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.
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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.
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FAQ
Questions people ask next
The short answers readers usually want after the first pass.
Sources & References
- 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)
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