Subprime residential mortgage loan securitization and its associated risks have been a major topic of discussion since the onset of the subprime mortgage crisis (SMC) in 2007. In this regard, the thesis addresses the issues of subprime residential mortgage loan (RML) securitization in discrete-, continuous-and discontinuous-time and their connections with the SMC. In this regard, the main issues to be addressed are discussed in Chapters 2, 3 and 4. In Chapter 2, we investigate the risk allocation choices of an investing bank (IB) that has to decide between risky securitized subprime RMLs and riskless Treasuries. This issue is discussed in a discrete-time framework with IB being considered to be regret- and risk-averse before and during the SMC, respectively. We conclude that if IB takes regret into account it will be exposed to higher risk when the difference between the expected returns on securitized subprime RMLs and Treasuries is small. However, there is low risk exposure when this difference is high. Furthermore, we assess how regret can influence IB's view - as a swap protection buyer - of the rate of return on credit default swaps (CDSs), as measured by the premium based on default swap spreads. We find that before the SMC, regret increases IB's willingness to pay lower premiums for CDSs when its securitized RML portfolio is considered to be safe. On the other hand, both risk- and regret-averse IBs pay the same CDS premium when their securitized RML portfolio is considered to be risky. Chapter 3 solves a stochastic optimal credit default insurance problem in continuous-time that has the cash outflow rate for satisfying depositor obligations, the investment in securitized loans and credit default insurance as controls. As far as the latter is concerned, we compute the credit default swap premium and accrued premium by considering the credit rating of the securitized mortgage loans. In Chapter 4, we consider a problem of IB investment in subprime residential mortgage-backed securities (RMBSs) and Treasuries in discontinuous-time. In order to accomplish this, we develop a Levy process-based model of jump diffusion-type for IB's investment in subprime RMBSs and Treasuries. This model incorporates subprime RMBS losses which can be associated with credit risk. Furthermore, we use variance to measure such risk, and assume that the risk is bounded by a certain constraint. We are now able to set-up a mean-variance optimization problem for IB's investment which determines the optimal proportion of funds that needs to be invested in subprime RMBSs and Treasuries subject to credit risk measured by the variance of IE's investment. In the sequel, we also consider a mean swaps-at-risk (SaR) optimization problem for IB's investment which determines the optimal portfolio which consists of subprime RMBSs and Treasuries subject to the protection by CDSs required against the possible losses. In this regard, we define SaR as indicative to IB on how much protection from swap protection seller it must have in order to cover the losses that might occur from credit events. Moreover, SaR is expressed in terms of Value-at-Risk (VaR). Finally, Chapter 5 provides an analysis of discrete-, continuous- and discontinuous-time models for subprime RML securitization discussed in the aforementioned chapters and their connections with the SMC. The work presented in this thesis is based on 7 peer-reviewed international journal articles (see [25], [44], [45], [46], [47], [48] and [55]), 4 peer-reviewed chapters in books (see [42], [50j, [51J and [52]) and 2 peer-reviewed conference proceedings papers (see [11] and [12]). Moreover, the article [49] is currently being prepared for submission to an lSI accredited journal. / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2010.

