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

Classical methods for computing the value-at-risk (VaR) do not account for the large price variations observed in financial markets. The historical method is subject to event risk and may miss some fundamental market evolution relevant to VaR; the variance/covariance method tends to underestimate the distribution tails and Monte Carlo simulation is subject to model risk. These methods are thereby usually completed with analyses derived from catastrophe scenarios. We propose a special case of the extreme-value approach for computing the value-at-risk of a stochastic multicurrency portfolio when alternative hedging strategies are considered. This approach is able to cover market conditions ranging from the usual VaR environment to financial crises. We implement a multistage portfolio model with an exchange rate dynamic with stochastic volatility. The parameters are estimated by GARCH-t models. The simulations are used to select multicurrency portfolios whose exchange rate risk is hedged and rebalanced each ten days, accounting for VaR. We compare the performances of the two most classical institutional options strategies - protective puts and covered calls to that of holding an unhedged portfolio in presence of extreme events.