Kostas Giannopoulos

VaR without correlations for portfolios of derivative securities

We propose filtering historical simulation by GARCH processes to model the future distribution of assets and swap values. Options’ price changes are computed by full reevaluation on the changing prices of underlying assets. Our methodology takes implicitly into account assets’ correlations without restricting their values over time or computing them explicitly. VaR values for portfolios of derivative securities are obtained without linearising them. Historical simulation assigns equal probability to past returns, neglecting current market conditions. Our methodology is a refinement of historical simulation.

Backtesting Derivative Portfolios with Filtered Historical Simulation (FHS)

Filtered historical simulation provides the general framework to our backtests of portfolios of derivative securities held by a large sample of financial institutions. We allow for stochastic volatility and exchange rates. Correlations are preserved implicitly by our simulation procedure. Options are repriced at each node. Overall results support the adequacy of our framework, but our VaR numbers are too high for swap portfolios at long horizons and too low for options and futures portfolios at short horizons.

Backtesting Derivative Portfolios with FHS

Filtered historical simulation provides the general framework to our backtests of portfolios of derivative securities held by a large sample of financial institutions. We allow for stochastic volatility and exchange rates. Correlations are maintained implicitly by our simulation procedure. Options are re-priced at each node. Overall results support the adequacy of our framework, but our VaR numbers are too high for swap portfolios at long horizons and too low for options and futures portfolios at short horizons.

Portfolio selection under VaR constraints.

Abstract.In this paper we show that by assuming a constant variance/covariance matrix over the holding period, the VaR limits can often be exceeded within the relevant horizon period. To minimize this risk, we formulate the problem in terms of portfolio selection and propose an innovative methodology using conditional VaR that minimizes the VaR at each point of the holding period. We rewrite the optimisation problem by taking into consideration the variability of risk on all assets eligible to be included in the portfolio.

VaR Modelling on Long Run Horizons

The Value-at-Risk (VaR) criterion as a measure of portfolios risk on long run horizons is considered. The method which makes possible to generate VaR estimates on longer horizons is suggested. The VaR estimation is based on the general method of Filtered Historical Simulation (FHS). The results of numerical experiments with real financial data are described.