Subprime residential mortgage loan securitization and its associated risks have been a major topic of discussion since the onset of the subprime mortgage crisis (SMC) in 2007. In this regard, the thesis addresses the issues of subprime residential mortgage loan (RML) securitization in discrete-, continuous-and discontinuous-time and their connections with the SMC. In this regard, the main issues to be addressed are discussed in Chapters 2, 3 and 4. In Chapter 2, we investigate the risk allocation choices of an investing bank (IB) that has to decide between risky securitized subprime RMLs and riskless Treasuries. This issue is discussed in a discrete-time framework with IB being considered to be regret- and risk-averse before and during the SMC, respectively. We conclude that if IB takes regret into account it will be exposed to higher risk when the difference between the expected returns on securitized subprime RMLs and Treasuries is small. However, there is low risk exposure when this difference is high. Furthermore, we assess how regret can influence IB's view - as a swap protection buyer - of the rate of return on credit default swaps (CDSs), as measured by the premium based on default swap spreads. We find that before the SMC, regret increases IB's willingness to pay lower premiums for CDSs when its securitized RML portfolio is considered to be safe. On the other hand, both risk- and regret-averse IBs pay the same CDS premium when their securitized RML portfolio is considered to be risky. Chapter 3 solves a stochastic optimal credit default insurance problem in continuous-time that has the cash outflow rate for satisfying depositor obligations, the investment in securitized loans and credit default insurance as controls. As far as the latter is concerned, we compute the credit default swap premium and accrued premium by considering the credit rating of the securitized mortgage loans. In Chapter 4, we consider a problem of IB investment in subprime residential mortgage-backed securities (RMBSs) and Treasuries in discontinuous-time. In order to accomplish this, we develop a Levy process-based model of jump diffusion-type for IB's investment in subprime RMBSs and Treasuries. This model incorporates subprime RMBS losses which can be associated with credit risk. Furthermore, we use variance to measure such risk, and assume that the risk is bounded by a certain constraint. We are now able to set-up a mean-variance optimization problem for IB's investment which determines the optimal proportion of funds that needs to be invested in subprime RMBSs and Treasuries subject to credit risk measured by the variance of IE's investment. In the sequel, we also consider a mean swaps-at-risk (SaR) optimization problem for IB's investment which determines the optimal portfolio which consists of subprime RMBSs and Treasuries subject to the protection by CDSs required against the possible losses. In this regard, we define SaR as indicative to IB on how much protection from swap protection seller it must have in order to cover the losses that might occur from credit events. Moreover, SaR is expressed in terms of Value-at-Risk (VaR). Finally, Chapter 5 provides an analysis of discrete-, continuous- and discontinuous-time models for subprime RML securitization discussed in the aforementioned chapters and their connections with the SMC. The work presented in this thesis is based on 7 peer-reviewed international journal articles (see [25], [44], [45], [46], [47], [48] and [55]), 4 peer-reviewed chapters in books (see [42], [50j, [51J and [52]) and 2 peer-reviewed conference proceedings papers (see [11] and [12]). Moreover, the article [49] is currently being prepared for submission to an lSI accredited journal. / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2010.

Schwarz (1997)提出均數回復過程（Mean-Reverting Process, MR）捕捉能源價格的動態過程，而Lucia and Schwarz (2002)將此模型結合確定季節性函數，並推導出期貨價格封閉解。然而，能源價格常會因為未預期事件的發生而產生大幅度的變動，為了描述價格跳躍的現象，Clewlow and Strickland (2000)延伸Schwarz的模型提出均數回復跳躍擴散模型（Mean-reverting jump diffusion process, MRJD），此模型除了保留均數回復模型對能源價格會回復至長期水準的描述外，再加上跳躍項來描述價格的異常變動。而Cartea and Figueroa (2005)則同時考慮季節性和跳躍因子，並推導出期貨價格封閉解。另外，雖然台灣目前並非京都議定書所規範的國家，但環境保護是未來的趨勢，故在衡量能源產業財務風險時，除了考慮相關原料和產品，應考慮碳權交易之影響。為了探討財務風險管理在能源產業之應用，本文以煉油廠為例，將其表示成特定期貨部位的投資組合，並透過計算投資組合風險值來衡量煉油廠的財務風險。文中使用結合季節性的均數回復過程、均數回復跳躍擴散過程進行模型配適。實證結果顯示，均數回復跳躍擴散模型在回溯測試下表現最佳；另外，考慮碳權交易後會使得煉油廠的財務風險上升。 / Schwarz (1997) proposes the mean-reverting process (MR) to model energy spot price dynamics, and Lucia and Schwarz (2002) extend this model by including mean reversion and a deterministic seasonality. This model can capture the mean-reversion of energy price, but fail to account for the huge and non-negligible price movement in the market. Clewlow and Strickland (2000) extend Schwarz’s model to mean-reverting jump diffusion process (MRJD). Cartea and Figueroa (2005) present a model which captures the most importance characteristics of energy spot prices such as mean reversion, jumps and seasonality, and provide a closed-form solution for the forward. Although Taiwan is not the member of Kyoto Protocol, but Environmental Protection is a trend in the future. In order to measure the financial risk induced by energy industries, we should consider the effect of emission trading. In this paper, we discuss the implication of financial risk management in energy industries by analyzing the exposure of refinery which represented certain energy futures portfolios. We use MR and MRJD process with seasonality to model energy spot price dynamics, and calibrate the parameters to historical data. And, we consider the interaction of all of positions and calculate the Value-at-Risk of portfolios. The results show that among various approaches the MRJD presents more efficient results in back-testing, and emission trading poses additional risk factors which will increase the financial risk for refineries.

