Comparison, in Risk & Portfolio Construction
Full Revaluation vs Delta-Gamma VaR
For a portfolio with options, the value does not change linearly with the underlying, so VaR and stress calculations must handle curvature. Full revaluation runs each scenario through the actual pricing model, capturing the true nonlinear payoff exactly. Delta-gamma approximates the value change with the first two derivatives, delta and gamma, a parabola fitted at the current point, which is cheap but only locally accurate. The tradeoff is precision against speed, and it sharpens as moves get larger and payoffs get more exotic, where the Taylor approximation breaks down. This matrix compares the two for option risk.
6 criteria. Published May 26, 2026. By AI Fin Hub Research.
Reprices every position with its actual pricing model under each scenario, capturing the exact nonlinear payoff with no approximation.
Pros
- Exact for any payoff, including options and path-dependent or exotic instruments
- Accurate for large moves and stress scenarios, where approximations fail
- No Taylor-expansion error, so the risk number reflects the true repricing
- The reliable reference against which approximations are validated
Cons
- Computationally expensive, especially with many scenarios and complex pricers
- Slow, which can make frequent intraday or large-portfolio VaR impractical
- Requires a full, correct pricing model for every instrument in the book
- Can be overkill for nearly linear books where curvature is negligible
Option-heavy or exotic books, large stress moves, and any case where pricing curvature must be captured exactly
Approximates each instrument's value change with a second-order Taylor expansion in the underlying, using delta and gamma. Fast but only locally accurate.
Pros
- Fast: it needs only the Greeks, not a full repricing under every scenario
- Scales to large portfolios and frequent recomputation cheaply
- Captures first-order curvature via gamma, far better than a delta-only linear approximation
- Adequate for books with modest optionality under small-to-moderate moves
Cons
- Loses accuracy for large moves, where higher-order terms the expansion drops matter
- Breaks down for strongly nonlinear or path-dependent payoffs the Greeks do not summarize
- Greeks themselves change with the move, which the static expansion ignores
- Can understate tail risk precisely when it matters most, in large shocks
Fast, frequent risk on books with limited optionality and small-to-moderate scenario moves
Decision table
See the tradeoffs side by side
| Criterion | Full Revaluation | Delta-Gamma Approximation |
|---|---|---|
| Approach | Exact repricing per scenario | Second-order Taylor in the underlying |
| Accuracy on large moves | Exact | Degrades |
| Exotic / path-dependent payoffs | Handled | Poorly approximated |
| Compute cost | High | Low |
| Speed at scale | Slow | Fast |
| Tail-risk reliability | High | Can understate |
Verdict
Pick by how nonlinear the book is and how large the scenarios get. Delta-gamma is the pragmatic choice for fast, frequent risk on portfolios with modest optionality under small-to-moderate moves, because adding gamma to a linear delta approximation captures most of the curvature for a tiny fraction of the compute. Its weakness is exactly where risk lives: for large shocks and strongly nonlinear or path-dependent payoffs, the dropped higher-order terms matter and the approximation can understate tail risk just when you most need it. Full revaluation removes that error by repricing exactly, at the cost of compute that can make large or intraday calculations slow. The common practical pattern is to run delta-gamma for routine, high-frequency risk and full revaluation for the tail scenarios, the stress tests, and the option-heavy sub-portfolios where the approximation is least trustworthy, using full revaluation periodically to validate that the delta-gamma error stays within tolerance.
Run the numbers next
- Playgrounds Options Greeks Calculator
Black-Scholes pricer + live Greeks visualizer. Drag spot, strike, vol, DTE, rate, dividend yield — see delta, gamma, theta, vega, rho update.
- Playgrounds VaR Backtest — Kupiec & Christoffersen
Paste P&L + VaR series and run Kupiec POF, Christoffersen independence, and joint conditional-coverage tests. Likelihood-ratio χ² p-values.
- Playgrounds Options Payoff Calculator
Build 1–4 leg option strategies. Pick call/put, long/short, strike, and contracts. See the at-expiry payoff diagram, break-even points, maximum profit.
Questions people ask next
Why does delta-gamma understate risk in large moves?
Delta-gamma is a second-order Taylor expansion fitted at the current price, so it matches the true payoff well nearby but diverges as the move grows, because it ignores third- and higher-order terms and assumes the Greeks stay constant. For options the curvature itself changes with the underlying, so a large shock pushes the position into a region the local parabola does not describe. The error often goes in the direction of understating the true loss, which is dangerous because large moves are precisely the tail scenarios VaR is meant to capture.
Is delta-only ever enough, or do I always need gamma?
A delta-only linear approximation is adequate only for nearly linear positions over small moves; for anything with meaningful optionality it can be badly wrong even for modest shocks, because it ignores curvature entirely. Adding gamma captures the leading curvature term and dramatically improves accuracy for small-to-moderate moves at little extra cost, which is why delta-gamma, not delta-only, is the standard fast approximation. Beyond that, only full revaluation captures the rest.
Can I mix the two methods in one risk run?
Yes, and it is common practice. You can apply delta-gamma to the largely linear or lightly optioned part of the book for speed, and full revaluation to the option-heavy or exotic sleeves where accuracy matters, then aggregate. Many desks also run full revaluation only on the tail scenarios and delta-gamma on the bulk, since the approximation error is small for moderate moves and concentrated in the extremes. Periodic full-revaluation benchmarking tells you whether the hybrid's error is acceptable.
Sources
- Value at Risk: The New Benchmark for Managing Financial Risk , Philippe Jorion, McGraw-Hill (2006)
- Options, Futures, and Other Derivatives , John C. Hull, Pearson (2021)
Keep the topic connected
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Value at Risk: the loss threshold you'll exceed with probability α. Why historical VaR is brittle and what it doesn't tell you about the tail.
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Expected shortfall: the average loss given a VaR breach. Why regulators are migrating from VaR and what ES catches that VaR misses.
- Learn Volatility
Volatility as the standard deviation of returns: realized vs implied, the annualization gotcha, and why volatility-of-volatility matters.
- Learn Monte Carlo Simulation
Monte Carlo simulation in trading: when it's the right tool, when it's overkill, and the seed-discipline gotcha that ruins most published examples.