamics of forward LIBOR rates and forward swap rates by modelling the state price density. It means that we are able to secure the arbitrage-free condition and positive interest rate feature when we model the volatility drifts of those dynamics. On the other hand, we develop the Potential Approach, particularly the Hughston-Rafailidis Chaotic Interest Rate Model. The early argument enables us to infer that the Chaos Models belong to the Stochastic Volatility Market Models. In particular, we propose One-variable Chaos Models with the application of exponential polynomials. This maintains the generality of the Chaos Models and performs well for yield curves comparing with the Nelson-Siegel Form and the Svensson Form. Moreover, we calibrate the One-variable Chaos Model to European Caplets and European Swaptions. We show that the One-variable Chaos Models can reproduce the humped shape of the term structure of caplet volatility and also the volatility smile/skew curve. The calibration errors are small compared with the Lognormal Forward LIBOR Model, the SABR Model, traditional Short Rate Models, and other models under the Potential Approach. After the calibration, we introduce some new interest rate models under the Potential Approach. In particular, we suggest a new framework where the volatility drifts can be indirectly modelled from the short rate via the state price density.

對一些退休基金或是壽險基金來說，因為它們的金額都相當龐大，進而影響的層面也相當廣泛；它們影響著金融市場的發展、有價證券的價格和市場的報酬。 所以，對現今市場投資在這樣長期資產的投資策略而言，以下我們要討論的議題將是非常重要。 以前的退休基金管理計畫是建立在單期的假設當中。根據目前所持有所有資產的部位、目前市場的狀況與對未來報酬的期望，基金管理人將尋求對下期的最適投資決策。傳統的方法都是用期望值-變異數方式(Mean-Variance approach)去極大化投資的報酬，以求取最適部位。但是單期的期望值-變異數方式(Mean-Variance approach)面對了二個問題： 一、 集合各個單期最適決策用多期的眼光來看不一定是最適。 二、 單期最適決策並不能同時處理投資面與集資面的問題。例如：退休基金同時間有每月的收入與每月的投資面。 不像單期的投資方式，使用多期的投資方法比較能符合這樣的投資問題與要求，也比較具有合理性。 投資在長期資產的部位與報酬率，最容易受到利率變動的影響。換句話說，利率變化是影響投資在長期性資產的最大變因。因此，我們將討論的問題：在利率是隨機變動時，以Vasicek (1977)的利率模型為主，加入投資人風險偏好的共同基金的分配原則。這樣的理論下，我們將利用風險中立的方法求出最適的投資組合，以滿足在長期投資觀點下避險與套利的需求。其中投資人的風險偏好是以Merton (1973)提出的常數相關風險偏好(Constant Relative Risk Aversion；CRRA)的效用函數去討論；在文章最後，我們將針對投資人的風險偏好做一些討論，包括：改變CRRA的參數、自然對數的效用函數(Logarithmic utility function)。 以往的研究都採用動態程式設計(Dynamic programming approach)的方法來解決這樣多期投資的問題，但是這樣的方法運用的計算相當複雜，也不一定求的出最適部位解；而利用Cox and Huang (1989)提出的風險中立方法(Martingale approach)將完全的解決以上遇到的問題。 / In this study, we investigate the dynamic mutual fund separation theorem applied to portfolio management for constant relative risk averse investors where, in particular, the interest rate risks are incorporated. Within this economy, the real interest rates and stock prices are assumed to follow the Markovian processes whose drifts and diffusion parameters are driven by certain state variables. Our approach involves the use of the martingale methodology developed by Cox and Huang (1989) as proposed in the work of Deelstra et al. (2003). Following their framework, we consider the economy of the investors that consists of cash, bond fund and stock indices. Adding to the previous works, we investigate the obtained optimal strategies through numerical examples in order to be compared to the allocations of popular advice and clarify the hedge and arbitrage demands in financial decision from long-term perspective. Finally, certain mutual funds are constructed to validate the validity of the popular advice.