Insurance contracts will be reported at fair values on insurers’ balance sheets from 2010. In this thesis, we will review the conceptual and theoretical backbone of the insurance fair valuation project while providing a summary of the key features of the fair valuation project. Then, we will conduct a case study aimed at finding, under the fair valuation regime, the best asset allocation strategy for a particular business unit that carries a hypothetical annuity portfolio using a single modelling framework for valuation, risk calculation and business appraisal.

Modern financial asset pricing theory is a broad, and at times, complex field. The literature review in this study covers many of the asset pricing techniques including factor models, random walk models, correlation models, Bayesian methods, autoregressive models, moment-matching models, stochastic jumps and mean reversion models. An important topic in finance is portfolio opti-misation with respect to risk and reward such as the mean variance optimisation introduced by Markowitz (1952). This study covers optimisation techniques such as single period mean variance optimisation, optimisation with risk aversion, multi-period stochastic programs, two-fund separa- tion theory, downside optimisation techniques and multi-period optimisation such as the Bellman dynamic programming model. The question asked in this study is, in the context of investing for South African individuals in a multi-asset portfolio, whether an active investment strategy is signi cantly di erent from a passive investment strategy. The passive strategy is built using stochastic programming with moment matching methods for non-Gaussian asset class distributions. The strategy is optimised in a framework using a downside risk metric, the conditional variance at risk. The active strategy is built with forward forecasts for asset classes using the time-varying transitional-probability Markov regime switching model. The active portfolio is finalised by a dynamic optimisation using a two-stage stochastic programme with recourse, which is solved as a large linear program. A hypothesis test is used to establish whether the results of two strategies are statistically different. The performance of the strategies are also reviewed relative to multi-asset peer rankings. Lastly, we consider whether the findings reveal information on the degree of effi ciency in the market place for multi-asset investments for the South African investor. / Operations Management / M. Sc. (Operations Research)

Abstract in Zulu, English and Afrikaans / This study examined the consequences of Principal-Agent and Corporate Governance interactions within South Africa’s FTSE/JSE Top40 listed companies from 2008 to 2016. The study’s objectives were to examine the prevalence of Principal-Agent and Corporate Governance problems, to ascertain potential costs of these problems, to establish their socio-economic consequences, and evaluate the effectiveness of the governance codes. The study is anchored in Principal-Agent theory. Mixed methods methodology was employed, specifically Concurrent and Exploratory Sequential Mixed Methods design logics. The main findings include that, 23.91% of sample companies experienced Principal-Agent and Corporate Governance problems- significantly exceeding the study’s expectations that negligible governance problems exist and reveals the pervasiveness of these problems; executive compensation plays a bigger role in exacerbating Principal-Agent and Corporate Governance problems than expected and often considered in governance mechanisms; multi-billion rands potential costs are ascribed to Principal-Agent and Corporate Governance problems incurred by principals; unjustifiable salary inequalities resulting in other inequalities