Package com.opengamma.strata.pricer.cms

Class SabrExtrapolationReplicationCmsPeriodPricer

java.lang.Object

com.opengamma.strata.pricer.cms.SabrExtrapolationReplicationCmsPeriodPricer

public final class SabrExtrapolationReplicationCmsPeriodPricer
extends Object

Computes the price of a CMS coupon/caplet/floorlet by swaption replication on a shifted SABR formula with extrapolation.

The extrapolation is done on call prices above a certain strike. See SabrExtrapolationRightFunction for more details on the extrapolation method.

The replication requires numerical integration. This is completed by RungeKuttaIntegrator1D.

The consistency between RatesProvider and SabrParametersSwaptionVolatilities is not checked in this class, but validated only once in SabrExtrapolationReplicationCmsLegPricer.

Reference: Hagan, P. S. (2003). Convexity conundrums: Pricing CMS swaps, caps, and floors. Wilmott Magazine, March, pages 38--44. OpenGamma implementation note: Replication pricing for linear and TEC format CMS, Version 1.2, March 2011. OpenGamma implementation note for the extrapolation: Smile extrapolation, version 1.2, May 2011.

Method Summary

Modifier and Type	Method	Description
double	adjustedForwardRate(CmsPeriod cmsPeriod, RatesProvider provider, SabrSwaptionVolatilities swaptionVolatilities)	Computes the adjusted forward rate for a CMS coupon.
double	adjustmentToForwardRate(CmsPeriod cmsPeriod, RatesProvider provider, SabrSwaptionVolatilities swaptionVolatilities)	Computes the adjustment to the forward rate for a CMS coupon.
void	explainPresentValue(CmsPeriod period, RatesProvider ratesProvider, SabrSwaptionVolatilities swaptionVolatilities, ExplainMapBuilder builder)	Explains the present value of the CMS period.
double	getCutOffStrike()	Returns the cut-off strike.
double	getMu()	Returns the tail thickness parameter.
DiscountingSwapProductPricer	getSwapPricer()	Returns the underlying swap pricer.
static SabrExtrapolationReplicationCmsPeriodPricer	of(double cutOffStrike, double mu)	Obtains the pricer with default swap pricer.
static SabrExtrapolationReplicationCmsPeriodPricer	of(DiscountingSwapProductPricer swapPricer, double cutOffStrike, double mu)	Obtains the pricer.
CurrencyAmount	presentValue(CmsPeriod cmsPeriod, RatesProvider provider, SabrSwaptionVolatilities swaptionVolatilities)	Computes the present value by replication in SABR framework with extrapolation on the right.
PointSensitivityBuilder	presentValueSensitivityModelParamsSabr(CmsPeriod cmsPeriod, RatesProvider provider, SabrSwaptionVolatilities swaptionVolatilities)	Computes the present value sensitivity to SABR parameters by replication in SABR framework with extrapolation on the right.
PointSensitivityBuilder	presentValueSensitivityRates(CmsPeriod cmsPeriod, RatesProvider provider, SabrSwaptionVolatilities swaptionVolatilities)	Computes the present value curve sensitivity by replication in SABR framework with extrapolation on the right.
double	presentValueSensitivityStrike(CmsPeriod cmsPeriod, RatesProvider provider, SabrSwaptionVolatilities swaptionVolatilities)	Computes the present value sensitivity to strike by replication in SABR framework with extrapolation on the right.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

of

public static SabrExtrapolationReplicationCmsPeriodPricer of(DiscountingSwapProductPricer swapPricer,
                                                             double cutOffStrike,
                                                             double mu)

Obtains the pricer.

Parameters:

swapPricer - the pricer for underlying swap

cutOffStrike - the cut-off strike value

mu - the tail thickness

Returns:

the pricer

of

public static SabrExtrapolationReplicationCmsPeriodPricer of(double cutOffStrike,
                                                             double mu)

Obtains the pricer with default swap pricer.

Parameters:

cutOffStrike - the cut-off strike value

mu - the tail thickness

Returns:

the pricer

getSwapPricer

public DiscountingSwapProductPricer getSwapPricer()

Returns the underlying swap pricer.

Returns:

the pricer

getMu

public double getMu()

Returns the tail thickness parameter.

