Where This Fits: Not a 4th or 5th VaR Method
It’s worth being precise about this before anything else, because it’s a common point of confusion. Parametric, Historical Simulation, and Monte Carlo are the three core VaR methodologies covered earlier in this series — each describes where the set of scenarios or the statistical assumption comes from.
Full Revaluation and Partial Revaluation are a different, cross-cutting choice: given a set of scenarios (whether from Historical Simulation or Monte Carlo), *how do you calculate the P&L under each one?* You can compute that P&L either by fully repricing the instrument, or by approximating it using sensitivities. Either historical or simulated scenarios can be run through either revaluation approach — the two dimensions are independent of each other.
| Full Revaluation | Partial Revaluation | |
| Historical Simulation | Reprice fully at each historical scenario | Use Greeks/Duration at each historical scenario |
| Monte Carlo | Reprice fully at each simulated scenario | Use Greeks/Duration at each simulated scenario |
The Parametric method is, by construction, always a form of Partial Revaluation — it never reprices anything; it goes straight from a sensitivity (or a covariance matrix of sensitivities) to a VaR figure using a formula. Full vs Partial Revaluation becomes a live design choice specifically when you’re already running a scenario-based approach (Historical Simulation or Monte Carlo) and need to decide how to compute each scenario’s P&L.
What Is Full Revaluation?
Full Revaluation means taking each scenario’s market conditions (a new stock price, a new yield, a new volatility surface — whatever has changed) and running the position’s complete, exact pricing model again from scratch, exactly as if you were pricing it fresh. The scenario P&L is simply the difference between this newly computed value and today’s value.
| Full Revaluation P&L (Scenario i) = Price(New Market Conditions_i) – Price(Today’s Conditions) For an option: re-run the full Black-Scholes formula at the new stock price For a bond: re-sum the discounted cash flows at the new yield |
Because it makes no simplifying assumption about how the price responds to the market move, Full Revaluation is exact — it automatically captures every non-linearity (Gamma, cross-Gamma, Convexity, and anything more complex the pricing model contains) with no additional modelling effort. The cost is computational: for a large portfolio with thousands of positions and thousands of scenarios, that’s potentially millions of individual full pricing runs, some of which (path-dependent options, callable bonds, structured products) can be computationally expensive even to run once.
What Is Partial Revaluation?
Partial Revaluation skips the full reprice entirely. Instead, it uses sensitivities the desk has typically already calculated for other purposes (Delta, Gamma for options; Duration, Convexity for bonds; DV01 for swaps) and estimates each scenario’s P&L via a Taylor-series approximation around today’s price.
| First-order (linear) Partial Revaluation: P&L ≈ Sensitivity × Change in Risk Factor (e.g., Delta × ΔS, or -Modified Duration × Δy) Second-order Partial Revaluation: P&L ≈ (Sensitivity × Change) + 0.5 × (Curvature × Change²) (e.g., Delta×ΔS + 0.5×Gamma×ΔS², or -ModDur×Δy + 0.5×Convexity×Δy²) |
This is dramatically faster — no repricing model needs to run at all, just simple arithmetic on numbers already on hand — but it is only as accurate as the Taylor approximation itself. A first-order-only approximation misses curvature entirely; adding the second-order term recovers most, but not all, of that missing accuracy.
Worked Example: Option — Full vs Partial Revaluation
This example matches the accompanying workbook exactly (Sheet ‘1. Option – Full vs Partial’): a long position of 10,000 in-the-money call options (Spot ₹1,000, Strike ₹900, 28% annual volatility, 6 months to expiry), run through 100 illustrative stock price scenarios.
| Method | 99% 1-Day VaR | How It’s Computed |
| Full Revaluation | ₹3,09,777 | Exact Black-Scholes reprice at each of the 100 scenario stock prices |
| Partial — Delta-Only | ₹3,23,008 | Delta × ΔS, no curvature term |
| Partial — Delta-Gamma | ₹3,10,631 | Delta × ΔS + 0.5 × Gamma × ΔS² |
| Reading the Result Delta-Only VaR overstates Full Revaluation VaR by about 4.3% (₹3,23,008 vs ₹3,09,777) — a meaningful gap, entirely explained by ignoring the option’s positive Gamma, which cushions losses on large adverse moves. Delta-Gamma VaR comes within about 0.3% of Full Revaluation (₹3,10,631 vs ₹3,09,777) — the second-order term recovers nearly all of the missing accuracy. This is exactly the same Delta-Gamma logic introduced in the Options & Swap VaR workbook earlier in this series — here, benchmarked directly against the true, exactly-computed answer for the first time. | ||
Worked Example: Bond — Full vs Partial Revaluation
This example matches the accompanying workbook exactly (Sheet ‘2. Bond – Full vs Partial’): a position of 50,000 units of a 10-year, 7% annual coupon bond priced at par (YTM = 7.00%, Modified Duration 7.02, Convexity 64.93), run through 100 illustrative daily yield-change scenarios.
