Dynamic max Var - applying the max Var concept to non-normal and heteroskadastic asset returns

Abstract

Risk management has become the buzz-word for many banks which involve themselves in huge financial transactions in volatile markets. For an investor to ensure that her position in the market does not lead to extreme losses, it is imperative that she has an estimate of how much risk is borne by holding on to the position. Hence risk assessment and management is a key factor to ensure that her risk appetite and discretion go hand in hand. One of the most popular risk management techniques is the Value-at-Risk (VaR) method to evaluate an investor’s exposure to risk. VaR gives the maximum loss that can be incurred at the end of the holding period for a given confidence level. For example, if a bank’s asset has a 1-day VaR of $ 5 million at 95% probability confidence level; it implies that the probability of incurring a loss of more than $ 5 million in one day is less than 5%. Certain key requirements for this calculation are the number of days the VaR of the asset is being calculated for (also called the VaR horizon), the probability distribution of the asset price at the last day of the holding period and the confidence level. One main feature of VaR calculation is that it depends on the probability distribution of the asset price on the last day of the holding period; in other words, it is dependent on the terminal value of the asset price distribution. This method is very apt for situations where one is certain that the asset will be held till the end of the holding period or that there will be no cash outflow as a result of the asset price movements during the intermediate days. However, in case of a mark-to-market environment of derivatives (such as a position in the commodity futures market), it is essential to respond to margin calls when an investor’s position undergoes big losses. In such a scenario, where there is a possibility of intermediate trading and cash outflow based on asset price movement during the holding period, it is vital to know one’s risk exposure not just at the end but also during this holding period. This problem can be handled by using the Maximum Value--at-Risk or MaxVaR measure, as proposed by Boudoukh et al (2005). The MaxVaR measure serves the same purpose that of VaR, which is to give an indication of one’s exposure to adverse movements in the asset prices, but differs from VaR that it is not only an estimate at the horizon but during the holding period. Section II of the paper describes the concept of Max VaR and talks about the work done so far in this field. Section III discussed the phenomena of heteroskedasticity observed in most of financial time series and the appropriate models to handle dynamic volatility. The Pearson Type IV distribution has been recently used in several works to model the return distribution and is described in section IV.