本研究分為兩大部份，第一部份為探討利率的變動，主要研究央行每日公開市場操作對利率的影響，此部份包含了兩篇文章，分別為「以門檻自我迴歸模型(TAR，Threshold auto-regression model，Tong(1983)，Tsay(1989))估計央行公開市場操作對利率的影響」及「以Multiple Criteria Selection Model (Maddala,1983)估計央行公開市場操作對利率的影響」，研究樣本為日資料。在第一篇文章利用門檻自我迴歸模型估計用以區分央行動態性或防禦性公開市場操作的指標 的門檻值，利用估計出的 推論央行進行動態性或防禦性操作。第二篇文章利用第一篇文章所估計出的 將樣本區分為央行進行防禦性操作或動態性操作的樣本，並同時考慮央行是否進行公開市場操作反應函數及央行一旦決定進行公開市場操作後其要採取防禦性或動態性公開市場操作的反應函數，以Multiple Criteria Selection Model估計，同時本文更進一步考慮央行對於公開市場操作態度改變對此影響效果的影響，實證結果發現在央行總裁表示將更積極公開市場操作後，即2003年3月14日之後，發現當央行進行動態性公開市場操作可以有效的改變市場利率，而當央行進行防禦性操作則可以有效的沖銷準備金市償的干擾因子，降低市場利率的波動。 本論文第二部份為分析衍生性金融產品避險對公司價值的影響，比較與檢定有避險公司與無避險公司其公司價值差異，並討論公司以衍生性金融商品避險的動機，同時也比較當公司決定避險後，選擇大範圍避險與小範圍避險對公司價值是否也有影響。研究的對象為台灣上市公司中的529家公司，結果發現出口比率與公司規模是公司選擇避險重要的考慮因素，同時發現避險公司的Tobin’s Q、ROA、ROE與PMS皆大於無避險公司。 / There are two issues we concern in this paper. The first one is to investigate the daily effect of open market operation on short-term interest rate. The second one is to analysis the effect of hedging with derivatives by the firms on the firm’s value. About the first issue, the net issue of central bank’s certificates of deposit (CD) is functioned as the open market operation instrument. At beginning, employing a simple linear regression model, the benchmark model in our paper, the counter-intuitive evidence that issuance of DC decreases the short-term interest rate is found. To solve this puzzle, first, we define an index of open market operation to disentangle the effect of the defensive operation from the dynamic operation and use TAR model to estimate the value of . Next, we apply the Multiple Criteria Selection Model (MCSM) to solve the problems of selection bias and to estimate the two decision functions and the effects of daily open market operations. At last, we also consider the change of central bank’s attitude toward the open market operations. We separate the sample by the date (13-April-2003) of the speech of the governor of CBC, Fai-Nan Perng. We find that after 13-April-2003, the issuance of CD increase the short-term interest rate under dynamic O.M.O. and the coefficient is significantly different from zero, which means the daily liquidity effect exists. About the second issue, we compare and test the firm’s value difference between the firms hedging with derivatives and the firms without hedging. We also try to find the determinants of firm’s hedging. Our sample is the 529 firms listed in TSEC (Taiwan stock exchange corp.).

This thesis aims at contributing to the study of the valuation of insurance liabilities and the management of the assets backing these liabilities. It consists of four parts, each devoted to a specific topic. In the first part, we study the pricing of a classical single premium life insurance contract with profit, in terms of a guaranteed rate on the premium and a participation rate on the (terminal) financial surplus. We argue that, given the asset allocation of the insurer, these technical parameters should be determined by taking explicitly into account the risk management policy of the insurance company, in terms of a risk measure such as the value-at-risk or the conditional value-at-risk. We then design a methodology that allows us to fix both parameters in such a way that the contract is fairly priced and simultaneously exhibits a risk consistent with the risk management policy. In the second part, we focus on the management of the surrender option embedded in most life insurance contracts. In Chapter 2, we argue that we should model the surrender time as a random time not adapted to the filtration generated by the financial assets prices, instead of assuming that the surrender time is an optimal stopping time as it is usual in the actuarial literature. We then study the valuation of insurance contracts with a surrender option in such a model. We here follow the financial literature on the default risk and in particular, the reduced-form models. In Chapter 3 and 4, we study the hedging strategies of such insurance contracts. In Chapter 3, we study their risk-minimizing strategies and in Chapter 4, we focus on their ``locally risk-minimizing' strategies. As a by-product, we study the impact of a progressive enlargement of filtration on the so-called ``minimal martingale measure'. The third part is devoted to the systematic mortality risk. Due to its systematic nature, this risk cannot be diversified through increasing the size of the portfolio. It is thus also important to study the hedging strategies an insurer should follow to mitigate its exposure to this risk. In Chapter 5, we study the risk-minimizing strategies for a life insurance contract when no mortality-linked financial assets are traded on the financial market. We here extend Dahl and Moller’s results and show that the risk-minimizing strategy of a life insurance contract is given by a weighted average of risk-minimizing strategies of purely financial claims, where the weights are given by the (stochastic) survival probabilities. In Chapter 6, we first study the application of the HJM methodology to the modelling of a longevity bonds market and describe a coherent theoretical setting in which we can properly define the longevity bond prices. Then, we study the risk-minimizing strategies for pure endowments and annuities portfolios when these longevity bonds are traded. Finally, the fourth part deals with the design of ALM strategies for a non-life insurance portfolio. In particular, this chapter aims at studying the risk-minimizing strategies for a non life insurance company when inflation risk and interest rate risk are taken into account. We derive the general form of these strategies when the cumulative payments of the insurer are described by an arbitrary increasing process adapted to the natural filtration of a general marked point process and when the inflation and the term structure of interest rates are simultaneously described by the HJM model of Jarrow and Yildirim. We then systematically apply this result to four specific models of insurance claims. We first study two ``collective' models. We then study two ``individual' models where the claims are notified at a random time and settled through time.

