This thesis deals with interest rate swaps. In addition to chapters on basic principles of interest rate swaps also provides insight into the current situation in the derivative markets. The main part is devoted to the valuation of interest rate swaps, where is in addition to the theoretical site also solved the problem of obtaining the necessary data for calculations in practice. The conclusion of this work is devoted to two practical examples, which are dealing with the problem of the valuation of interest rate swaps.

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.

雖然跨通貨股酬交換在國際投資市場扮演著重要的角色，但文獻上關於股酬交換評價模式的相關探討並不多，且多集中於國內市場或以本國貨幣做為支付幣別的股酬交換。對於跨通貨股酬交換而言，其評價模式較國內股酬交換之評價模式複雜許多，如何將影響其價值之股價指數、匯率與利率此三個主要因子間的交互相關性同時加入考量，即是此產品之評價過程的重點。 本文在完全市場的假設下，同時放寬傳統評價方法之各變數之相關係數為固定值的假設，提出一新的股酬交換評價方法，即以『兩階段兩步驟』之較具經濟含意的複製方式，推導出股酬交換的一般化評價公式。透過此複製方法，可更清楚得知股酬交換於存續期間的價值變動，更可進一步求得其避險方式，以提供股酬交換交易商在面臨不對稱風險(mismatch risk)時的避險方法。而本文的第二個貢獻在於，將本文所提出之『兩階段兩步驟』的複製方法應用於利率交換的評價上，推導出跨通貨利率交換的一般化評價模式，以進一步比較股酬交換與利率交換此兩種商品的差異性，並試圖釐清市場上對於跨通貨股酬交換評價上的誤解。 與傳統評價公式最大的差異在於：本文評價公式額外考慮了一修正項，複製投資組合可藉由此修正項，對未來各參數間的變動隨時做出調整，以使投資組合能完全複製跨通貨股酬交換的價值。 本文發現，對於國內投資人支付固定利率，以交換B市場的股價指數報酬，且以C國的貨幣做為支付幣別的跨通貨股酬交換而言，其價值除了受到當期利率期間結構的影響外，在期初或每期交換後，其價值與股價指數無直接關聯，但在兩支付間，其價值則會受到當時股價指數與前期股價指數之相對比例的影響。同時，C國對本國的未來匯率並未直接影響跨通貨股酬交換的價值。且若假設各國遠期利率的波動度為零下，則當B國股價指數與C國對本國的匯率呈現正關係或當B國股價指數與B國對本國的匯率呈現負關係時，跨通貨股酬交換的價值愈大。另外，市場上投資人通常誤認股酬交換的價值等於利率交換價值，對於股酬交換與利率交換的比較，本文發現在大多數的情況下，股酬交換的價值與利率交換的價值並不相等。

[pt] Esta tese investiga a estimação de curvas de juros sob o ponto de vista de métodos não-paramétricos. O texto está dividido em dois blocos. O primeiro investiga a questão do critério utilizado para selecionar o método de melhor desempenho na tarefa de interpolar a curva de juros brasileira em uma dada amostra. Foi proposto um critério de seleção de método baseado em estratégias de re-amostragem do tipo leave-k-out cross validation, onde K k £ £ 1 e K é função do número de contratos observados a cada curva da amostra. Especificidades do problema reduzem o esforço computacional requerido, tornando o critério factível. A amostra tem freqüência diária: janeiro de 1997 a fevereiro de 2001. O critério proposto apontou o spline cúbico natural -utilizado com método de ajuste perfeito aos dados - como o método de melhor desempenho. Considerando a precisão de negociação, este spline mostrou-se não viesado. A análise quantitativa de seu desempenho identificou, contudo, heterocedasticidades nos erros simulados. A partir da especificação da variância condicional destes erros e de algumas hipóteses, foi proposto um esquema de intervalo de segurança para a estimação de taxas de juros pelo spline cúbico natural, empregado como método de ajuste perfeito aos dados. O backtest sugere que o esquema proposto é consistente, acomodando bem as hipóteses e aproximações envolvidas. O segundo bloco investiga a estimação da curva de juros norte-americana construída a partir dos contratos de swaps de taxas de juros dólar-Libor pela Máquina de Vetores Suporte (MVS), parte do corpo da Teoria do Aprendizado Estatístico. A pesquisa em MVS tem obtido importantes avanços teóricos, embora ainda sejam escassas as implementações em problemas reais de regressão. A MVS possui características atrativas para a modelagem de curva de juros: é capaz de introduzir já na estimação informações a priori sobre o formato da curva e sobre aspectos da formação das taxas e liquidez de cada um dos contratos a partir dos quais ela é construída. Estas últimas são quantificadas pelo bid-ask spread (BAS) de cada contrato. A formulação básica da MVS é alterada para assimilar diferentes valores do BAS sem que as propriedades dela sejam perdidas. É dada especial atenção ao levantamento de informação a priori para seleção dos parâmetros da MVS a partir do formato típico da curva. A amostra tem freqüência diária: março de 1997 a abril de 2001. Os desempenhos fora da amostra de diversas especificações da MVS foram confrontados com aqueles de outros métodos de estimação. A MVS foi o método que melhor controlou o trade- off entre viés e variância dos erros. / [en] This thesis investigates interest rates curve estimation under non-parametric approach. The text is divided into two parts. The first one focus on which criterion to use to select the best performance method in the task of interpolating Brazilian interest rate curve. A selection criterion is proposed to measure out-of-sample performance by combining resample strategies leave-k-out cross validation applied upon the whole sample curves, where K k £ £ 1 and K is function of observed contract number in each curve. Some particularities reduce substantially the required computational effort, making the proposed criterion feasible. The data sample range is daily, from January 1997 to February 2001. The proposed criterion selected natural cubic spline, used as data perfect-fitting estimation method. Considering the trade rate precision, the spline is non-biased. However, quantitative analysis of performance determinant factors showed the existence of out-of-sample error heteroskedasticities. From a conditional variance specification of these errors, a security interval scheme is proposed for interest rate generated by perfect-fitting natural cubic spline. A backtest showed that the proposed security interval is consistent, accommodating the evolved assumptions and approximations. The second part estimate US free-for-floating interest rate swap contract curve by using Support Vector Machine (SVM), a method derived from Statistical Learning Theory. The SVM research has got important theoretical results, however the number of implementation on real regression problems is low. SVM has some attractive characteristics for interest rates curves modeling: it has the ability to introduce already in its estimation process a priori information about curve shape and about liquidity and price formation aspects of the contracts that generate the curve. The last information set is quantified by the bid-ask spread. The basic SVM formulation is changed in order to be able to incorporate the different values for bid-ask spreads, without losing its properties. Great attention is given to the question of how to extract a priori information from swap curve typical shape to be used in MVS parameter selection. The data sample range is daily, from March 1997 to April 2001. The out-of-sample performances of different SVM specifications are faced with others method performances. SVM got the better control of trade- off between bias and variance of out-of-sample errors.