With the substantial size of the interest rate markets, the importance of accurate pricing, risk measurement and performance attribution can not be understated. However, the models used on the markets often have underlying issues with capturing the market's fundamental behavior. With this thesis, we aim to improve the pricing, risk measurement, and performance attribution of interest rate swap portfolios. The paper is divided into six main parts, by subject, to aid in achieving these goals. To begin with, we validate all cash flows with SEB to increase the validity of the results. Next, we implement an optimization-based model developed by Jörgen Blomvall to estimate multiple yield curves.  By considering innovations of the daily in-sample curves, risk factors are computed with principal component analysis. These risk factors are then used to simulate one-day and ten-day ahead scenarios for the multiple yield curves using a Monte Carlo method. Given these simulated scenarios, risk measures are then computed. When backtested, these risk measurements give an indication on the overall accuracy of the methodology, including the estimated curves, the derived risk factors, and the simulation methodology. Along with the simulation, on each out-of-sample day, monetary performance attribution for the portfolios is also performed. The performance attribution indicates what drives the value change in the portfolio. This can be used in order to evaluate the estimated yield curves and derived risk factors. The risk measurement and performance attribution is done for three different portfolios of interest rate swaps on the EUR, USD, and SEK markets. However, the risk factors are only estimated for EUR data and used for all portfolios.  The main difference to previous work in this area is that, for all implementations, a multiple yield curve environment is studied. Different PCA algorithms are evaluated to increase the precision and speed of the risk factor calculation. Mean reverting risk factors are developed in the simulation framework, along with a Latin hypercube sampling method accounting for dependence in the random variables to reduce variance. We also study the EUR and SEK markets, while the focus in previous literature is on the USD market. Lastly, we calculate and backtest the risk measures value-at-risk and expected shortfall for one-day and ten-day horizons. Four different PCA methods are implemented, a bidiagonal divide and conquer SVD algorithm, a randomized SVD method, an Arnoldi method, and an optimization-based PCA algorithm. We opt to use the first one due to high accuracy and the ability to calculate all eigenpairs. However, we recommend to use the Arnoldi method in future implementations and to further study the optimization-based method. The Latin hypercube sampling with dependence method is able to produce random variables with the same correlation as the input variables. In the simulation, we are able to produce results that pass all backtests for the risk measures considering the USD portfolio. For the EUR and SEK portfolios, it is shown that the risk measures are too conservative. The results of the mean reversion method indicate that it produces slightly less conservative estimates for the ten-day horizon. In the performance attribution, we show that we are able to produce results with small error terms, therefore indicating accurately estimated term structures, risk factors, and pricing. We conclude that we are partly able to fulfill the stated purpose of this thesis due to having produced accurate pricing and satisfactory performance attribution results for all portfolios, and stable risk measures for the USD portfolio. However, it is not possible to state with certainty that improved risk measurements have been achieved for the EUR and SEK portfolios. Although, we present several alternative approaches to remedy this in future implementations.

Master of Agribusiness / Department of Agricultural Economics / Bryan Schurle / Quantifying the impact of various economic events is essential for risk management in community banks. Interest rate shocks of either rapidly increasing or decreasing rates, in magnitudes of at least 200 basis points, is one of the more common risks modeled. Liquidity crises that impact deposits or loan demand can arise from either local or national economic events is another risk factor that regulators are requiring banks to quantify and plan for. Excel spreadsheets can be used to develop models to measure and quantify these risks. Simulation tools and what-if analysis using data table and scenario manager identify possible outcomes for differing interest rate scenarios, interest rate shocks and liquidity stresses. Data table was used for simulation of a stochastic model to produce a cumulative distribution function of two hundred results each on three different interest rate environments. Scenario manager was used to narrow the simulation to a certain set of expectations affecting the balance sheet of the bank and another set of expectations from an interest rate shock. Changes in the bank’s balance sheet resulting from three different commodity price expectations were modeled. An interest rate shock of four hundred basis points over a two year period was also modeled. These models are simple and cost effective. Once data are captured, the time required to develop and generate scenarios is manageable. The model can be used for a wide range of what-if alternatives as an individual bank may see fit. These models are adequate to meet present regulatory requirements for a community bank of smaller size that is not complex and does not possess a high risk profile.