that build social mistrust; and there is limited conviction that current governance codes are effective. This study’s contributions include; proposing an executive remuneration model that considers governance of the company in determining executive compensation; formulating a governance index calculated based on King III and King IV recommendations to standardise the measurement of the quality of governance in companies; the salary Gini was used to establish compensation gaps and red-flag potential Principal-Agent problems and flaws in governance systems; and used value at risk procedures to quantify potential Principal-Agent and Corporate Governance costs. The main theoretical implications of the study’s findings are; agency theory needs extension to capture socio-economic costs and not only focus on the principal; remuneration models should consider the executive’s company governance and social and economic egalitarianism; flexibility of ‘comply or explain’ should subordinate socio-economic consequences, suggesting a hybrid approach which makes certain governance code provisions compulsory; and finally, behavioural finance theories should be used in governance research for better insights. / Lolu cwaningo lwacubungula futhi lwahlolisisa imiphumela yokuxhumana phakathi kwesimo seNhloko ne-Ejenti, i-Principal-Agent, (lapho umuntu eqoka omunye ukuba athathe izinqumo kanye/noma izinyathelo egameni lakhe) nokuPhathwa nokuLawulwa Kwenkampani, ezinkampanini ezingama-40 ebezikleliswe phezulu ohlwini lwe-FTSE/JSE eNingizimu Afrika kusukela ngowezi-2008 kuya kowezi-2016. Izinhloso zalolu cwaningo kwabe kuwukubheka ukuthi zivamise kangakanani futhi zisabalele kangakanani izinkinga eziphathelene neNhloko ne-Ejenti kanye nokuPhathwa Nokulawulwa Kwenkampani ukuze kutholakale ukuthi zingakanani izindleko ezibangelwa yilezi zinkinga, nokuthola umthelela walokhu kwinhlalomnotho, kanye nokuhlola ukuthi zisebenza kahle kangakanani izinkambiso zokuphathwa nokulawulwa kwezinkampani. Lolu cwaningo lwakhelwe phezu kwethiyori yeNhloko ne-Ejenti. Kwasetshenziswa izindlela zocwaningo ezixubile, ikakhulukazi izindlela ezixubile zokuhlola kusetshenziswa izinyathelo ezenziwa kanyekanye noma ngesikhathi esisodwa kanye nezinyathelo ezilandelanayo. Okusemqoka okwatholakala ocwaningweni kubandakanya nokuthi izinkampani okwenziwa kuzona ucwaningo ezingama-23.91% zahlangabezana nezinkinga eziphathelene neNhloko ne-Ejenti kanye nokuPhathwa Nokulawulwa Kwenkampani – okuyinani elingaphezulu kakhulu kwalokho obekulindelekile ocwaningweni, ngoba phela kwakulindeleke ukuthi zibe yingcosana kakhulu izinkinga ezikhona eziphathelene nalokhu, kepha-ke ucwaningo lwaveza ukuthi lezi zinkinga zixhaphakile impela; imiholo yabaphathi abakhulu bezinkampani idlala indima enkulu ekubhebhethekiseni izinkinga eziphathelene neNhloko ne-Ejenti kanye nokuPhathwa Nokulawulwa Kwenkampani kunalokho obekulindelekile futhi esikhathini esiningi lokhu akuyona neze into evamise ukubhekisiswa uma kwenziwa izinqubo zokuphatha nokulawula; zibalelwa kwizigidigidi zamarandi izindleko ezingena kuzona izinhloko zezinkampani okucatshangwa ukuthi zibangelwa yizinkinga eziphathelene neNhloko ne-Ejenti kanye nokuPhathwa Nokulawulwa Kwenkampani; ukungalingani ngokwemiholo, ngaphandle kwesizathu esizwakalayo salokhu, okuyinto eholela kokunye futhi ukungalingani, okudala ukungathembani emphakathini; futhi kuncane kakhulu ukuqiniseka nokukholelwa ekutheni zisebenza kahle izinkambiso zokuphatha nokulawula ezikhona njengamanje. Igalelo lalolu cwaningo libandakanya isiphakamiso semodeli yemiholo yabaphathi abakhulu ebhekisisa nodaba lokuphathwa nokulawulwa kwenkampani ngenkathi kucutshungulwa udaba lwemiholo yabaphathi abakhulu; ukuhlanganiswa kwenkomba yokuphathwa nokulawulwa kwenkampani ebalwa ngokususela