Applying the Cornish–Fisher expansion to value-at-risk estimation in Islamic banking

Hylmun Izhar

Journal of Risk

Abstract: ABSTRACT Methodological-empirical analysis of risk management in Islamic banking is rather scarce. This is due to either a lack of comprehensive understanding in the latest development of empirical modeling or analysts'failure to grasp the underlying assumptions that underpin the model. Such an inability could be detrimental, particularly in the investigation of operational risk exposures in Islamic banking. This study therefore contributes to this field by deliberating upon a proposed delta-gamma sensitivity analysis-extreme value theory (DGSA-EVT) model that focuses on the assessment of risk exposures represented by the value of value-at-risk (VaR) in three incomegenerating channels: one in investment, one in financing and one in services. A data analysis demonstrates that risk variables in this study exhibit nonnormality, which understandably does not fit with the underlying assumption of VaR, namely the normality of the variables under the analysis. Hence, in order to mitigate this, our study employs a parametric approach called the Cornish-Fisher expansion, under which the confidence interval of assigned risk variables is a function of their respective skewness, kurtosis and volatility. Such an approach has proven to be effective in mitigating the likelihood of over- or underestimating theVaR in the income-generation channels analyzed as a result of misaddressing the nonnormality of risk variables.

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