Risk Measurement and Performance Attribution for IRS Portfolios Using a Generalized Optimization Method for Term Structure Estimation

Sammanfattning: 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.