kwizincomo ze-King III kanye ne-King IV zokusetshenziswa kwesikali esifanayo sokukala ikhwalithi yokuphathwa nokulawulwa kwezinkampani; isikali semiholo se-Gini sasetshenziswa ukuhlonza amagebe akhona phakathi kwemiholo kanye nokuxwayisa ngezinkinga ezingahle zivele eziphathelene neNhloko ne-Ejenti kanye nokuPhathwa Nokulawulwa Kwenkampani kanye namaphutha nobuthakathaka obukhona ezinhlelweni zokuphatha nokulawula; futhi kwasetshenziswa izinqubo zezikali zobungozi bokulahlekelwa kwenkampani ukubala inani lezindleko okungenzeka kungenwe kuzona ngenxa yezinkinga eziphathelene neNhloko ne-Ejenti kanye nokuPhathwa Nokulawulwa Kwenkampani. Imibonongqangi evele kulokho okutholakale ocwaningweni yilena elandelayo; ithiyori echaza ubudlelwano phakathi kwenhloko ne-ejenti kumele yelulwe ukuze ifake phakathi nezindleko eziphathelene nenhlalomnotho futhi lokhu kungagcini nje kuphela kwinhloko; amamodeli omholo kumele abhekisise nendlela ephethwe ngayo inkampani ngabaphathi abakhulu kanye nemfundiso yokulingana kwabantu bonke ngokwenhlalo nangokomnotho; ukuguquguquka ‘kokuthobela umthetho noma ukuchaza’ (‘comply or explain’) kumele kube ngaphansi uma kuqhathaniswa nemiphumela yenhlalomnotho, ukuze kuqhanyukwe nendlela exubile ephoqelela ukusetshenziswa kwezinkambiso zokuphatha nokulawula ezithile; kanti futhi, okokugcina, ocwaningweni lokuphatha nokulawula kumele kusetshenziswe amathiyori aphathelene nesimo somqondo sabaphathi ngenkathi bethatha izinqumo nezinyathelo eziphathelene nokuphathwa nokusetshenziswa kwezimali ukuze kuqondakale kangcono konke okuphathelene nalokhu. / Hierdie studie het van 2008 tot 2016 die gevolge van die wisselwerking tussen hoofagent- en korporatiewe regering in Suid-Afrikaanse FTSE/JSE Top 40- genoteerde maatskappye bestudeer. Die oogmerke was om die voorkoms van probleme met hoofagent- en korporatiewe regering te ondersoek; die moontlike koste en die sosio-ekonomiese gevolge daarvan te bepaal; en die doeltreffendheid van die regeerkodes te evalueer. Hierdie studie berus op die hoofagentteorie. Gemengde metodes is as metodologie gebruik, in die besonder gelyklopende en verkennende, opeenvolgende metodes. Die belangrikste bevindings is dat 23,91% van steekproefmaatskappye probleme met hoofagent- en korporatiewe regering ondervind. Dit is beduidend hoër as die persentasie wat verwag is, en ʼn aanduiding van hoe diepgaande hierdie probleme is. Die vergoeding van uitvoerende beamptes is ʼn groter oorsaak van die probleme met hoofagent- en korporatiewe regering as wat verwag is en waarvoor in regeermeganismes voorsiening gemaak word. Die potensiële koste, wat miljarde rande beloop, word gewyt aan die probleme met hoofagent- en korporatiewe regering wat prinsipale hulle op die hals haal. Onregverdigbare salarisverskille lei tot ongelykheid wat sosiale wantroue wek. Hierbenewens is daar bedenkinge oor die doeltreffendheid van die huidige regeerkodes. Die bydrae van hierdie studie behels ʼn vergoedingsmodel vir uitvoerende beamptes wat korporatiewe regering in ag neem. Hierdie studie formuleer ʼn regeerindeks wat op King III- en King IV-aanbevelings berus, en die meting van die gehalte van korporatiewe regering standaardiseer. Verskille in vergoeding, potensiële rooivlag-hoofagentprobleme en gebreke in regeerstelsels is met behulp van die salaris-gini bepaal. Waarde-op-risikoprosedures is gebruik om die potensiële koste van hoofagent- en korporatiewe regering te kwantifiseer. Die belangrikste teoretiese implikasie van die bevindings is dat die agentskapsteorie uitgebrei moet word sodat die sosio-ekonomiese koste vasgestel word, en daar nie alleen op die hoofsom gekonsentreer word nie. Afgesien hiervan moet vergoedingsmodelle rekening hou met ʼn uitvoerende beampte se korporatiewe regering en met maatskaplike en ekonomiese egalitarisme. Voorts moet die sosio-ekonomiese gevolge ondergeskik wees aan die buigsaamheid van “voldoen of verduidelik”. Dit impliseer ʼn hibridiese benadering wat die bepalings van sekere regeerkodes verpligtend maak. Ten slotte behoort finansieringsgedragteorieë in regeernavorsing aangewend te word om groter insig te verkry. / Business Management / D. Phil. (Management Studies (Finance))