立法院於1992年2月26日修定保險法第146條，將國外投資正式列入保險業資金運用之項目，引導保險業參與國外金融市場。保險業因國內利率環境與資本市場欠缺長天期金融工具下，衍生顯著利差損問題，而國外金融商品的多樣性、高創新能力與高收益率似乎提供保險業資金投資選擇。 本研究嘗試透過不同構面的探討，將國外投資所面臨的風險與金融主管機關的監理措施加以說明，並詳細分析資產負債管理策略－資產負債區隔，建議保險業者應從資產負債管理出發，考量不同性質負債，尋找適合金融資產做為支撐之標的，如此才能透過搭配性質相近且年期適合的國外金融工具進行負債面的管理，使得國外投資能充份地發揮其多樣性與享有較高之投資收益。 亦應利用支撐負債面之金融資產組合所計算出來市場利率做為負債面評價基礎，做到資產與負債皆採用市價評估，更能反應保險公司真實的價值，並可做為主管機關監理參考。保險業者除透過資產負債區隔了解本身國外資產配置的適當性外，應輔以嚴謹的風險管理機制與自律機制，如此才能保有永續經營的能力。 / The article 146 of Insurance Law had been amended by Legistrative Yuan on 26 February 1992. It allows insurance company invests funds into foreign financial assets and across boundary to attend foreign markets. Taiwan insurance industry face significant losses from the actual credit interest lower than the credit interest rate due to economic environments and lack of long-term investment vehicles. The foreign financial market with multiplicity, innovation and higher yield seems to provide Taiwanese insurance companys a channel to resolve its interest rate gap problem. This research employs boarder discussions on the foreign investment risk of the life insurance industry from various angles. This paper also analyzes the control issues from regulator’s rerspective and outlines the asset-liability management tool “segmentation”. We also provide suggestions to Taieanese life insurance industry to adopt the asset and liability segmentation as their major tool in performing oversea investment. In the same time, the realistic surplus of the insurance company can be monitored by measuring the difference between mark to market assets and contingency liability that is calculated by market yield from replicated portfolio. In recent years, the foreign investment play a major role in Taiwanese Life insurance company’s asset portfolio, hence they are required to carefully monitor appropriate financial assets to support their liabilities. It also includes enhancing the risk management framework and self-control mechanism in order to maintain their business ability.

無 / Existing literature has shown that force of mortality has amazing resemblance of interest rate. It is then tempting to extend existing model of interest rate model context to mortality modeling. We apply the model in Diebold and Li (2006) and other models that belong to family of yield rate model originally proposed by Nelson and Siegel (1987) to forecast (force of) mortality term structure. The fitting performance of extended Nelson-Siegel model is comparable to the benchmark Lee-Carter model. While forecasting performance is no better than Lee-Carter model in younger ages, it is at the same level in elder ages. The forecasting performance increases for 5-year ahead forecast is better than 1-year ahead comparing to Lee-Carter forecast. In the end, the forecast outperforms Lee-Carter model when age dimension is trimmed to age 20-100.