Performance of a Hedged portfolio Model in 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.