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to pricing and hedging interest rate derivatives. This study implemented the extended HJM framework introduced by Eberlein and Raible (1999), in which a Brownian motion (BM) is replaced by a wide class of processes with jumps. In particular, the HJM driven by the generalised hyperbolic processes was studied. This approach was motivated by empirical evidence proving that models driven by a Brownian motion have several shortcomings, such as inability to incorporate jumps and leptokurticity into the price dynamics. Non-homogeneous Lévy processes and the change of measure techniques necessary for simplification and derivation of pricing formulae were also investigated. For robustness in numerical valuation, several transform methods were investigated and compared in terms of speed and accuracy. The models were calibrated to liquid South African data (ATM) interest rate caps using two methods of optimisation, namely the simulated annealing and secant-Levenberg–Marquardt methods. Two numerical valuation approaches had been implemented in this study, the COS method and the fractional fast Fourier transform (FrFT), and were compared to the existing methods in the context. Our numerical results showed that these two methods are quite efficient and very competitive. We have chose the COS method for calibration due to its rapidly speed and we have suggested a suitable approach for truncating the integration range to address the problems it has with short-maturity options. Our calibration results provided a nearly perfect fit, such that it was difficult to decide which model has a better fit to the current market state. Finally, all the implementations were done in MATLAB and the codes included in appendices. / AFRIKAANSE OPSOMMING : Die standaard-Heath–Jarrow–Morton-raamwerk (kortom die HJM-raamwerk) is daarvoor bekend dat dit op die prysbepaling en verskansing van afgeleide finansiële instrumente vir rentekoerse toegepas kan word. Hierdie studie het die uitgebreide HJM-raamwerk geïmplementeer wat deur Eberlein en Raible (1999) bekendgestel is en waarin ’n Brown-beweging deur ’n breë klas prosesse met spronge vervang word. In die besonder is die HJM wat deur veralgemeende hiperboliese prosesse gedryf word ondersoek. Hierdie benadering is gemotiveer deur empiriese bewyse dat modelle wat deur ’n Brown-beweging gedryf word verskeie tekortkominge het, soos die onvermoë om spronge en leptokurtose in prysdinamika te inkorporeer. Nie-homogene Lévy-prosesse en die maatveranderingstegnieke wat vir die vereenvoudiging en afleiding van prysbepalingsformules nodig is, is ook ondersoek. Vir robuustheid in numeriese waardasie is verskeie transformmetodes ondersoek en ten opsigte van spoed en akkuraatheid vergelyk. Die modelle is vir likiede Suid-Afrikaanse data vir boperke van rentekoerse sonder intrinsieke waarde gekalibreer deur twee optimiseringsmetodes te gebruik, naamlik die gesimuleerde uitgloeimetode en die sekans-Levenberg–Marquardt-metode. Twee benaderings tot numeriese waardasie is in hierdie studie gebruik, naamlik die kosinusmetode en die fraksionele vinnige Fourier-transform, en met bestaande metodes in die konteks vergelyk. Die numeriese resultate het getoon dat hierdie twee metodes redelik doeltreffend en uiters mededingend is. Ons het op grond van die motiveringspoed van die kosinus-metode daardie metode vir kalibrering gekies en ’n geskikte benadering tot die trunkering van die integrasiereeks voorgestel ten einde die probleem ten opsigte van opsies met kort uitkeringstermyne op te los. Die kalibreringsresultate het ’n byna perfekte passing gelewer, sodat dit moeilik was om te besluit watter model die huidige marksituasie die beste pas. Ten slotte is alle implementerings in MATLAB gedoen en die kodes in bylaes ingesluit.

published_or_final_version / Business Administration / Master / Master of Business Administration

一般優惠房貸是政府提供購屋家戶進入房市購屋之貸款利息補助；然而，這項全面性的補貼措施究竟補貼到哪些購屋者？此問題將牽涉到該補貼措施是否公平。是以，本文試圖從申貸人及其所購產品之屬性探討該措施之公平性，透過二項羅吉特模型（Binomial Logistic Model）探究「什麼樣的購屋者，購買了什麼樣的房屋，會選擇申貸使用政府優惠房貸？」；另一方面，購屋者在具有其他政策性房貸申貸資格的情況下，「何種特質的特殊身份補貼購屋者會選擇搭配一般政府優惠房貸？」，本研究希望藉由上述兩項問題之討論，企圖了解優惠房貸政策對於個體家戶之影響，在補貼公平層面中究竟是扮演著「雪中送炭」或是「錦上添花」的角色。 研究結果發現，一般優惠房貸之提供在住宅補貼公平面成效上之效果是弊多於利。首先在補貼對象上，購屋目的為自住之購屋者，其選擇使用政府優惠房貸的發生比較非自住目的購屋者高出約2倍；而首購購屋者選擇使用政府優惠房貸之發生比較非首購購屋者多出了54%。這代表一般優惠房貸的提供讓首購自住購屋者有相對較高的機率使用政府優惠房貸達成購屋目標，在補貼對象上相對達到了部分效果；然而，由於政府過度利用貸款補貼方式刺激房市以達景氣復甦之效果，以及貸款利息補貼制度設計上的盲點（包括申貸資格之缺乏限制與多種補貼措施並行等），高所得貸款購屋者傾向選擇使用政府優惠房貸之發生比較低所得購屋者高出約3.23倍，因而造成這些購屋者得以接受雙重補貼；此外，當購屋者購買品質越好之住宅，其使用一般政府優惠房貸的機率也越大，上述結果皆表示這項補貼措施並不能排除高所得購屋者獲得政府優惠房貸補貼，也因而造成政府優惠房貸在補貼公平性之負面作用。是故，在未來的補貼政策中，除應繼續整合現行住宅貸款利息補貼措施外，並應試圖建立一套更嚴謹的申貸資格審查標準，以確保政府所提供之住宅補貼能夠對最需要的民眾有所幫助。