This thesis is composed of three chapters which propose some novel approaches to model and forecast financial time series. The first chapter focuses on high frequency financial returns and proposes a quantile regression approach to model their intraday seasonality and dynamics. The second chapter deals with the problem of forecasting the yield curve including large datasets of macroeconomics information. While the last chapter addresses the issue of modelling the term structure of interest rates. <p><p>The first chapter investigates the distribution of high frequency financial returns, with special emphasis on the intraday seasonality. Using quantile regression, I show the expansions and shrinks of the probability law through the day for three years of 15 minutes sampled stock returns. Returns are more dispersed and less concentrated around the median at the hours near the opening and closing. I provide intraday value at risk assessments and I show how it adapts to changes of dispersion over the day. The tests performed on the out-of-sample forecasts of the value at risk show that the model is able to provide good risk assessments and to outperform standard Gaussian and Student’s t GARCH models.<p><p>The second chapter shows that macroeconomic indicators are helpful in forecasting the yield curve. I incorporate a large number of macroeconomic predictors within the Nelson and Siegel (1987) model for the yield curve, which can be cast in a common factor model representation. Rather than including macroeconomic variables as additional factors, I use them to extract the Nelson and Siegel factors. Estimation is performed by EM algorithm and Kalman filter using a data set composed by 17 yields and 118 macro variables. Results show that incorporating large macroeconomic information improves the accuracy of out-of-sample yield forecasts at medium and long horizons.<p><p>The third chapter statistically tests whether the Nelson and Siegel (1987) yield curve model is arbitrage-free. Theoretically, the Nelson-Siegel model does not ensure the absence of arbitrage opportunities. Still, central banks and public wealth managers rely heavily on it. Using a non-parametric resampling technique and zero-coupon yield curve data from the US market, I find that the no-arbitrage parameters are not statistically different from those obtained from the Nelson and Siegel model, at a 95 percent confidence level. I therefore conclude that the Nelson and Siegel yield curve model is compatible with arbitrage-freeness.<p> / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Este trabajo se plantea la cuestión que millones de inversores se han planteado en algún momento: ¿cuál es la mejor opción para sus ahorros, fondos de inversión, inversión aleatoria o estrategias de análisis técnico? Para este propósito se describen en primer lugar las normas que regulan a las instituciones de inversión colectiva (IIC) en España, distinguiendo entre los diferentes tipos de fondos en cuanto a su forma legal. A continuación se repasan las teorías sobre eficiencia en los mercados financieros. Estas teorías se enlazan con los estilos de gestión; gestión pasiva para aquellos ortodoxos que defienden la eficiencia fuerte y gestión activa para los gestores que no toman la eficiencia como un dogma. Estos últimos creen en las anomalías de mercado y recurren a estrategias basadas en fundamentos contables (estimación de beneficios, ventas, etc.). Esta primera parte concluye con una evaluación del rendimiento de los fondos españoles según su estilo de inversión. Puesto que esta no es del todo favorable para las gestoras se intentan aportar motivos por los cuales los fondos siguen disfrutando de amplia aceptación. La segunda parte del trabajo describe la metodología empleada para estudiar el comportamiento de una cartera de inversión gestionada mediante estrategias de análisis técnico. Con este fin ha sido necesario desarrollar un software capaz de realizar la gestión de carteras y que se alimenta de cotizaciones históricas desde 1/2003 hasta 1/2012. Los datos se separan en dos estudios paralelos, uno para Europa y el otro para EE.UU con el objetivo de analizar diferencias y semejanzas. El programa permite el control completo sobre la cartera, gestión de liquidez, stop-loss, etc.; y nos abastece al mismo tiempo de una gran cantidad de información estadística. La particularidad del software es la capacidad de poder variar los parámetros de las estrategias mediante barrido, obteniendo así no solamente una única simulación sino una población de simulaciones referidas a una estrategia. En la tercera parte se recurre a este conjunto de simulaciones a las que denominaremos estudios y están compuestas por varios millones de operaciones de compra y venta. Estos estudios se aproximan a funciones normales que describen la esperanza de rentabilidades que tendría un inversor que decidiera participar en el mercado siguiendo alguna de las estrategias descritas. Para poder comparar el comportamiento de las estrategias técnicas se utilizan diferentes métodos aleatorios que pretenden simular una operativa al azar. Por último se confrontan los tres métodos de inversión: fondos, análisis técnico y aleatorio; comparados con los índices de referencia correspondientes. / Plá María, M. (2014). Evaluación del comportamiento de carteras con gestión automatizada comparada con los rendimientos de carteras aleatorias y fondos de inversión [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/38987

本論文含蓋三篇文章，分別從評價、避險和風險控管三方面，分析上限型股權連結保本票券。 第一篇文章為上限型股權連結保本票券之設計、評價和比較。本文考量投資人保守的投資行為與設限型股權連結票券所存在的delta跳躍(delta jump)現象，延伸Brennan and Schwartz (1976)模型，提出一個能在股價波動之際，使發行的避險部位delta呈現平滑變動且兼具保本(protected principal)功用的一般化模型(general form)。相較於一般的設限型股權連結保本模型，本模型具有以下特色。第一，加入股價成長率的調整因子(adjustable factor)，當景氣低靡，股價不停下跌時，正的調整因子可減緩股價下滑之勢，進而增加投資人在票券到期日時獲取更多資本利得(capital gain)的機會。同時，調整因子縮小了當期股價成長率與股價上限成長率(capped stock growth rate)之間的差距，繼而減緩delta 跳躍的幅度，降低發行者的避險成本。並且在HJM利率模型下，delta隨股價與股價波動度的變化更顯平滑(smooth)。第二，在保本率(protection rate)和參與率 (participation rate)不變之下，本模型的期初合理價格(fair price)較低，投資人能以較低的成本取得同等的投資保障。第三，若將本票券的名目面額(notional principal)視作共同基金(mutual fund)的淨值(net value)，而該淨值與股價連動，則本模型即成為股權連結的保本型基金(principal-protected fund)。 第二篇文章是路徑依賴之上限型股權連結保本模型之評價和風險測量。該文是擴展Brennan and Schwartz (1976)模型發展一個路徑依賴之上限型股權連結保本模型，並且提出一個比二元數模型更精確的封閉解。此外，也對七個時間序列進行股價波動度之精確檢定，得知AR-ARCH(1)模型對上限型股權連結保本票券而言，較其它時間序列模型，更能有效估計股價之波動度。 第二篇文章是外國資產的風險管理。目前在國內金融市場上，國外金融商品很多，大都以外幣計價，因此匯率風險是投資人不可忽視的因子。本文拓展Kupiec(1999)模型，將匯率風險加入模型中，使投資人更有效進行風險管理。 / This thesis studies valuation, hedge and risk management of capped equity-linked and principal-protected notes by means of the following essays: (1) Design, Valuation and Comparison of Capped Equity-linked and Principal-protected Notes (2) Valuation and Risk Measurement of Capped Equity-linked and Principal-protected Notes with Path Dependence (3) Risk Management of Foreign Assets Capped equity-linked and principal-protected notes are similar with barrier options. There exists delta jump as stock price or growth rate reaches the barrier. But previous studies about equity-linked and principal-protected notes with a restricted growth rate of stock price never explicitly discussed how the