Bump and Reprice Theta ladder

It answers what one period of time costs the book. Every other figure on a sensitivity run moves a market, and this one moves the clock. Theta period states the length of the period, and the engine values the book at the end of it with every market held still. The decision it feeds is whether a position pays for the time it takes, and how a book that holds options across a weekend will read on the next business day. A position that earns less in a day than its theta costs does not survive a quiet market, and this ladder is the page that says so.

ThetaPeriod moves the clock rather than a market. The factor key the engine writes is Theta//0/1D, so a reader sees at once that the row is not a curve and not a surface. The period is the bucket list of the theta statement. Theta is therefore a ladder of its own, and it is not a rates ladder. A rates ladder bumps a curve at each tenor and reads the same Delta column. This ladder changes the valuation date and reads the value change that follows.

The market risk function reads the ladder to check the value it carries into the next day. The trading desk reads it to decide whether a position pays for the time it takes.

The cycle is end of day. A ladder is read as the risk statement of record and compared across days. A live ladder would be priced against a body that is not reproducible, so the same row on two runs would not be the same figure. A theta figure also depends on the date it is taken from, so a run at the close is the one that a reader can compare with the run of the day before.

The family seeds no intraday variant of any ladder. A live ladder would need a definition whose cut selection is LIVE, a run settings row whose market data type is live, and the same sensitivity configuration. The store seeds none of the three for this ladder.

• Trades selected by scope. The scope is the book or the portfolio that the definition states, and the run prices the trades the gather step selects.
• Market data for the valuation date. The risk_report_config row states the market data type. This ladder is end of day, so the type is eod and the valuation date is the weekday before the run date. Holiday calendars are not consulted. The theta figure is the value change from that date forward by the period the configuration states.
• The six configuration documents the definition binds, one for each configuration type. The types are conventions, curve_configuration, todays_market, pricing_engines, risk_report_config and engine_settings. A definition that omits one of the first five cannot run, because ORE reads all of them before it prices.
• The sensitivity configuration document, sensitivity.xml, which states ThetaPeriod.

The run produces the engine's own output archive. The archive holds sensitivity.csv with a row for the theta factor and the Delta and Gamma columns, and scenario.csv with the scenario value behind it. The run records where the archive landed against the run instance.

The tables that would carry the rows a reader queries are designed on Report post-processing and are not built. So a reader opens the CSV files in the archive, and the columns in the next section are the columns of those files.

The values below are the ones the files carry. The definitions of the measures the catalogue names are on Risk reporting and are not repeated here.

A reader places a theta figure by the factor key and by the period. The bucket column is the period, and it appears in the factor key itself.

The theta factor key is written Theta//0/1D. A reader selects the rows whose Factor_1 is that key and drops every other row, because the curve, the spot and the volatility rows belong to the other ladders of the family. The bucket is the period, and there is one of it in a run.

A definition of this report binds the sensitivity analytic. The analytic names the sensitivity configuration document, and that document is the one whose root is SensitivityAnalysis. ORE validates it against external/ore/xsd/sensitivity.xsd. The analytic element in the run document states the parameters below.

<Analytic type="sensitivity">
  <Parameter name="active">Y</Parameter>
  <Parameter name="marketConfigFile">simulation.xml</Parameter>
  <Parameter name="sensitivityConfigFile">sensitivity.xml</Parameter>
  <Parameter name="recalibrateModels">Y</Parameter>
  <Parameter name="parSensitivity">Y</Parameter>
  <Parameter name="outputSensitivityThreshold">0.000001</Parameter>
</Analytic>

The SensitivityAnalysis document carries one block for each group of risk factors. The groups are the discount curves, the index curves, the yield curves, the FX spots, the FX volatilities, the swaption volatilities, the cap and floor volatilities, the CDS volatilities, the default and credit curves, the equity spots and volatilities, the two inflation curve families, the two inflation cap and floor families, the dividend yields, the base correlations, the security spreads, the commodity curves and volatilities, the intraday power curves, the correlations and the bond future volatilities. It also carries four switches that are not factors, and this page uses ThetaPeriod, which is one of them.

Every factor block states four things. ShiftType is Relative, Absolute or EqualTo. ShiftSize is a real, with an optional key for an alternative size. ShiftScheme is Forward, Backward or Central. The bucket list is one of ShiftTenors, ShiftExpiries, ShiftStrikes, ShiftLossLevels or ShiftTerms. ShiftType and ShiftScheme are enums in external/ore/xsd/ore_types.xsd.

The fragment below is the FX volatility block of the shipped external/ore/examples/MarketRisk/Input/sensitivity.xml, trimmed to the first currency pair. It is a factor block, and the theta statement sits beside the factor blocks rather than inside one.