The jump phenomenons of many financial assets prices have been observed in many empirical papers. In this paper we extend the Heath-Jarrow-Morton model to include the jump component to derive the European-style pricing formula of the interest rate futures options. We use numerical method to simulate the options prices and analyze how each component of HJM model under jump-diffusion processes affects the interest rate futures options. Finally, we utilize LSM method which are presented by Longstaff and Schwartz to derive American options prices and compare it with European options.

本研究的目的在於探討兩個問題：一、上市公司因應財務會計準則公報第三十五號公報的採用而宣告資產減損，市場的反應是正面的(positive)還是負面的(negative)？亦即，資產減損宣告對公司價值的影響為何？二、投資人對於資產減損宣告會過度反應(over-reaction)還是反應不足(under-reaction)？由於財務會計準則公報第三十五號公報的實施截至目前為止尚不足兩年，本研究對於本課題的研究著重在資產減損宣告和股價的關係突顯了這個課題的獨特性和重要性。本研究係採事件研究法以檢驗台灣上市公司採用財務會計準則公報第三十五號公報對於其股價的表現是否會造成影響。除了全數樣本的分析之外，亦將全數樣本依照減損公司的特性和減損資產的特性分成子樣本；或在事件研究法中傳統的市場模型當中加入利率因素或產業因素兩個控制變數並區分成對金融業和非金融業加以分析——目的在於探討這些分類或因素是不是造成資產減損宣告對股價反應的原因。實證結果發現：一、不論是採用哪一種子樣本的分類方式，市場對資產減損宣告的反應都是負向的；二、和利率因素相比，產業因素比較能解釋資產減損宣告前後的股價反應，且對於金融業或非金融業結論皆然；三、30天期的股價反應顯示，投資人對於資產減損宣告有過度反應的現象，因為在產業分類之下股價在12天至18天左右有迴轉(reversal)的現象。 / The purpose of this paper is to answer two questions: 1. Does the market react positively or negatively to asset write-down announcements? Or, what is the impact of asset impairment on the firm value? 2. Do investors over-react or under-react to asset write-down announcements? Given the recent enforcement of SFAS No.35 about asset write-down, this study supplements the importance of that pronouncement by demonstrating the relation between write-downs and security prices. This study employs the event study methodology to examine the impact of SFAS No.35 on the stock performance of those listed firms (i.e., whose stocks are listed on the Taiwan Stock Exchange) that apply the regulation. Partitions methods based on write-down asset and write-down firm characteristics are adopted. Moreover, two other control variables—industry factor or interest rate factor—are added to the traditional market model for the financial industry and non-financial industries to see if these factors can also explain the market reaction around write-down announcements. The result shows that the market reacts negatively to asset written-down announcement whatever the partition method is adopted. And the industry return is proved to be the better factor that can explain the market reaction than the interest rate factor. The near-term stock performance in the (-30, 30) period shows that investors tend to over-react to write-down announcements, for the stock price signals a reversal after the announcement date.

