FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

Validating VaR Data Inputs, Risk Factor Mapping and Assumptions

Updated 11 October 2026 · Fact-checked

Validating VaR inputs means checking that the data, risk factors, position mappings, volatility and correlation estimates, and distributional assumptions are accurate, complete and fit for the portfolio. You test each input, compare it with the actual risks, and judge whether errors would understate VaR. Then you document findings and fixes.

Understand Data Inputs, Risk Factor Mapping and Model Assumptions

A VaR model is only as good as what goes into it. Validators therefore review the inputs and assumptions before they look at output. A model can pass a backtest by luck while its inputs are poor.

Start with data quality. Market data must be complete, accurate, timely and consistent. Typical problems are stale prices, missing days, bad ticks, gaps filled by interpolation, and inconsistent time stamps across markets. Validators compare internal data with independent sources and check how outliers and gaps are treated. Position data must also reconcile to the books.

Next is risk factor selection and mapping. A bank cannot model every instrument price, so positions are mapped to a smaller set of risk factors such as interest rate curve points, equity indices, FX rates and volatilities. Validators ask whether all material risk factors are captured. Missing factors, such as basis risk, credit spreads, or volatility for options, can hide risk. They also check that proxies are reasonable and that mapping does not remove too much idiosyncratic risk. Nonlinear positions mapped with linear (delta-only) approximations can badly misstate risk for large moves.

Then come volatility and correlation estimates. Equal-weighted windows react slowly. EWMA or GARCH react faster but depend on the decay factor or parameters. A short window is noisy, a long one is slow to adapt. Correlations are unstable and tend to rise in stress, so estimates from calm periods can overstate diversification. Validators check that the covariance matrix is valid (positive semi-definite) and that stressed periods are represented.

Finally, review the distributional assumptions. Parametric VaR assumes a distribution, often normal, which understates fat tails and skewness. Historical simulation makes no distributional assumption but depends on the chosen window, assumes the past represents the future, and reacts slowly unless weighted. Monte Carlo depends on the chosen process and parameters. The validator compares methods, tests fit and judges whether the choice suits the portfolio.

Key formulas to remember

Parametric VaR (normal): VaR = z × σ × V × √h; z is the normal quantile (1.645 at 95%, 2.326 at 99%), σ is daily volatility, V is position value, h is horizon in days. Valid under square-root-of-time scaling, which needs i.i.d. returns.
EWMA variance: σ²(t) = λ × σ²(t−1) + (1 − λ) × r²(t−1); Lower λ reacts faster to new data; higher λ is smoother. λ = 0.94 is the common RiskMetrics daily value.
Portfolio variance (two assets): σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2; Higher ρ means less diversification and higher VaR. Understated ρ understates VaR.
Historical simulation VaR: VaR at confidence c = loss at the (1 − c) quantile of the sorted scenario P&L; With 500 scenarios at 99%, VaR is roughly the 5th worst loss. Window length drives the result.
Delta-normal option approximation: ΔP ≈ Delta × ΔS; Ignores gamma and vega. Understates risk for large moves in options.

How to solve Data Inputs, Risk Factor Mapping and Model Assumptions questions

Use this order for any question on VaR inputs and assumptions. It keeps you on the validator's logic.

1Identify which input the question targets: data, risk factors, mapping, volatility or correlation, or distribution.
2Identify the VaR method in use (historical, parametric or Monte Carlo), because each has different input weaknesses.
3Name the specific weakness, such as stale data, missing factor, linear mapping of options, slow window, or normality with fat tails.
4Decide the direction of the error: does it understate or overstate VaR, and in which market conditions?
5If a calculation is needed, apply the formula carefully with consistent units (daily vs annual, percent vs decimal).
6Choose the validation test or remedy: independent data comparison, factor coverage review, benchmark model, sensitivity test, stress test or backtest.
7State the conclusion in one line: is the input acceptable, and what documented action follows?

Quickest way: Match the flaw to the method

When to use it: Use when a multiple-choice question describes a model feature and asks for the main weakness or best validation step.

Normal distribution assumed: think fat tails, understated tail VaR.
Historical simulation: think window length, slow response, no new scenarios beyond history.
Delta-only mapping of options: think missing gamma and vega.
Calm-period correlation or volatility: think understatement in stress.
Proxy or missing factor: think basis risk and hidden concentrations.
Pick the answer that tests the input independently, not one that only repeats the model output.

