Caplet stripping by bootstrap #1422
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yukiiwashita
commented
Nov 28, 2016
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yukiiwashita
commented
- Two implementations of caplet stripping based on bootstrapping: SurfaceIborCapletFloorletVolatilityBootstrapper and SabrIborCapletFloorletVolatilityBootstrapper.
- Created IborCapletFloorletDefinition.
- Added a new metadata, GenericVolatilitySurfacePeriodParameterMetadata.
- Implemented StepUpperCurveInterpolator.
| * The chi-square value. | ||
| * <p> | ||
| * The chi square is 0 if the volatilities are computed by root-finding. | ||
| * The chi square is generally non-zeoro if the volatilities are computed by least square method. |
| * @param chiSquare the chi-square value | ||
| * @return the instance | ||
| */ | ||
| public static IborCapletFloorletVolatilityCalibrationResult ofLestSquare( |
| * Default implementation. | ||
| */ | ||
| public static final SabrIborCapletFloorletVolatilityBootstrapper DEFAULT = of( | ||
| VolatilityIborCapFloorLegPricer.DEFAULT, SabrIborCapletFloorletPeriodPricer.DEFAULT, 1.0e-10, ReferenceData.standard()); |
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Do we need both leg and period pricer?
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The first pricer is used to convert the market vols to prices, whereas the second pricer is used for calibration to SABR model, that is, the second one must be SABR rather than generic VolatilityIborCapletFloorletPeriodPricer. In this case, 'validate(IborCapletFloorletVolatilities)' is overridden and the pricer works only when IborCapletFloorletVolatilities is an instance of SabrIborCapletFloorletVolatilities. Thus this pricer (or its leg version SabrIborCapFloorLegPricer) can not be used for the vol-to-price conversion.
| TRANSFORMS[0] = new SingleRangeLimitTransform(0, LimitType.GREATER_THAN); // alpha > 0 | ||
| TRANSFORMS[1] = new DoubleRangeLimitTransform(0.0, 1.0); // 0 <= beta <= 1 | ||
| TRANSFORMS[2] = new DoubleRangeLimitTransform(-RHO_LIMIT, RHO_LIMIT); // -1 <= rho <= 1 | ||
| TRANSFORMS[3] = new SingleRangeLimitTransform(0, LimitType.GREATER_THAN); |
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Stability for large nu? See SabrModelFitter
| /** | ||
| * The period of the surface node. | ||
| * <p> | ||
| * This is the period to maturity that the node on the surface is defined as. |
| * <p> | ||
| * The caplet volatilities are computed by bootstrapping along the expiry time dimension. | ||
| * The result is an interpolated surface spanned by expiry and strike. | ||
| * The position of the node points on the resultant surface corresponds to market caps. |
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Which part of the cap on the expiry dimension? Last expiry date?
| /** | ||
| * Definition of caplet volatilities calibration. | ||
| */ | ||
| public interface IborCapletFloorletDefinition { |
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Should we have 'Volatility' in the name?
| DoubleArray strikeShifted = DoubleArray.of(nTotal, n -> strikeList.get(n) + shiftCurve.yValue(timeList.get(n))); | ||
| DoubleArray volArray = DoubleArray.copyOf(volList); | ||
| if (capFloorData.getDataType().equals(NORMAL_VOLATILITY)) { // correct initial surface | ||
| metadata = Surfaces.blackVolatilityByExpiryStrike(bsDefinition.getName().getName(), bsDefinition.getDayCount()) |
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If says 'NORMAL_VOLATILITY' but metadata is 'blackVolatility'? Calibrate only Black surfaces?
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Added javadoc on input vol types and output vol types.
| * The beta will be treated as one of the calibration parameters if this field is not specified. | ||
| */ | ||
| @PropertyDefinition(get = "optional") | ||
| private final Curve betaCurve; |
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What about other curves? Beta and rho are usually not calibrated at the same time.
| int[] startIndex = new int[nExpiries + 1]; | ||
| for (int i = 0; i < nExpiries; ++i) { | ||
| LocalDate endDate = baseDate.plus(expiries.get(i)); | ||
| DoubleArray volatilityData = capFloorData.getData().row(i); |
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Where is the difference between Normal and Black dealt with?
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The vol type difference is handled in volatilitiesFunction created by volatilitiesFunction.
| * The result is an interpolated surface spanned by expiry and strike. | ||
| * The position of the node points on the resultant surface corresponds to last expiry date of market caps. | ||
| * The nodes should be interpolated by a local interpolation scheme along the time direction. | ||
| * See {@link SurfaceIborCapletFloorletBootstrapDefinition} for detail. |
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The name of this class has changed: 'SurfaceIborCapletFloorletVolatilityBootstrapDefinition'
| * <p> | ||
| * If the shift curve is not present in {@code SurfaceIborCapletFloorletBootstrapVolatilityDefinition}, | ||
| * the resultant volatility type is the same as the input volatility type, i.e., | ||
| * Black caplet volatilities are returned if Balck cap volatilities are plugged in, and normal caplet volatilities are |
| * The result is a complete set of curves for the SABR parameters spanned by the expiry time. | ||
| * The position of the node points on the resultant curves corresponds to market cap expiries, | ||
| * and are interpolated by a local interpolation scheme. | ||
| * See {@link SabrIborCapletFloorletBootstrapDefinition} for detail. |
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Name has changed to 'SabrIborCapletFloorletVolatilityBootstrapDefinition'