本研究以隨機利率模型應用至淨現值法、邊際年利率法、比較利率法及內部報酬率法等保單成本評價方法中，藉此觀察多期保單年度的價值變化，進而找出保單的報酬率、成本值或指數所呈現的趨勢，並考量在相同的情況下，比較各險種的成本或報酬優劣，最後希望消費者能在合理的隨機利率下更清楚了解保單成本的概念，並基於消費者對於合理的保單成本分析需求，能提供主管機關對於揭露保單成本的規範有更多的參考。 / 本研究發現各種保單在隨機利率變化的情況下，分紅終身壽險於各種成本分析方法中皆有良好的表現，不論是在考量淨成本結構的淨現值法，或是考量儲蓄性質、投資報酬為主的比較利率法以及各年度的邊際報酬利率等方法，整體而言分紅終身壽險對於消費者及保險公司應該是最優質的選擇。 / 再者以內部報酬率法應用隨機利率模型分析年金保險，可得知傳統遞延年金的報酬優於利率變動型年金。另外由於各種成本評價方法所著重的要素不同，想要了解保單完整全面性的評價，透過數個不同性質的保單成本分析方法計算較能呈現客觀且適切評價結果。 / This research is applied in the Stochastic Interest Model to the appraised method of insurance policy cost, such as Net Present Value Method, Marginal Yield Method, Comparative Interest Rate Method and Internal Rate of Return…etc., so as to observe the annual variation of value for different term of insurance policies, and then find out the rate of returns, cost value or trend appeared of index of the insurance policy, and consider it in the same cases to compare the good and bad from the cost or remuneration of every insurance. Hope consumers can finally clearer understand the concept of the insurance policy cost under the rational Stochastic Interest Rate, and on the basis of consumers’ demand for the rational insurance policy cost analysis can offer the competent authority more reference in revealing norms of the insurance policy cost. / In this research discovered that various insurance policies in changing of Stochastic Interest Rate, its Participating Whole-Life Insurance in varied cost analytical methods has good representation, no matter in considering the Net Present Value Method of the net cost structure, or considering Comparative Interest Rate Method of the main nature of deposits or main invest remuneration, and the annual marginal return interest rate…etc., the Participating Whole-Life Insurance should be generally the most high-quality choice to consumer and insurance company. / Moreover, according to the Internal Rate of Return, using the Stochastic Interest Model to analyze the annuity insurance can learn the remuneration of the Traditional Deferred Annuity is superior to the Interest Sensitive Annuity. In addition, as various cost appraised methods focused on different elements, if want to comprehension overall appraisal of insurance policy, then it can represent more objective and appropriate calculation through the analytical method of several different nature insurance policy cost.

Equity Risk Premium (ERP) is the cornerstone in Financial Economics. It is a basic requirement in stock valuation, evaluation of portfolio performance and asset allocation. For the last decades, several studies have attempted to investigate the relationship between macroeconomic drivers of ERP. In this work, I empirically investigate the macroeconomic determinants of UK ERP. For this I parsimoniously cover a large body of literature stemming from ERP puzzle. I motivate the empirical investigation based on three mutually exclusive theoretical lenses. The thesis is organised in the journal paper format. In the first paper I review the literature on ERP over the past twenty-eight years. In particular, the aim of the paper is three fold. First, to review the methods and techniques, proposed by the literature to estimate ERP. Second, to review the literature that attempts to resolve the ERP puzzle, first coined by Mehra and Prescott (1985), by exploring five different types of modifications to the standard utility framework. And third, to review the literature that investigates and develops relationship between ERP and various macroeconomic and market factors in domestic and international context. I find that ERP puzzle is still a puzzle, within the universe of standard power utility framework and Consumption Capital Asset Pricing Model, a conclusion which is in line with Kocherlakota (1996) and Mehra (2003). In the second paper, I investigate the impact of structural monetary policy shocks on ex-post ERP. More specifically, the aim of this paper is to investigate the whether the response of UK ERP is different to the structural monetary policy shocks, before and after the implementation of Quantitative Easing in the UK. I find that monetary policy shocks negatively affect the ERP at aggregate level. However, at the sectoral level, the magnitude of the response is heterogeneous. Further, monetary policy shocks have a significant negative (positive) impact on the ERP before (after) the implementation of Quantitative Easing (QE). The empirical evidence provided in the paper sheds light on the equity market’s asymmetric response to the Bank of England’s monetary policy before and after the monetary stimulus. In the third paper I examine the impact of aggregate and disaggregate consumption shocks on the ex-post ERP of various FTSE indices and the 25 Fama-French style value-weighted portfolios, constructed on the basis of size and book-to-market characteristics. I extract consumption shocks using Structural Vector Autoregression (SVAR) and investigate its time-series and cross-sectional implications for ERP in the UK. These structural consumption shocks represent deviation of agent’s actual consumption path from its theoretically expected path. Aggregate consumption shocks seem to explain significant time variation in the ERP. At disaggregated level, when the actual consumption is less than expected, the ERP rises. Durable and Semi-durable consumption shocks have a greater impact on the ERP than non-durable consumption shocks. In the fourth and final paper I investigate the impact of short and long term market implied volatility on the UK ERP. I also examine the pricing implications of innovations to short and long term implied market volatility in the cross-section of stocks returns. I find that both the short and the long term implied volatility have significant negative impact on the aggregate ERP, while at sectoral level the impact is heterogeneous. I find both short and long term volatility is priced negatively indicating that (i) investors care both short and long term market implied volatility (ii) investors are ready to pay for insurance against these risks.

This paper uses Federal Funds Futures and the industry returns to analyze the Federal Reserve Policy's influence on Wall Street firms. According to the results, Wall Street produces high returns in response to the monetary policy when compared to other industries. While this positive response is consistent to both interest hikes and cuts, there exists significant cross-firm and cross-period variation. Besides, the result is robust to the alternative measure of event days and employment release.