Reverse stress testing approaches based on multivariate normality
Abstract: Reverse stress testing is a way of finding a combination of market risk factors, called a scenario, that leads to a specific loss for e.g. a portfolio. A market risk factor can for example be a stock return. In this project, we use reverse stress tests to find a scenario that would make a clearing house insolvent in case of a clearing house member default. When a member defaults, the clearing house must cover for the member's positions. If the clearing house's resource pool is not enough for this purpose, the clearing house defaults as well. To find out when this happens is of interest for regulatory purposes, as the default of a clearing house might lead to severe negative effects on the financial market. Cinnober's currently used method, SPS, uses a bisection-like iterative algorithm to find the scenario which makes the clearing house insolvent. The scenario found by SPS is restricted to be a multiple of a predefined scenario, which is clearly a limitation in the consideration of possible scenarios. To investigate the possibility of finding scenarios without this restriction, two other reverse stress tests were implemented and compared to SPS. The first test, PCA/G-S, assumes multivariate normal distribution of the profits and losses of the assets in the defaulting member's portfolio. PCA/G-S yields scenarios of asset profits and losses, for which the portfolio return is the specified loss - the clearing house resource pool. The second test, called RF, assumes multivariate normal distribution of the risk factors affecting the prices of the assets in the portfolio. RF outputs a scenario of market risk factors causing the portfolio loss to be the specified loss. The assets in the portfolio were restricted to stocks, European stock options and stock futures. PCA/G-S was shown to imply negative asset prices, as the assumption of multinormality does not consider that the loss can never be greater than the asset price itself. Negative prices appeared more frequently for options than for futures and stocks. Furthermore, the scenarios found by PCA/G-S were in terms of profits and losses, and were generally only convertible to risk factors if the portfolio only consisted of stocks. The advantage compared to SPS, however, was that PCA/G-S was numerically faster. As the results of the RF method are risk factor scenarios, no conversion problems appear. Moreover, it cannot yield negative asset prices, which is advantageous compared to PCA/G-S. However, the RF method was slower than SPS, and especially slow for options. All the multivariate normal distribution assumptions, for the profits and losses as well as the risk factors, were rejected by multinormality tests. Thus, the assumptions for PCA/G-S and RF were not consistent with reality. Nonetheless, the tests indeed provide scenarios where the resource pool is depleted.
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