Class LognormalCmsSpreadPricer
- Namespace
- NanoQL.Experimental
- Assembly
- NanoQL.dll
The CMS spread coupon pricer of Brigo and Mercurio, 13.6.2, with the extensions for shifted lognormal and normal
dynamics of http://ssrn.com/abstract=2686998: QuantLib's LognormalCmsSpreadPricer.
[Experimental("NQL0001")]
public sealed class LognormalCmsSpreadPricer : CmsSpreadCouponPricer- Inheritance
-
LognormalCmsSpreadPricer
- Inherited Members
Remarks
The two swap rates' convexity adjustments are the CMS pricer's, on its swaption volatility, whose type and shifts the spread model inherits by default; or the type is given, and on a lognormal model the shifts, 0 when not given. An at-the-money surface takes only the inherited type; a cube is read on the model's type and shifts through its smile sections. The correlation is clamped to ±0.9999, so that the integrand never divides by 0; at the default 16 Gauss-Hermite points its value at 0.9999 is 1.5e-3 off the 256-point value, the points the caller's choice. References: Brigo and Mercurio, Interest Rate Models - Theory and Practice, 2nd edition, Springer, 2006, chapter 13.6.2.
With unequal shifts, the integrand branches on the displaced strike k + g₁s₁ + g₂s₂, and its negative branch shifts
the second rate by its own shift, as QuantLib's master does after 1.44 (#2874); QuantLib 1.44 branches on the strike
and shifts the second rate by the first's, which prices NaN caplets and floorlets at strikes 0.008 and 0.002 on
#2874's set-up and breaks put-call parity by 2.03e-2 at others (Divergences/CmsSpreadUnequalShiftsTests.cs).
Equal shifts take the same branch either way.
Without a coupon discount curve, each coupon is discounted on its own first swap index's curve, its discounting
curve when exogenous and its forwarding curve otherwise; QuantLib's pricer keeps the first coupon's curve for every
later coupon, so one pricer serving coupons on different indexes discounts them all on the first's
(Divergences/CmsSpreadCouponDiscountCurveTests.cs). A pricer is stateless here, as every nanoql pricer: what
QuantLib's initialize stores is computed per call, one state serving a capped coupon's three rates.
Constructors
LognormalCmsSpreadPricer(CmsCouponPricer, double?, YieldTermStructure?, int, VolatilityType?, double?, double?)
Initializes a new instance of the LognormalCmsSpreadPricer class.
public LognormalCmsSpreadPricer(CmsCouponPricer cmsPricer, double? correlation, YieldTermStructure? couponDiscountCurve = null, int integrationPoints = 16, VolatilityType? volatilityType = null, double? shift1 = null, double? shift2 = null)Parameters
cmsPricerCmsCouponPricerThe pricer of the two CMS coupons, whose swaption volatility the model reads.
correlationdouble?The correlation of the two swap rates, or null, QuantLib's empty handle, refused when a future fixing is priced.
couponDiscountCurveYieldTermStructureThe curve the coupons are discounted on, or null for each coupon's first swap index's.
integrationPointsintThe number of Gauss-Hermite points, at least 4.
volatilityTypeVolatilityType?The spread model's volatility type, or null to inherit the swaption volatility's.
shift1double?The first rate's shift on a given lognormal type, 0 when null.
shift2double?The second rate's shift on a given lognormal type, 0 when null.
Exceptions
- ArgumentNullException
cmsPriceris null.- NanoQLException
There are fewer than 4 points, shifts are given with an inherited type, or the type is inherited from a CMS pricer with no swaption volatility, with QuantLib's texts.
Methods
CapletPrice(FloatingRateCoupon, double, EvaluationContext)
The price of a caplet on the coupon's rate.
public override double CapletPrice(FloatingRateCoupon coupon, double effectiveCap, EvaluationContext context)Parameters
couponFloatingRateCouponThe coupon.
effectiveCapdoubleThe cap on the index fixing.
contextEvaluationContextThe evaluation context.
Returns
- double
The price.
Exceptions
- ArgumentException
The coupon isn't a CMS spread coupon.
- NanoQLException
CapletRate(FloatingRateCoupon, double, EvaluationContext)
The rate of a caplet on the coupon's rate.
public override double CapletRate(FloatingRateCoupon coupon, double effectiveCap, EvaluationContext context)Parameters
couponFloatingRateCouponThe coupon.
effectiveCapdoubleThe cap on the index fixing.
contextEvaluationContextThe evaluation context.
Returns
- double
The rate.
Exceptions
- ArgumentException
The coupon isn't a CMS spread coupon.
- NanoQLException
FloorletPrice(FloatingRateCoupon, double, EvaluationContext)
The price of a floorlet on the coupon's rate.
public override double FloorletPrice(FloatingRateCoupon coupon, double effectiveFloor, EvaluationContext context)Parameters
couponFloatingRateCouponThe coupon.
effectiveFloordoubleThe floor on the index fixing.
contextEvaluationContextThe evaluation context.
Returns
- double
The price.
Exceptions
- ArgumentException
The coupon isn't a CMS spread coupon.
- NanoQLException
FloorletRate(FloatingRateCoupon, double, EvaluationContext)
The rate of a floorlet on the coupon's rate.
public override double FloorletRate(FloatingRateCoupon coupon, double effectiveFloor, EvaluationContext context)Parameters
couponFloatingRateCouponThe coupon.
effectiveFloordoubleThe floor on the index fixing.
contextEvaluationContextThe evaluation context.
Returns
- double
The rate.
Exceptions
- ArgumentException
The coupon isn't a CMS spread coupon.
- NanoQLException
SwapletPrice(FloatingRateCoupon, EvaluationContext)
The swaplet's price: the coupon's amount, discounted.
public override double SwapletPrice(FloatingRateCoupon coupon, EvaluationContext context)Parameters
couponFloatingRateCouponThe coupon.
contextEvaluationContextThe evaluation context.
Returns
- double
The price.
Exceptions
- ArgumentException
The coupon isn't a CMS spread coupon.
- NanoQLException
The gearings aren't of opposite signs, a curve, the volatility or the correlation is missing, or the volatility type isn't inherited on an at-the-money surface.
SwapletRate(FloatingRateCoupon, EvaluationContext)
The swaplet's rate: the coupon's rate.
public override double SwapletRate(FloatingRateCoupon coupon, EvaluationContext context)Parameters
couponFloatingRateCouponThe coupon.
contextEvaluationContextThe evaluation context.
Returns
- double
The rate.
Exceptions
- ArgumentException
The coupon isn't a CMS spread coupon.
- NanoQLException