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Option Value at Risk (VaR): Full-Revaluation Guide

Build, interpret, and validate option-portfolio VaR with joint scenarios, full revaluation, explicit quantile rules, backtesting, and stress controls.

Updated

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

Option Value at Risk (VaR) is a model-estimated loss quantile for a defined portfolio, horizon, confidence level, data set, scenario process, and valuation convention. Let positive L denote loss, with L = -P&L. Then:

VaR_alpha = inf { l : P(L <= l) >= alpha }

A one-day 99% VaR of $20,000 says that, under the model and its inputs, the loss is no more than $20,000 in 99% of one-day outcomes. It does not say loss is impossible beyond that threshold, that the worst loss is $20,000, or that exactly 1 exception must occur in every 100 trading days.

Options need special care because their values are nonlinear and change with time, volatility, spot or forward price, rates, dividends, borrow, and exercise features. For material option exposure, joint scenarios plus full revaluation are usually a more reliable control than a Delta-normal shortcut. VaR is still only one model output; expected shortfall and independent stress tests are needed to describe tail severity and states absent from the model.

Specify the measure before calculating it

Every reported VaR should identify the following choices:

Input What must be fixed
Portfolio Exact positions, quantities, multipliers, cash, stock, hedges, and valuation timestamp
Loss Sign convention, base currency, model P&L or executable P&L, and included costs
Horizon Calendar or trading time, time advanced in option valuation, and holding or liquidation assumption
Confidence alpha and the empirical quantile or interpolation convention
Data Lookback window, sampling frequency, cleaning, weights, and treatment of missing or stale observations
Model Risk factors, joint scenario dynamics, valuation model, volatility-surface rule, and exercise treatment

Two VaR numbers are not comparable merely because both say 99%. Portfolio scope, horizon, data, weighting, scenario construction, valuation, currency, and liquidity conventions must also match. Regulatory VaR parameters apply to the entities and purposes named by the relevant rule; they are not universal settings for every investor or risk decision.

Build option VaR in two layers

First generate coherent joint changes in all material risk factors. Then advance the clock by the horizon and revalue the unchanged position snapshot under each state. If the risk question assumes dynamic hedging or liquidation, encode that rule, its timing, and its costs explicitly rather than mixing it into a static VaR.

Approach Scenario layer Main option-specific weakness
Delta-normal Assumes a parametric distribution and maps factor moves through local Delta Misses material Gamma, Vega, skew, jumps, barriers, and changing sensitivities
Historical simulation Applies observed joint factor changes to today’s positions Cannot include an event absent from the selected window and may overweight one regime
Monte Carlo Simulates joint factor states or paths from chosen dynamics Depends on distribution, correlation, volatility-surface, jump, and calibration assumptions

A robust full-revaluation workflow is:

  1. Freeze the position snapshot, market data timestamp, base currency, and marking convention.
  2. Map spot or forward, volatility by strike and expiry, rates, dividends, borrow, FX, correlation, and basis risks.
  3. Generate joint scenarios with documented windows, weights, dynamics, and random seeds where relevant.
  4. Advance time by the stated horizon and fully reprice every option, including exercise and path rules where material.
  5. Add stock, cash, hedge, financing, fee, spread, and modeled liquidation P&L without double counting.
  6. Convert total portfolio P&L to loss, sort or weight the losses, and apply the stated quantile convention.
  7. Store scenario attribution, data snapshot, model version, and controls so the result can be reproduced.

Do not mechanically multiply short-horizon VaR by the square root of time. That scaling needs strong assumptions such as independent, identically distributed changes and stable linear exposure; option curvature, time decay, path dependence, jumps, changing hedges, and illiquidity can break it.

Worked full-revaluation example

Assume a $2,000,000 option portfolio is frozen and fully repriced under 10,000 equally weighted one-day scenarios. Losses are sorted from smallest to largest. Under the convention “the smallest loss whose cumulative probability reaches 99%,” the observation at rank 9,900 is $20,000. Exactly 100 modeled losses are larger in this no-tie example.

The average of those 100 worse losses is $46,000, and the largest modeled loss is $75,000. The report should therefore distinguish:

  • VaR_99% = $20,000: the modeled quantile threshold.
  • ES_99% = $46,000: the average loss in the modeled worst 1% under the stated tail convention.
  • Worst scenario loss = $75,000: the largest loss in this scenario set, not the maximum possible loss.

If the next day’s comparable P&L is -$31,000, the realized loss of $31,000 exceeds the preceding $20,000 VaR and is an exception. One exception does not by itself prove or disprove the model. Its cause, size, clustering, position changes, price sources, and consistency between forecast and P&L definitions all matter.

Validate the number before using it

  • Backtest coverage: compare each prior VaR with the corresponding subsequent P&L and count consistently defined exceptions.
  • Investigate dependence: exceptions that cluster can reveal regime change or omitted dynamics even when the total count looks plausible.
  • Reconcile P&L: separate market moves, time decay, volatility-surface moves, new trades, fees, and unexplained residuals.
  • Benchmark methods: compare full revaluation with Delta-normal or Delta-Gamma approximations and explain material gaps.
  • Test stability: vary lookback windows, weights, scenario counts, seeds, quantile conventions, and volatility-surface mappings.
  • Stress independently: include historical crises, hypothetical gaps, volatility shocks, correlation breaks, and liquidity withdrawal.
  • Review tail severity: report expected shortfall and the worst scenarios rather than only the VaR threshold.
  • Escalate changes: rerun and review after positions, models, markets, liquidity, or data quality change materially.

Backtesting is diagnostic, not a guarantee of future validity. The Basel market-risk framework uses expected shortfall for internal-model capital while retaining VaR-based backtesting, and U.S. fund rule 18f-4 prescribes its own VaR and backtesting requirements. These examples show why purpose and rule set must be stated, not why one parameter set fits every portfolio.

Risks and limitations

  • VaR does not measure how severe losses become beyond the selected quantile.
  • A short option, barrier, concentrated Gamma position, or near-expiry option can change sharply between sampled states.
  • Historical data may omit a crash; simulated data may impose the wrong tails, correlations, or volatility dynamics.
  • A close-based model mark can understate executable loss when spreads widen, depth disappears, or trading is halted.
  • Exercise, assignment, settlement, margin, funding, and liquidation cash needs are not included unless modeled.
  • Netting can hide concentration in one issuer, expiry, strike, volatility point, or common scenario driver.
  • More scenarios reduce sampling noise only within the chosen model; they do not repair missing risk factors or bad assumptions.

Common misconceptions

“99% VaR is the maximum loss.” It is a quantile. Losses beyond it can be much larger, and losses outside the modeled support can exceed every simulated result.

“99% VaR means a 1% chance of losing money.” It refers to exceeding the VaR loss threshold, not to the probability of any loss.

“Full revaluation removes model risk.” It captures nonlinear valuation within each supplied state, but the states, pricing model, data, and execution assumptions can still be wrong.

“A successful backtest proves the model.” It checks historical coverage under specific P&L and exception definitions; it cannot certify future regimes.

“A lower VaR makes a trade better.” VaR measures one modeled loss dimension. It does not establish expected return, suitability, liquidity, or total risk capacity.

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