lognormalcmsspreadpricer.hpp

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/*
 Copyright (C) 2018 Quaternion Risk Management Ltd
 All rights reserved.
 
 This file is part of ORE, a free-software/open-source library
 for transparent pricing and risk analysis - http://opensourcerisk.org
 
 ORE is free software: you can redistribute it and/or modify it
 under the terms of the Modified BSD License.  You should have received a
 copy of the license along with this program.
 The license is also available online at <http://opensourcerisk.org>
 
 This program is distributed on the basis that it will form a useful
 contribution to risk analytics and model standardisation, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 FITNESS FOR A PARTICULAR PURPOSE. See the license for more details.
*/
 
/*
  Copyright (C) 2014, 2015, 2018 Peter Caspers
 
  This file is part of QuantLib, a free-software/open-source library
  for financial quantitative analysts and developers - http://quantlib.org/
 
  QuantLib is free software: you can redistribute it and/or modify it
  under the terms of the QuantLib license.  You should have received a
  copy of the license along with this program; if not, please email
  <quantlib-dev@lists.sf.net>. The license is also available online at
  <http://quantlib.org/license.shtml>.
 
 
  This program is distributed in the hope that it will be useful, but
  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  or FITNESS FOR A PARTICULAR PURPOSE. See the license for more details. */
 
/*! \file lognormalcmsspreadpricer.hpp
    \brief cms spread coupon pricer as in Brigo, Mercurio, 13.6.2, with
           extensions for shifted lognormal and normal dynamics as
           described in http://ssrn.com/abstract=2686998
*/
 
#ifndef quantext_lognormal_cmsspread_pricer_hpp
#define quantext_lognormal_cmsspread_pricer_hpp
 
#include <ql/cashflows/cmscoupon.hpp>
#include <ql/experimental/coupons/cmsspreadcoupon.hpp>
#include <ql/experimental/coupons/swapspreadindex.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/math/integrals/gaussianquadratures.hpp>
 
#include <qle/quotes/exceptionquote.hpp>
#include <qle/termstructures/correlationtermstructure.hpp>
 
namespace QuantLib {
class CmsSpreadCoupon;
class YieldTermStructure;
} // namespace QuantLib
 
namespace QuantExt {
using namespace QuantLib;
 
//! base pricer for vanilla CMS spread coupons with a correlation surface
class CmsSpreadCouponPricer2 : public CmsSpreadCouponPricer {
public:
    explicit CmsSpreadCouponPricer2(
        const Handle<CorrelationTermStructure>& correlation = Handle<CorrelationTermStructure>())
        : CmsSpreadCouponPricer(Handle<Quote>(QuantLib::ext::make_shared<ExceptionQuote>(
              "CmsSpreadPricer2 doesn't support 'correlation()', instead use 'correlation(Time, Strike)'"))),
          correlationCurve_(correlation) {
        registerWith(correlationCurve_);
    }
 
    Real correlation(Time t, Real strike = 1) const { return correlationCurve_->correlation(t, strike); }
 
    void setCorrelationCurve(const Handle<CorrelationTermStructure>& correlation = Handle<CorrelationTermStructure>()) {
        unregisterWith(correlationCurve_);
        correlationCurve_ = correlation;
        registerWith(correlationCurve_);
        update();
    }
 
private:
    Handle<CorrelationTermStructure> correlationCurve_;
};
 
//! CMS spread - coupon pricer
/*! The swap rate adjustments are computed using the given
    volatility structures for the underlyings in every case
    (w.r.t. volatility type and shift).
 
    For the bivariate spread model, the volatility type and
    the shifts can be inherited (default), or explicitly
    specified. In the latter case the type, and (if lognormal)
    the shifts must be given (or are defaulted to zero, if not
    given).
 
    References:
 
    Brigo, Mercurio: Interest Rate Models - Theory and Practice,
    2nd Edition, Springer, 2006, chapter 13.6.2
 
    http://ssrn.com/abstract=2686998
*/
 
class LognormalCmsSpreadPricer : public CmsSpreadCouponPricer2 {
 
public:
    LognormalCmsSpreadPricer(const QuantLib::ext::shared_ptr<CmsCouponPricer> cmsPricer,
                             const Handle<QuantExt::CorrelationTermStructure>& correlation,
                             const Handle<YieldTermStructure>& couponDiscountCurve = Handle<YieldTermStructure>(),
                             const Size IntegrationPoints = 16,
                             const boost::optional<VolatilityType> volatilityType = boost::none,
                             const Real shift1 = Null<Real>(), const Real shift2 = Null<Real>());
 
    /* */
    virtual Real swapletPrice() const override;
    virtual Rate swapletRate() const override;
    virtual Real capletPrice(Rate effectiveCap) const override;
    virtual Rate capletRate(Rate effectiveCap) const override;
    virtual Real floorletPrice(Rate effectiveFloor) const override;
    virtual Rate floorletRate(Rate effectiveFloor) const override;
 
private:
    void initialize(const FloatingRateCoupon& coupon) override;
    Real rho() const { return std::max(std::min(correlation(fixingTime_), 0.9999), -0.9999); }
    Real optionletPrice(Option::Type optionType, Real strike) const;
 
    Real integrand(const Real) const;
    Real integrand_normal(const Real) const;
 
    class integrand_f;
    friend class integrand_f;
 
    QuantLib::ext::shared_ptr<CmsCouponPricer> cmsPricer_;
 
    Handle<YieldTermStructure> couponDiscountCurve_;
 
    const CmsSpreadCoupon* coupon_;
 
    Date today_, fixingDate_, paymentDate_;
 
    Real fixingTime_;
 
    Real gearing_, spread_;
    Real spreadLegValue_;
    Real discount_;
 
    QuantLib::ext::shared_ptr<SwapSpreadIndex> index_;
 
    QuantLib::ext::shared_ptr<CumulativeNormalDistribution> cnd_;
    QuantLib::ext::shared_ptr<GaussianQuadrature> integrator_;
 
    Real swapRate1_, swapRate2_, gearing1_, gearing2_;
    Real adjustedRate1_, adjustedRate2_;
    Real vol1_, vol2_;
    Real mu1_, mu2_;
 
    bool inheritedVolatilityType_;
    VolatilityType volType_;
    Real shift1_, shift2_;
 
    mutable Real phi_, a_, b_, s1_, s2_, m1_, m2_, v1_, v2_, k_;
    mutable Real alpha_, psi_;
    mutable Option::Type optionType_;
 
    QuantLib::ext::shared_ptr<CmsCoupon> c1_, c2_;
};
 
} // namespace QuantExt
 
#endif