Value-at-Risk for Nonlinear Financial Instruments – Linear Approximation or Full Monte-Carlo?

The most widely used tool to measure, gear and control market risk is value-at-risk (VaR).VaR quantifies the worst loss over a specified target horizon with a given statisticalconfidence level. In other words, it represents a quantile of an estimated profit-lossdistribution. Various organizations and interest groups have recommended VaR as a portfoliorisk-measurement tool. Moreover, since the publication of the market-risk-measurementsystem RiskMetricsTM of J.P. Morgan in 1994 VaR has gained increasing acceptance and cannow be considered as the industry’s standard tool to measure market risks.While the basic concept of VaR is simple, many complications can arise in practical use. Animportant complication is caused by nonlinearity in the portfolio payoff structure. Thisproblem arises for all portfolios that include assets with highly nonlinear payoffs, such asoption positions. For such nonlinear portfolios, VaR can not be computed directly from a riskfactor distribution. Instead, the risk factor distribution first needs to be converted into a profitlossdistribution for the portfolio. VaR is then computed from this profit-loss distribution.Several methods for computing VaR of nonlinear portfolios have been proposed. Parametricmodels such as delta-normal are based on statistical parameters....