Bump and Reprice Gamma ladder

It answers a question about one factor at a time. As this factor moves, does the money-per-shift figure stay the same, or does it grow? A reader who knows only the first-order figure treats the answer as a straight line. This report states how far the line bends, and it states that bend at each bucket.

The decision it feeds is the size of a hedge and the comfort taken from it. A book whose second-order figure is large needs a wider hedge than its first-order figure suggests, and a limit that reads only Delta will allow a position that moves more than the limit intends.

This ladder is end of day, and so are the gamma, theta, cross-gamma and par DV01 readers. A ladder is read as the risk statement of record and compared across days. The volatility ladders and the rates delta ladder also hold a live definition, which their own pages state, and a live ladder is indicative where this one stands.

The definition selects the EOD cut, and the run settings row it binds states market data type eod. The run therefore values the portfolio at the weekday before the run date, and holiday calendars are not consulted.

• Trades selected by the definition's scope. The scope is a row of the definition and the taxonomy fixes the shapes it accepts, on Risk reporting.
• Market data at the authorised end of day cut. The run records the cut it read against the run instance, with its label, kind and instant.
• The risk report configuration the definition binds. It switches on the sensitivity analytic, states the base currency and names sensitivity.xml as the sensitivityConfigFile. The analytic states recalibrateModels Y, outputSensitivityThreshold 0.000001, parSensitivity Y and marketConfigFile simulation.xml.
• A sensitivity document that switches gamma on, through ComputeGamma or through a Central shift scheme. The shipped document sets neither for the FX volatility blocks, so a gamma ladder needs a document a person writes. See What is not built.

The run produces the engine's own output archive and records where that archive landed against the run instance. The archive holds sensitivity.csv, which carries the Gamma column beside the Delta column, and scenario.csv, which carries the scenario value behind each row.

The rows a reader would query in a table are a later phase. The result store is designed on Report post-processing and is not built yet.

Gamma is ComputeGamma or a Central shift scheme. The first switch asks the engine for the second-order column. The second changes the arithmetic, because a central shift reprices the book on both sides of the base value and reads the curvature from the pair.

Delta is a value change and not a derivative, and the same holds for the second order. The shift size is already inside the figure. A reader who wants the curvature for another size changes ShiftSize in the document and runs again.

A cross gamma is ComputeGamma plus a CrossGammaFilter that lists pairs of factor keys as substrings. The engine writes a cross gamma into sensitivity.csv as a row with both Factor_1 and Factor_2 populated. At engine version 1.8.17.0 no writer reads sensitivity.crossGammaOutputFile, so crossgamma.csv never appears.

The reader opens the engine's CSV files, because the result store is not built. The tables below state the columns of the two files this report writes. The definitions are on ORE output formats.

The buckets are the same as those of the Delta ladder, because the two reports read one document and one run. A reader places a figure by the bucket columns. Factor_1 carries the risk class and the bucket, and ShiftSize_1 states the shift that produced the figure. A volatility factor states the pair, the strike and the expiry, as in FxVolatility/<pair>/<strike>/<expiry>. A swaption volatility adds the term, as in SwaptionVolatility/<key>/<strike>/<expiry>/<term>. A curve factor names the curve and the bucket, as in IndexCurve/EUR-EURIBOR-6M/11/10Y, and a discount curve factor starts DiscountCurve/<ccy>.

The mechanism has four parts. First, the generated run document carries an analytic of type sensitivity, and that analytic names sensitivity.xml through sensitivityConfigFile. Second, the root of that document is SensitivityAnalysis, and ORE validates it against external/ore/xsd/sensitivity.xsd. Third, the document carries one block for each group of risk factors, among them discount curves, index curves, FX spots, FX volatilities, swaption volatilities, cap and floor volatilities, credit curves and equity volatilities. Fourth, every factor block states ShiftType, ShiftSize, ShiftScheme and the bucket list, which is ShiftTenors, ShiftExpiries, ShiftStrikes, ShiftLossLevels or ShiftTerms.

ShiftType is Relative, Absolute or EqualTo. ShiftScheme is Forward, Backward or Central. Both are enumerations in external/ore/xsd/ore_types.xsd. The document also carries switches that are not factors, and ComputeGamma, CrossGammaFilter, ThetaPeriod and the par conversion group are four of them.