Returns:

the parameter

getCutOffStrike

public double getCutOffStrike()

Returns the cut-off strike.

Returns:

the strike

presentValue

public CurrencyAmount presentValue(CmsPeriod cmsPeriod,
                                   RatesProvider provider,
                                   SabrSwaptionVolatilities swaptionVolatilities)

Computes the present value by replication in SABR framework with extrapolation on the right.

Parameters:

cmsPeriod - the CMS

provider - the rates provider

swaptionVolatilities - the swaption volatilities

Returns:

the present value

adjustedForwardRate

public double adjustedForwardRate(CmsPeriod cmsPeriod,
                                  RatesProvider provider,
                                  SabrSwaptionVolatilities swaptionVolatilities)

Computes the adjusted forward rate for a CMS coupon.

The adjusted forward rate, is the number such that, multiplied by the notional, the year fraction and the payment date discount factor, it produces the present value. In other terms, it is the number which used in the same formula used for Ibor coupon pricing will provide the correct present value.

For period already fixed, this number will be equal to the swap index fixing.

For cap or floor the result is the adjusted forward rate for the coupon equivalent to the cap/floor, i.e. the coupon with the same dates and index but with no cap or floor strike.

Parameters:

cmsPeriod - the CMS period, which should be of the type CmsPeriodType.COUPON

provider - the rates provider

swaptionVolatilities - the swaption volatilities

Returns:

the adjusted forward rate

adjustmentToForwardRate

public double adjustmentToForwardRate(CmsPeriod cmsPeriod,
                                      RatesProvider provider,
                                      SabrSwaptionVolatilities swaptionVolatilities)

Computes the adjustment to the forward rate for a CMS coupon.

The adjustment to the forward rate, is the quantity that need to be added to the forward rate to obtain the adjusted forward rate. The adjusted forward rate is the number which used in the same formula used for Ibor coupon pricing (forward * notional * accrual factor * discount factor) will provide the correct present value.

For cap or floor the result is the adjustment to the forward rate for the coupon equivalent to the cap/floor, i.e. the coupon with the same dates and index but with no cap or floor strike.

Parameters:

cmsPeriod - the CMS period, which should be of the type CmsPeriodType.COUPON

provider - the rates provider

swaptionVolatilities - the swaption volatilities

Returns:

the adjusted forward rate

presentValueSensitivityRates

public PointSensitivityBuilder presentValueSensitivityRates(CmsPeriod cmsPeriod,
                                                            RatesProvider provider,
                                                            SabrSwaptionVolatilities swaptionVolatilities)

Computes the present value curve sensitivity by replication in SABR framework with extrapolation on the right.

Parameters:

cmsPeriod - the CMS

provider - the rates provider

swaptionVolatilities - the swaption volatilities

Returns:

the present value sensitivity

presentValueSensitivityModelParamsSabr

public PointSensitivityBuilder presentValueSensitivityModelParamsSabr(CmsPeriod cmsPeriod,
                                                                      RatesProvider provider,
                                                                      SabrSwaptionVolatilities swaptionVolatilities)

Computes the present value sensitivity to SABR parameters by replication in SABR framework with extrapolation on the right.

Parameters:

cmsPeriod - the CMS

provider - the rates provider

swaptionVolatilities - the swaption volatilities

Returns:

the present value sensitivity

presentValueSensitivityStrike

public double presentValueSensitivityStrike(CmsPeriod cmsPeriod,
                                            RatesProvider provider,
                                            SabrSwaptionVolatilities swaptionVolatilities)

Computes the present value sensitivity to strike by replication in SABR framework with extrapolation on the right.

Parameters:

cmsPeriod - the CMS

provider - the rates provider

swaptionVolatilities - the swaption volatilities

Returns:

the present value sensitivity

explainPresentValue

public void explainPresentValue(CmsPeriod period,
                                RatesProvider ratesProvider,
                                SabrSwaptionVolatilities swaptionVolatilities,
                                ExplainMapBuilder builder)

Explains the present value of the CMS period.

This returns explanatory information about the calculation.

Parameters:

period - the product

ratesProvider - the rates provider

swaptionVolatilities - the volatilities

builder - the builder to populate