Comparing the Three VaR Methods
The three VaR engines trade speed, flexibility, and realism. Parametric (delta-normal) is fastest and data-light but assumes normality and handles only linear positions well. Historical simulation makes no distributional assumption and captures real fat tails, but it is bound to its window and blind to unseen shocks. Monte Carlo is the most flexible, repricing nonlinear payoffs across invented scenarios, at the cost of heavy computation and model risk. No method dominates; the right choice depends on the portfolio, the data, and the resources available.
Try it yourself
How much could this book lose on a bad day? VaR draws a line in the loss tail at confidence 95%. The parametric line assumes a normal curve, VaR = (z·σ·√h − μ·h)·V with z = 1.645 (one-tailed). The historical and Monte-Carlo methods read VaR off a simulated loss distribution instead. Under normality the three roughly agree; fat tails pull the historical figure deeper.
Why it matters
Think of a triangle of speed, accuracy, and flexibility, where you cannot have all three. Parametric buys speed by assuming a bell curve. Historical buys realism by trusting the past but cannot see beyond it. Monte Carlo buys flexibility by simulating anything you can model, then bills you in computer time and exposes you to whatever model you chose. A risk desk often runs more than one and compares, treating agreement as comfort and disagreement as a warning to look closer.
Formulas
Worked examples
A portfolio of plain government bonds versus a portfolio of exotic, path-dependent options. Which VaR method fits each, and why?
The linear bond portfolio suits parametric (delta-normal) VaR: positions move proportionally with rates, so the normal approximation is fast and adequate. The exotic-options book needs Monte Carlo with full valuation to capture path dependence and convexity that a linear method cannot. If a long, relevant data history exists, historical simulation is a useful cross-check on both, since it carries real tail behaviour without a distributional assumption.
Common mistakes
- ✗One method is best for every portfolio. Each method trades speed, realism, and flexibility differently; the right choice depends on the positions, data, and resources.
- ✗Historical simulation is always more accurate than parametric. It captures real tails but is bound to its window; for a linear portfolio in calm markets, parametric can be just as good and far faster.
- ✗Monte Carlo is the safest because it is the most sophisticated. Its sophistication adds model risk; a misspecified process can make it less reliable than a simple method.
- ✗If two methods disagree, one must be coded wrong. Disagreement often reflects genuine differences in assumptions (normality, window, model) and is a signal to investigate, not necessarily a bug.
Revision bullets
- •Parametric: fast, data-light, but assumes normality and linearity
- •Historical: no distribution assumed, but window-bound and backward-looking
- •Monte Carlo: flexible and nonlinear-capable, but costly with model risk
- •All three read VaR as a loss quantile
- •No method dominates; match the method to the portfolio
Quick check
Which VaR method is best suited to a portfolio dominated by exotic, path-dependent options?
A correct statement about the three VaR methods is that
Connected topics
Sources
- Jorion (2007), Ch. 5-12Jorion, P. Value at Risk: The New Benchmark for Managing Financial Risk. 3rd ed. McGraw-Hill, 2007. ISBN 978-0-07-146495-6.Compares delta-normal, historical-simulation, and Monte Carlo VaR and their respective strengths and weaknesses.
- GARP (2023), FRM Part I: Valuation and Risk ModelsGlobal Association of Risk Professionals. FRM Part I: Valuation and Risk Models. GARP / Pearson, 2023.Summarises the trade-offs across the three standard VaR estimation approaches.