The fragment below is trimmed from external/ore/examples/MarketRisk/Input/sensitivity.xml. It shows the Central scheme the shipped file states for the alternative size keyed IR_FD.

<DiscountCurve ccy="EUR">
  <ShiftType>Absolute</ShiftType>
  <ShiftSize>0.0001</ShiftSize>
  <ShiftSize key="IR_FD">0.001</ShiftSize>
  <ShiftScheme>Forward</ShiftScheme>
  <ShiftScheme key="IR_FD">Central</ShiftScheme>
  <ShiftTenors>2W,1M,3M,6M,9M,1Y,2Y,3Y,4Y,5Y,7Y,10Y,15Y,20Y,25Y,30Y</ShiftTenors>
</DiscountCurve>

The shipped document sets no ComputeGamma element. A gamma ladder over the curves therefore reads the keyed Central scheme, and a gamma ladder over a surface needs a document that adds ComputeGamma.

The engine writes sensitivity.csv with the columns the reader saw above, and it writes scenario.csv with the scenario value and the difference behind each figure.

The bump is a setting of the configuration and not the identity of the report. Two reports over one book that differ only in shift size differ only in the document they bind. Nothing in the name of this report fixes a shift, and nothing in the engine knows a ladder by name.

A definition of this report states the rows below. The shift itself is not a parameter of the store, and no seed states a shift size anywhere.

1. Open the archive the run recorded and take sensitivity.csv.
2. Keep the rows that state a figure in the Gamma column. A row with an empty Gamma column carries no second-order figure.
3. Choose one risk class and one bucket from the segments of Factor_1.
4. Read ShiftSize_1. The gamma figure belongs to that shift, and it does not carry to another size.
5. Read the Gamma column together with the Delta column of the same row. The pair states the line and its bend.
6. Open scenario.csv and read the rows of one factor. The Up/Down column states which side of the base value each row holds, and a central shift reads both sides.
7. Compare the gamma figure against the delta figure of the same bucket. A small gamma against a large delta states a line that holds for the shift in the document.
8. Read the same bucket on the previous close. Two closes state whether the curvature grew or shrank.
9. Do not add gamma figures across buckets into one total without saying what the total is for. A sum of curvatures is not a hedge.

• No mapper reads or writes a SensitivityAnalysis document. The document is a name in a lookup and a row in the file library, and it is not a modelled entity.
• The run package carries only the four Setup documents, which are conventions, curve configuration, today's market and pricing engines. An analytic document that no owner exports never reaches the engine.
• No volatility market data is seeded. The ACME dataset holds 420 quotes and all of them are IR_SWAP/RATE/.... The engine therefore refuses at the point it needs a volatility, and the run records that refusal.
• No shift size is stated anywhere in the store. This matters more for gamma than for delta, because a curvature belongs to one size and to no other.
• No stored shape holds a bucketed ladder. The bucket is a segment of a factor key in a CSV file.
• The result store is not built, so no table carries the rows a reader queries.
• No writer reads sensitivity.crossGammaOutputFile at engine version 1.8.17.0, so a cross-gamma ladder reads rows of sensitivity.csv and no file of its own.

The sensitivity configuration type is seeded with root SensitivityAnalysis, the parameter sensitivityConfigFile and the owner ores.analytics. The document and its two surface variants sit in the ORE file library with their descriptions, the schema is vendored as sensitivity_schema, and the worked configurations are vendored.

No substitute is defined for this report, so a test run executes every phase and assembles its own bundle. The report is exercised by the full-pipeline proof and not by a smoke test. The machinery that proves a bundle without gathering one is Sample bundle smoke test.

• Reports, where this page is listed.
• Risk reporting, which holds the classification taxonomy and the measures catalogue.
• ORE output formats, which states the columns of sensitivity.csv and scenario.csv.
• Bump and Reprice Delta ladder, which carries the first-order column over the same buckets.
• Bump and Reprice Cross-gamma ladder, which reads the rows that name two factors.
• Bump and Reprice Volga ladder, which reads gamma on a volatility factor.
• Report execution pipeline, which states the phases every run goes through.
• The cut is the body a run prices from, which states what an end of day cut holds.
• Light the intraday reports on the LIVE cut, the task that lit the sibling reports.

• Report families — the structure note that orders this cluster, and where to read this page in it.
• Open Source Risk Engine: the engine whose ComputeGamma switch writes the second-order column.