Common mistakes in Data Inputs, Risk Factor Mapping and Model Assumptions

Treating a passed backtest as proof that inputs are sound.
Backtesting looks like a complete check, so students stop there.
Fix: Remember that backtests have low power and can hide offsetting errors. Inputs and assumptions need direct review.
Saying historical simulation has no assumptions.
It does not assume a distribution, so students overgeneralise.
Fix: It still assumes the past window represents the future, that observations are equally likely, and that the data are reliable.
Assuming normal VaR is conservative.
The normal quantile looks standard and familiar.
Fix: Real returns have fat tails, so normal VaR at high confidence often understates loss. Compare with historical or fat-tailed alternatives.
Ignoring the direction of the error.
Students list weaknesses without saying what they do to VaR.
Fix: Always state whether VaR is understated or overstated, and when (calm or stress).
Mixing units in volatility scaling.
Annual and daily volatility are used interchangeably.
Fix: Convert annual to daily by dividing by √252 (or the stated day count), then scale to the horizon by √h.
Assuming correlations are stable.
A single matrix is used in the formula, which hides its variability.
Fix: Remember correlations tend to rise in crises, so diversification benefits shrink when needed most. Test with stressed correlations.

Worked examples

Example 1

A bank holds a ₹50,00,00,000 equity position with daily volatility of 1.2%. Using normal parametric VaR, calculate the 10-day 99% VaR. Use z = 2.326 and √10 = 3.162.

Show the solution

Daily 99% VaR = 2.326 × 0.012 × ₹50,00,00,000.
2.326 × 0.012 = 0.027912.
0.027912 × ₹50,00,00,000 = ₹1,39,56,000.
Scale to 10 days: ₹1,39,56,000 × 3.162 = ₹4,41,30,072 approximately.
This assumes i.i.d. normal returns. Fat tails or volatility clustering would make the true loss larger.

Answer: About ₹4.41 crore (₹4,41,30,072), understated if returns are fat-tailed or autocorrelated.

Example 2

A validator finds that a bank's VaR model maps a portfolio of short-dated equity options to delta-only exposures, and uses a 1,000-day equal-weighted historical window dominated by a calm period. Which issues should the validator raise, and what is the likely effect on VaR?

Show the solution

Delta-only mapping ignores gamma and vega. For large market moves, an option's loss differs from the linear estimate, and short option positions lose more than delta suggests.
So VaR for these positions is likely understated in volatile markets.
The long equal-weighted window gives little weight to recent data and is dominated by calm observations, so the window adapts slowly to a rise in volatility.
Both flaws push VaR down when markets turn volatile.
Recommended actions: map options with full revaluation or delta-gamma-vega, use weighted or shorter plus stressed windows, and benchmark against an alternative model.

Answer: Raise the missing gamma and vega risk and the slow, calm-dominated window. Both likely understate VaR in stress. Recommend full revaluation and a weighted or stressed window.

Exam tips

Always link a weakness to its effect on VaR: understated or overstated, and in which conditions.
Know the weakness list for each method: parametric (normality, linear mapping), historical (window, past equals future), Monte Carlo (process and parameter choice).
Expect options and nonlinear positions to be the usual trap for delta-only or linear mapping.
In calculations, check units first: daily versus annual volatility, and the z-value for the stated confidence level.
Prefer answers that call for independent verification and documented challenge over answers that simply accept model output.

Practice questions from Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

Data Inputs, Risk Factor Mapping and Model Assumptions: frequently asked questions

What does a validator check in VaR data inputs?

They check completeness, accuracy, timeliness and consistency of market and position data. They look for stale prices, gaps, outliers and how these are treated. They also reconcile positions to the books and compare with independent data sources.

What is risk factor mapping in a VaR model?

It is the process of expressing each position as exposure to a limited set of risk factors, such as rate curve points, equity indices and FX rates. Validators check that material factors are covered and that proxies and approximations do not hide risk.

Historical simulation vs parametric VaR: which is better to validate?

Neither is always better. Historical simulation avoids a distributional assumption but depends on the window and the past. Parametric VaR is simple and fast but relies on normality and often linear mapping. Validation should compare the two and test against actual outcomes.

Why do correlation estimates matter in VaR validation?

Correlations drive the diversification benefit. They tend to rise in stress, so estimates from calm periods can understate VaR. Validators test stressed correlations and check the covariance matrix is valid.