Performance of a Hedged Dynamic Portfolio Model in the Presence of Extreme Events

As outlined by many authors, the methods to compute the Value at Risk (VaR) based on the classical approach do not take into account the very large price variations observed in financial markets. The historical method is subject to event risk, and it may miss some fundamental evolution of the markets relevant to VaR. The variance/covariance method tend to underestimate the distribution tails; Monte Carlo simulation is subject to model risk. For these reasons, often due to the difficulties of modeling the tails of the statistical distribution, the VaR methods are usually completed with analyses derived from catastrophe scenarios that are usually subjectively defined without specifying their likelihood. In this paper, we propose an application of the univariate extreme-value theory to the computation of the value at risk of a multicurrency dynamic portfolio when different and alternative hedging strategies are considered. The extreme-value approach has the powerful feature of covering market conditions ranging from the usual environment considered by the existing VaR method to the financial crises. In fact, extreme-price movements can be observed both during usual periods corresponding to the normal functioning of the currency markets and during highly volatile periods corresponding to financial crises. With the extreme-value approach, we are able to obtain interesting results about the distribution of the extremes. As in previous works by Castellano and Giacometti, we implement a multistage portfolio model assuming that the exchange-rate dynamic is governed by a diffusion process with stochastic volatilities whose parameters are estimated by GARCH models. Using a discretisation of such a process we generate different scenarios and compute different performance measures for portfolios where currency risk is hedged using options. So far, the results of the studies focusing on hedging strategies are very different. Hence, there is no clear evidence in favour of a specific option strategy. Our contribution is to compare the performance of the two most classical institutional options strategies - protective puts and covered calls - to the performance of holding an unhedged currency portfolio in the presence of extreme events. The study focuses on the performance evaluation of these strategies over the period 1992-1993 in presence of the extreme event represented by the currency crisis of 1992.