Valuation of initial margin and model risk
The research work of the thesis focuses on two themes: the valuation of initial margin and model risk quantiﬁcation. The ﬁrst theme addresses matters arising from the valuation of initial margin for over-the-counter derivatives in the real market with outstanding gross notional amount smaller than two billion, but acknowledging the present work for high outstanding gross notional amount in developed ﬁnancial institutions. The initial margin requirement for uncleared derivatives is well in place for developed countries and for the high risk ﬁnancial institutions, but the spill-over of the ﬁnancial crises from developing institutions, the gradual phasing in of initial margin and the impact thereof are yet to be known. Hence, the major interest is drawn to this work. To mitigate risk due to unforeseen ﬁnancial markets turmoil, we propose a bootstrap initial margin valuation process that can be applicable during normal and stressed ﬁnancial markets. The proposed parametric bootstrap method is in favour of the bootstrap initial margin (BIM) amounts for the simulated and real datasets. These BIM amounts are reasonably exceeding the traditional initial margin amounts when-ever the signiﬁcance level increases. The proposed valuation of initial margin reduces spill-over eﬀects by ensuring that collateral, such as initial margin, is available to ﬀset losses caused by the default of an over-the-counter derivatives. The second theme of the thesis addresses three components of model risk quantiﬁcation: model risk due to inappropriate statistical distribution; model misspeciﬁcation; and inappropriate parameter estimation methods. Inappropriate statistical distribution was assessed using four bootstrap conﬁdence interval techniques. The modiﬁed hybrid percentile bootstrap method was a superior technique because it reveals that with the same sample size and very small simulation iterations the other conﬁdence methods produces similar goodness-of-ﬁt results but completely diﬀerent and insignificant performance measures. By way of illustrating the model misspeciﬁcation for some credit risk models, we carry out quantitative analysis of two speciﬁc statistical predictive response models using simulated balanced dataset and Taiwan credit card default dataset. The maximum likelihood estimation technique is employed for pa-rameter estimation and inference, precisely the goodness of ﬁt and model performance assessments. The binary logistic regression technique for the balanced datasets reveals prominent goodness of ﬁt and performance measures as opposed to the complemen-tary log-log technique. To deal with model risk due to parameter estimation methods, several statistical and mathematical numerical methods for determining the param-eter values are utilized for predicting probability of default through binary logistic regression model and determining optimum parameters that minimize the objective model’s cost function. The Mini-Batch Gradient Descent method is revealed to be the better parameter estimator among the chosen parameter estimation methods. The banking industry utilises models on a daily basis. This research will assist banks to manage model risk better, particularly the selection of an appropriate statistical distribution, the identiﬁcation of model misspeciﬁcation and the quantiﬁcation of an appropriate parameter estimation method. Researchers and practitioners will be able to compare the results of model risk techniques and choose the optimum method for their current market conditions. However, this practice needs to be validated and exercised regularly as the ﬁnancial markets evolves rapidly.