Reverse Stress Test Optimization : A study on how to optimize an algorithm for reverse stress testing

Sammanfattning: In this thesis we investigate how to optimize an algorithm that determines a scenario multiplier for a reverse stress test with a method where predefined scenarios are scaled. The scenarios are composed by different risk factors that represents market events. A reverse stress test is used for risk estimation and explains for what market condition a given portfolio will lose a particular amount. In this study we consider a reverse stress test where the goal is to find for what scenario a clearing house become insolvent, that is when the clearing house's loss is equal to its resource pool. The goal with this work is to find a more efficient algorithm than the current bisection algorithm for finding the scenario multiplier in the reverse stress test. The algorithms that were examined were one bracketing algorithm (the false-position algorithm) and two iterative algorithms (the Newton-Raphson and Halley's algorithms), which were implemented in MATLAB. A comparative study was made where the efficiency of the optimized algorithms were compared with the bisection algorithm. The algorithms were evaluated by comparing the running times and number of iterations needed to find the scenario multiplier in the reverse stress test. Other optimization strategies that were investigated were to reduce the number of scenarios in the predefined scenario matrix to decrease the running time and determine an appropriate initial multiplier to use in the iterative algorithms. The reduction of scenarios consisted of removing the scenarios that were multiples of other scenarios by comparing the risk factors in each scenario. We used Taylor approximation to simplify the loss function and thereby approximate an initial multiplier, which would reduce the manually input from the user. Furthermore, we investigated the running times and number of iterations needed to find the scenario multiplier when several initial multipliers were used in the iterative algorithms to increase the chance of finding a solution.   The result shows that both the Newton-Raphson algorithm and Halley's algorithm are more efficient and need less iterations to find the scenario multiplier than the current bisection algorithm. Halley's algorithm is the most efficient, which is on average 200-470% faster than the current algorithm depending on how many initial multipliers that are used (one, two or three), while the Newton-Raphson algorithm is on average 150-300% faster than the current algorithm. Furthermore, the result shows that the false-position algorithm is not efficient for this aim. The result from the reduction of scenarios shows that scenarios could be removed by this approach, where the real scenario obtained from performing a reverse stress test was never among the removed scenarios. Moreover, the initial multiplier approximation could be used when the scenario matrix contains a certain type of risk factors. Finally, this study shows that the current bisection algorithm can be optimized by the Newton-Raphson algorithm and Halley's algorithm.