Realised volatility of the Polish sovereign curve
Realised normal (basis-point) volatilities of constant-maturity zero yields: standard deviations of h-month changes at each tenor, annualised by √(12/h), the realised counterpart of a swaption surface. Plus a short-long probability plane: twelve-month moves of the 3M and 10Y rates, with Gaussian percentile ellipses centred on the latest move.
How to read this page (methodology and glossary)
The realisations are month-end changes of the LW-NSS-fitted constant-maturity zero curve at eight tenors from 3 months to 10 years. For each horizon h the realised normal volatility at a tenor is the standard deviation of h-month yield changes annualised by √(12/h), in basis points per year: a realised analogue of a normal swaption surface with expiry h on a swap of the tenor's length. The probability plane takes the twelve-month move of the short rate (3M zero, coordinate s) and of the long rate (10Y zero, coordinate ℓ), giving one (s, ℓ) pair per month. The percentile ellipses are those of a bivariate Gaussian centred on the latest observed pair, with no drift and the sample covariance of the pairs; the Mahalanobis radius of the p-th percentile is √(−2 ln(1−p)).
Caveats
The Polish constant-maturity yields are model-fitted (LW-NSS), so sub-1y tenors inherit some smoothing from the fit where quote-based constant-maturity series would not. Changes at horizons above one month overlap when sampled monthly, so the table cells are descriptive volatilities, not independent-sample estimates. The plane summarises the curve move by its two endpoints; belly moves that leave the 3M and 10Y unchanged are invisible to it.
Glossary
| normal vol | Volatility of yield changes in basis points (not log-normal price vol), the convention of swaption markets for rates. |
| h | Horizon of the yield change in months: 1, 3, 6 or 12. Annualisation by √(12/h). |
| (s, ℓ) | Twelve-month change of the 3M zero rate (s) and of the 10Y zero rate (ℓ), in bp. |
| ellipse p | The p-th percentile contour of the fitted bivariate Gaussian: half of future moves inside the 50% ring if the past covariance holds and moves are Gaussian with no drift. |
| pricer | Bachelier (normal) model on the synthetic IRS. Payer = A[(F−K)Φ(d)+σ√Tφ(d)], d=(F−K)/(σ√T). Vols are realised forward-par-rate vols scaled by the user's Q-adjustment factor; prices are actuarial benchmarks, not market quotes. |
| full / 10y | Sample toggle: full month-end history from 2005, or the last ten years of moves only. |
Realised normal volatility, bp per year
Standard deviation of the h-month change in the constant-maturity zero yield at each tenor, annualised by √(12/h).
Vol term structure
Realised vol against tenor, one line per horizon (solid), with the best-fitting one-factor Hull-White shape σr·(1−e−aτ)/(aτ) overlaid (dotted). Under Hull-White the decay of vol in tenor identifies the mean-reversion speed a from realised data alone, with no options market: the diagnostic transplanted from the implied-vol calibration of Dec (2019). Where the realised row is hump-shaped (short horizons), one summand cannot fit, echoing that paper's finding that Hull-White needs two summands on PLN data.
Rolling realised vol
Rolling standard deviation of one-month yield changes, annualised, at the 2y, 5y and 10y tenors. Choose the window length.
Vol surface (horizon × tenor)
The vol table as a heatmap: realised normal vol in bp per year by horizon and tenor, matching the sample toggled above the term-structure chart.
Probability plane: short × long twelve-month moves
Historical (s, ℓ) pairs (dots), the latest pair (diamond), Gaussian percentile ellipses centred on it. s = 3M move, ℓ = 10Y move, no drift.
Hypothetical swaption pricer (Bachelier on realised vol)
Prices a swaption on a synthetic IRS: annual fixed leg against the 6m zero rate reset semi-annually, both legs off the LW-NSS PLN curve, so forward par rate and annuity are pure curve arithmetic. The normal (basis-point) convention and the very need for a realised-vol benchmark both trace to the structure of the PLN options market documented in Dec (2019): a thin swaption surface, no active caps and floors market, and log-normal quotes distorted near zero strikes.
Measure caveat: the volatility input is realised (P-measure, backward-looking); a traded swaption is priced on implied (Q-measure) volatility, which normally exceeds realised by a volatility risk premium. The Q-adjustment factor multiplies the realised vol to approximate this wedge (default 1.10, adjust to taste); at factor 1.00 the outputs are actuarial prices, not market prices.
ATM premium grid, bp of notional
Bachelier at-the-money premia under the toggled realised vol and the current Q-adjustment factor.
ATM strikes, % (forward par rates)
The at-the-money strike of each cell: today's forward par rate of the synthetic IRS starting at expiry.
Source-by-source observation timestamps for every input feeding this page are listed in the Data lineage & freshness block on the landing page.