delta jump could be solved. In my first essay, I present a new design for capped equity-linked and principal-protected notes and add an adjustable factor to growth rate of stock price in such a way that the adjustable factor narrows the gap between the current stock growth rate and the capped stock growth rate and thus really reduces the magnitude of the delta jump and hence lowers the hedging cost for brokers. Recently, the focus of previous studies about principal-protected notes has been on either the restriction on the rate of stock return or the path dependence on the underlying asset, but not both in the same context. In my second essay, I develop a model on the capped, equity-linked and principal-protected notes with path dependence. There are two issues in this article. The first issue is valuation on the capped, equity-linked and principal-protected notes with path dependence. I find a closed-form approximation using the 2nd-order Taylor approximation and the method of Vorst (1992) that has higher accuracy than binomial tree model as maturity time or volatility becomes large. The second issue is risk measurement. I use VaR model to evaluate market risk of the principal-protected notes, and employ seven univariate time series models to forecast volatility and examine the accuracy. Additionally, investors may well encounter potential loss as the prices of financial products are reduced in the secondary market. The VaR is mainly concerned with the downside risk and becomes a standard measure of financial market risk that is increasingly used by investors. But if we want to apply 〝textbook〞formulation to risk management of foreign assets, there leaves exchange rate risk out of consideration. Therefore, I extend the work by Kupiec (1999) to present VaR formula with exchange rate risk for foreign assets and then to manage market risk usefully.

風險值大多是在假設資產報酬為常態分配下計算而得的，但是這個假設與實際的資產報酬分配不一致，因為很多研究者都發現實際的資產報酬分配都有厚尾的現象，也就是極端事件的發生機率遠比常態假設要來的高，因此利用常態假設來計算風險值對於真實損失的衡量不是很恰當。 針對這個問題，本論文以歷史模擬法、變異數-共變異數法、混合常態模型來模擬報酬率的分配，並依給定的信賴水準估算出風險值，其中混合常態模型的參數是利用準貝式最大概似估計法及EM演算法來估計；然後利用三種風險值的評量方法：回溯測試、前向測試與二項檢定，來評判三種估算風險值方法的優劣。 經由實證結果發現： 1.報酬率分配在左尾臨界機率1％有較明顯厚尾的現象。 2.利用混合常態分配來模擬報酬率分配會比另外兩種方法更能準確的捕捉到左尾臨界機率1％的厚尾。 3.混合常態模型的峰態係數值接近於真實報酬率分配的峰態係數值，因此我們可以確認混合常態模型可以捕捉高峰的現象。 關鍵字：風險值、厚尾、歷史模擬法、變異數-共變異教法、混合常態模型、準貝式最大概似估計法、EM演算法、回溯測試、前向測試、高峰 / Initially, Value at Risk (VaR) is calculated by assuming that the underline asset return is normal distribution, but this assumption sometimes does not consist with the actual distribution of asset return. Many researchers have found that the actual distribution of the underline asset return have Fat-Tail, extreme value events, character. So under normal distribution assumption, the VaR value is improper compared with the actual losses. The paper discuss three methods. Historical Simulated method - Variance-Covariance method and Mixture Normal .simulating those asset, return and VaR by given proper confidence level. About the Mixture Normal Distribution, we use both EM algorithm and Quasi-Bayesian MLE calculating its parameters. Finally, we use tree VaR testing methods, Back test、Forward tes and Binomial test -----comparing its VaR loss probability We find the following results: 1.Under 1% left-tail critical probability, asset return distribution has significant Fat-tail character. 2.Using Mixture Normal distribution we can catch more Fat-tail character precisely than the other two methods. 3.The kurtosis of Mixture Normal is close to the actual kurtosis, this means that the Mixture Normal distribution can catch the Leptokurtosis phenomenon. Key words: Value at Risk、VaR、Fat tail、Historical simulation method、 Variance-Covariance method、Mixture Normal distribution、Quasi-Bayesian MLE、EM algorithm、Back test、 Forward test、 Leptokurtosis