Value at Risk: methods

Last updated 10 November 2026

This page describes how GIAnalyzer computes Value at Risk (VaR) and expected shortfall: the three methods, how scenarios are built from market history, how positions are revalued in each scenario, how VaR is read from the results, and what the methods do not do. It describes GIAnalyzer version 5.12.0. It is provided for information and is not a contractual specification.

The function-level detail is in the function reference.

Coverage

Historical simulation

Scenarios

Scenarios come from market history supplied by the user: share prices, exchange rates, points of interest rate and credit spread curves, inflation rates and CPI, between a start and an end date.

• Each scenario is the change in every market variable over the VaR horizon, ending on one date of the history. Scenarios overlap: there is one for each date, measured back over the horizon, which is in calendar days.
• Changes are relative for share prices, exchange rates and CPI levels, and absolute for interest rates, credit spreads and inflation rates.
• Each change is applied to today's market data, and the portfolio is revalued at today's valuation date.
• The n-day change is used directly; one-day VaR is not scaled by the square root of time.

Revaluation

• FX and equity positions are revalued in full in every scenario, with the pricing models described on the FX and equity pages.
• Bonds, interest rate and inflation derivatives can be revalued in full, or approximated from their key-rate sensitivities (KR01) to the curve changes, plus the effect of exchange-rate changes.
• In combined portfolios, bonds, interest rate and inflation derivatives use the key-rate approximation; FX and equity positions are revalued in full.
• Option volatilities are held at today's levels, unless a history of volatilities is supplied for FX or equity options.

Reading VaR from the scenarios

The profit or loss of each scenario is the scenario value less today's value. VaR is the loss at the chosen confidence level in this distribution:

• Interpolated between the two scenarios either side of the percentile, in the way of Excel's PERCENTILE function; or
• The scenario itself: the one just below, just above, or nearest to that point.

Expected shortfall is the average profit or loss of the scenarios worse than the VaR.

VaR and expected shortfall are reported as a profit or loss, so a loss is a negative number.

Breakdown

• Component VaR: the profit or loss of chosen positions in the VaR scenario.
• Incremental VaR: the change in VaR when chosen positions are removed.
• Marginal VaR: the change in VaR for a small change in chosen positions.

Other results

For any history, GIAnalyzer also gives the profit or loss of every scenario, the date behind the VaR scenario (or the k-th worst), the change in any market variable on that date, and the value of chosen positions in any scenario.

Hybrid historical simulation

The same scenarios, weighted by their age: recent scenarios count more, with weights that decline exponentially at a daily rate set by the user (in the spirit of Boudoukh, Richardson and Whitelaw, 1998). VaR is read from the weighted distribution of profits and losses. With no decay, it is the same as historical simulation.

The age of a scenario is measured in calendar days.

Monte Carlo simulation

For FX and equity portfolios:

• Each share price or exchange rate follows geometric Brownian motion to the horizon, with a risk-neutral drift from the interest rates (and dividend yield) and the volatility given.
• Moves are correlated through a correlation matrix supplied by the user, by Cholesky decomposition.
• Every position is revalued in full in every simulation. VaR and expected shortfall are read from the simulated profits and losses as above.
• The number of simulations and the random seed are set by the user.

Market data handling

• Missing data: gaps in a history can be filled with the previous observation, or the dates can be limited to those common to all series.
• Calendars: scenarios are matched by calendar days; there are no holiday calendars.
• CPI publication dates: a CPI history can be re-dated from the month it measures to the date it was published, so that scenarios reflect what was known at each date.
• Interest rate derivative portfolios: positions identical in every term are merged, and exactly offsetting (back-to-back) positions removed, before the VaR is computed.

What the methods do not do

The VaR methods:

• do not scale one-day results to longer horizons, and do not age the portfolio over the horizon: every scenario is valued at today's date;
• use first-order key-rate sensitivities for bonds, interest rate and inflation derivatives in combined portfolios, with no convexity;
• hold option volatilities constant, except where a volatility history is given for FX or equity;
• offer Monte Carlo only for FX and equity, with correlations supplied by the user rather than estimated;
• do not model default or credit migration: credit enters only through credit spread changes on bonds.

References

• Boudoukh, J., Richardson, M. and Whitelaw, R. (1998). The best of both worlds. Risk 11(5), 64–67.
• Hull, J. C. (2023). Risk Management and Financial Institutions, 6th edition. Wiley.
• Jorion, P. (2006). Value at Risk: The New Benchmark for Managing Financial Risk, 3rd edition. McGraw-Hill.

Document history