Peter Urbani' Statistics: Intra-Horizon Value at Risk
Intra-Horizon Value at Risk (VaR-I) - An idea whose time has come
During the recent financial crises, many financial institutions suffered losses much larger than their Value-at-Risk (VaR) models predicted and found that traditional end-of horizon risk measures are inadequate for managing longer-term risks.
There has been a considerable amount of literature on the measurement of financial risk; however, almost all the existing risk measures, either the popular Value-at-Risk (hereafter VaR) or expected shortfall (hereafter ES), mainly focus on quantifying the possible large losses at the end of the predetermined time horizon. This focus may be appropriate when dealing with short-term risks such as those mandated by the Basel Banking Committee.
But, this risk measurement methodology is inadequate for measuring longer-term risks, since it does not take into account the "intra-horizon risk," i.e. the possibility that the losses incurred before the end of the specified time horizon might trigger other problems such as position rebalancing, early liquidation, or margin calls.
The standard VaR approach considers only terminal risk, completely ignoring the sample path of portfolio values. In reality interim risk may be critical in a mark-to-market environment. Sharp declines in value may generate margin calls and affect trading strategies. Boudoukh introduced the notion of MaxVaR, analogous to VaR in every way except it quantifies the probability of seeing a given loss on or before......................
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