| Method | 99% 1-Day VaR | How It’s Computed |
| Full Revaluation | ₹4,06,311 | Exact bond reprice (sum of discounted cash flows) at each scenario yield |
| Partial — Duration-Only | ₹4,08,498 | -Modified Duration × Δy, no curvature term |
| Partial — Duration+Convexity | ₹4,06,302 | -ModDur × Δy + 0.5 × Convexity × Δy² |
| Reading the Result Duration-Only VaR overstates Full Revaluation VaR by about 0.5% (₹4,08,498 vs ₹4,06,311) — present, but much smaller than the option’s gap. Duration+Convexity VaR is within roughly 0.002% of Full Revaluation (₹4,06,302 vs ₹4,06,311) — for this instrument, the second-order approximation is essentially indistinguishable from the exact answer. | ||
Why the Option Shows a Bigger Approximation Gap Than the Bond
This is the single most useful comparison in this guide, and it’s worth understanding rather than memorising. Both instruments have a “first derivative” sensitivity (Delta / Duration) and a “second derivative” curvature measure (Gamma / Convexity) — but options are structurally far more non-linear relative to their own Delta than a plain bond’s price-yield curve is relative to its Duration.
A bond’s price-yield relationship is a relatively gentle, smooth curve across normal yield ranges. An option’s price, by contrast, can change character dramatically — Delta itself moves from near 0 to near 1 as an option goes from deep out-of-the-money to deep in-the-money, and Gamma is largest exactly around the strike price. This makes a linear (Delta-Only) approximation break down faster and more severely for options than a linear (Duration-Only) approximation does for an everyday bond. The practical lesson: the more non-linear (option-like) a portfolio’s holdings, the more a Partial Revaluation shortcut costs in accuracy — and the more it matters to use at least a second-order approximation, or switch to Full Revaluation entirely.
The Trade-off in Practice: Speed vs Accuracy
| Consideration | Favours Full Revaluation | Favours Partial Revaluation |
| Portfolio has significant optionality | ✓ | |
| Very large portfolio / many scenarios | ✓ (speed matters) | |
| Regulatory capital calculation | ✓ (more defensible) | |
| Intraday / real-time risk monitoring | ✓ (speed matters) | |
| Large market moves being scenario-tested | ✓ | |
| Portfolio is mostly linear instruments (bonds, FX spot, futures) | ✓ (gap is small anyway) | |
| Computational budget/infrastructure is limited | ✓ |
In practice, many institutions use a hybrid: Partial Revaluation (with at least second-order terms) for daily, portfolio-wide risk monitoring where speed matters, and Full Revaluation for regulatory capital calculations, less liquid or heavily optioned sub-portfolios, and periodic validation checks — precisely to catch cases like the option example above, where a purely linear shortcut would meaningfully understate genuine risk.
https://www.investopedia.com/articles/04/092904.asp
Frequently Asked Questions
Is Partial Revaluation the same thing as Parametric VaR?
Not quite — Parametric VaR is always a form of Partial Revaluation (it never fully reprices anything), but Partial Revaluation is a broader technique that can also be applied inside a Historical Simulation or Monte Carlo framework, exactly as demonstrated in this workbook. Every Parametric VaR calculation is a Partial Revaluation; not every Partial Revaluation is a Parametric VaR calculation.
Why not just always use Full Revaluation, since it’s more accurate?
Computational cost, primarily. A large derivatives portfolio, priced with complex models (Monte Carlo pricers for exotics, for instance), run across thousands of historical or simulated scenarios, can turn Full Revaluation into a genuinely heavy overnight (or longer) batch calculation. Partial Revaluation exists specifically to make daily or intraday risk monitoring computationally feasible at scale.
Does adding more Taylor-series terms always keep closing the gap?
In general, yes, up to a point — a third-order term would typically recover further accuracy for instruments with strong higher-order effects. In practice, second-order (Gamma/Convexity) is usually judged the reasonable stopping point for standard risk monitoring, balancing the diminishing accuracy gains against the added complexity of calculating and maintaining higher-order sensitivities.
Does this distinction matter for Historical Simulation VaR specifically, covered earlier in this series?
Yes — worth flagging explicitly: the Historical Simulation VaR workbook earlier in this series used Full Revaluation implicitly, since it applied historical returns directly to position values without any Delta/Duration shortcut. This workbook makes that choice explicit, and shows what would have changed had a Partial Revaluation shortcut been used instead within that same historical-scenario framework.