Operational risk of option hedging

a r t i c l e i n f o Operational risk is increasingly being recognised as a significant area of risk and regulation, yet there exists relatively little research on it. In this paper we show that operational risk represents a fundamental risk to option hedging and investigate it by proposing a new theoretical model. We derive an exposure indicator for the operational risk of option hedging and the resulting operational risk distribution. We obtain analytical results for various risk measures including the Value at Risk equation; this includes deriving a new analytical result for the quantile function of the half-normal distributions (which will be of interest to Statisticians in general). We determine an analytical solution to the price of options under operational risk. We conduct numerical experiments on empirical option data to validate our model and estimate the operational Value at Risk for option hedging. The events of the global credit crunch and past financial crises have demonstrated the necessity for adequate risk management and measurement (see for instance Operational risk has become increasingly important as banks and regulators are recognising that adequate risk management must incorporate operational risk. Regulation has been adapted in response to financial crises (such as the credit crunch) but also to take into account operational risk. The Basel 2 Accord requires operational risk management in risk regulation. In Basel 2.5 there has been an increased emphasis on credit risk; now capital charges of institutions are calibrated to ratings from recognised credit agencies such as Standard and Poor's. Both Basel 2.5 and 3 introduce new regulation with a greater emphasis on credit and market risk; however there still exists a necessity to manage and regulate operational risk. For instance, Basel 3 discusses protecting against model and measurement error risks. Some commentators have speculated that the global credit crunch and other significant losses in industry (e.g. Long Term Capital Management) have been partly attributed to operational risk. In particular , institutions assumed that models themselves did not contain any inherent model risk, or that sufficient systems and controls were in place to limit losses. Despite the importance of operational risk, the research literature is scarce and tends to focus on modelling the impact on an entire department or institution (to be discussed in more detail in Section 2), rather than the sources and causes. This significantly limits our ability to understand operational risk but …