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

Abstract

Classical methods for computing the value-at-risk(VaR) do not account for the large price variationsobserved in financial markets. The historical methodis subject to event risk and may miss some fundamentalmarket evolution relevant to VaR; thevariance/covariance method tends to underestimate thedistribution tails and Monte Carlo simulation issubject to model risk. These methods are therebyusually completed with analyses derived fromcatastrophe scenarios.We propose a special case of the extreme-valueapproach for computing the value-at-risk of a stochasticmulticurrency portfolio when alternative hedgingstrategies are considered. This approach is able tocover market conditions ranging from the usual VaRenvironment to financial crises.We implement a multistage portfolio model with anexchange rate dynamic with stochastic volatility. Theparameters are estimated by GARCH-t models. Thesimulations are used to select multicurrencyportfolios whose exchange rate risk is hedged andrebalanced each ten days, accounting for VaR. Wecompare the performances of the two most classicalinstitutional options strategies – protective puts andcovered calls – to that of holding an unhedgedportfolio in presence of extreme events.