<FxVolatilities>
  <FxVolatility ccypair="USDEUR">
    <ShiftType>Relative</ShiftType>
    <ShiftSize>0.01</ShiftSize>
    <ShiftScheme>Forward</ShiftScheme>
    <ShiftExpiries>1Y,2Y,3Y,5Y</ShiftExpiries>
    <ShiftStrikes/>
  </FxVolatility>
</FxVolatilities>

The theta statement in the same file is one line. The period it names is the bucket list of the theta statement, and the engine puts the period into the factor key.

<ThetaPeriod>1D</ThetaPeriod>

The engine writes sensitivity.csv with the columns TradeId, IsPar, Factor_1, ShiftSize_1, Factor_2, ShiftSize_2, Currency, Base NPV, Delta, Gamma, Currency(Trade), Base NPV(Trade), Delta(Trade), Gamma(Trade) and Scenario. It writes scenario.csv with the columns TradeId, Factor, Up/Down, Base NPV, ShiftSize_1, ShiftSize_2, Scenario NPV, Difference and Base Currency. The factor key of the theta row is Theta//0/1D, so the period is readable on the row itself and a reader does not need the document to know it.

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. A theta report configured for one day and a theta report configured for one week differ in ThetaPeriod and in nothing else. The store states no period for this ladder and no shift size for any ladder.

A definition of this report states the rows below. Where the store states no value, the column says so. A parameter is declared with its domain on ore parameter, and a configuration binds it on configuration parameter.

1. Open sensitivity.csv from the run's output archive. Open scenario.csv beside it, because it holds the values behind the columns.
2. Keep the rows whose Factor_1 is Theta//0/1D. Drop the rows for the curves, the spots and the volatilities, which the other ladders read.
3. Confirm that Factor_2 is empty. A theta row names one factor, the clock.
4. Read the period from the key, and check it against ThetaPeriod in the configuration. A figure for one day and a figure for one week are not comparable.
5. Read the Delta column. That figure is theta, and it is the value change for the stated period with every market held still. A negative figure says the book loses that value as the time passes.
6. Read the Gamma column if the configuration switches it on. It states how the theta figure itself changes over the period.
7. For one row you doubt, open scenario.csv on the same TradeId and the same factor. Read Scenario NPV and Difference. The difference is the value change for the period that row states.
8. Check the valuation date of the two runs before you compare them. The theta of a book that holds an option changes as the option approaches its expiry, so a run on the day before an expiry reads differently from a run a week earlier.
9. Do not add a theta figure to a rates figure. The two ladders read the same Delta column, and they describe different moves. One bumps a curve and the other moves the clock.

• No mapper reads or writes a SensitivityAnalysis document. The document is a name in a lookup and a row in the file library, not a modelled entity.
• The run package carries only the four Setup documents, 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 seeded quotes and all of them are IR_SWAP/RATE/.... so a volatility factor has nothing to shift, and no volatility sensitivity can be computed until the store holds that data. A theta run over an option book needs a volatility, so this ladder cannot be priced in the seeded environment.
• No shift size is stated anywhere in the store, and no theta period is stated for this ladder either. The document that would set it has no stored value to read.
• No stored shape holds a bucketed ladder. The bucket of this page is the period, and no table holds a period as a key.
• The result store is not built, so a reader opens the CSV files and no table answers a query over them.

The report has no smoke test of its own. The smoke test that proves the machinery without gathering anything is Sample bundle smoke test.

A test run of this ladder executes the whole pipeline from the gather step and records the run. It stops before the engine has a volatility to price, and the run package carries no analytic document either. So the report is exercised by the full-pipeline proof and not by a run that writes rows.

• Reports, the inventory this page is listed in.
• Risk reporting, the classification taxonomy and the measures catalogue.
• ORE output formats, the columns of sensitivity.csv and scenario.csv.
• Bump and Reprice Delta ladder, the first order column read on a market factor.
• Bump and Reprice Gamma ladder, the second order column on a market factor.
• Bump and Reprice Rho ladder, the rates ladder this page is not.
• Bump and Reprice Cross-gamma ladder, the rows that pair two factors of one risk class.
• The cut is the body a run prices from, what the end of day cut holds.
• Report execution pipeline, the phases every run goes through.
• Report definition and schedule, the definition that states the cycle and the cut.

• Report families — the structure note that orders this cluster, and where to read this page in it.
• Open Source Risk Engine, the valuation engine whose sensitivity analytic writes the two files.
• Open Source Risk, the project home of the engine.