text: /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
  
  /*
   Copyright (C) 2018 Klaus Spanderen
  
   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 fdcevvanillaengine.hpp
      \brief Finite-Differences pricing engine for the CEV model
  */
  
  #include <ql/exercise.hpp>
  #include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>
  #include <ql/methods/finitedifferences/meshers/fdmcev1dmesher.hpp>
  #include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
  #include <ql/methods/finitedifferences/operators/fdmcevop.hpp>
  #include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
  #include <ql/methods/finitedifferences/solvers/fdm1dimsolver.hpp>
  #include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
  #include <ql/methods/finitedifferences/utilities/fdmdiscountdirichletboundary.hpp>
  #include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
  #include <ql/methods/finitedifferences/utilities/fdmtimedepdirichletboundary.hpp>
  #include <ql/pricingengines/vanilla/analyticcevengine.hpp>
  #include <ql/pricingengines/vanilla/fdcevvanillaengine.hpp>
  #include <ql/termstructures/yieldtermstructure.hpp>
  #include <utility>
  
  namespace QuantLib {
  
      namespace {
          class PriceAtBoundary {
            public:
              PriceAtBoundary(Time maturityTime,
                              ext::shared_ptr<StrikedTypePayoff> payoff,
                              ext::shared_ptr<YieldTermStructure> rTS,
                              ext::shared_ptr<CEVCalculator> calculator)
              : maturityTime_(maturityTime), payoff_(std::move(payoff)),
                calculator_(std::move(calculator)), rTS_(std::move(rTS)) {}
  
              Real operator()(Real t) const {
                  const Time time2Expiry = std::max(1/365., maturityTime_ - t);
                  const DiscountFactor df =
                      rTS_->discount(maturityTime_) / rTS_->discount(t);
  
                  return  df * calculator_->value(
                      payoff_->optionType(), payoff_->strike(), time2Expiry);
              }
  
            private:
              const Time maturityTime_;
              const ext::shared_ptr<StrikedTypePayoff> payoff_;
              const ext::shared_ptr<CEVCalculator> calculator_;
              const ext::shared_ptr<YieldTermStructure> rTS_;
          };
      }
  
      FdCEVVanillaEngine::FdCEVVanillaEngine(Real f0,
                                             Real alpha,
                                             Real beta,
                                             Handle<YieldTermStructure> discountCurve,
                                             Size tGrid,
                                             Size xGrid,
                                             Size dampingSteps,
                                             Real scalingFactor,
                                             Real eps,
                                             const FdmSchemeDesc& schemeDesc)
      : f0_(f0), alpha_(alpha), beta_(beta), discountCurve_(std::move(discountCurve)), tGrid_(tGrid),
        xGrid_(xGrid), dampingSteps_(dampingSteps), scalingFactor_(scalingFactor), eps_(eps),
        schemeDesc_(schemeDesc) {
          registerWith(discountCurve_);
      }
  
      void FdCEVVanillaEngine::calculate() const {
  
          // 1. Mesher
          const ext::shared_ptr<StrikedTypePayoff> payoff =
              ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
          QL_REQUIRE(payoff, "non-striked payoff given");
  
          const ext::shared_ptr<YieldTermStructure> rTS =
              discountCurve_.currentLink();
  
          const DayCounter dc = rTS->dayCounter();
  
          const Date referenceDate = rTS->referenceDate();
          const Date maturityDate = arguments_.exercise->lastDate();
          const Time maturityTime = dc.yearFraction(referenceDate, maturityDate);
  
          const ext::shared_ptr<Fdm1dMesher> cevMesher =
              ext::make_shared<FdmCEV1dMesher>(
                  xGrid_,
                  f0_, alpha_, beta_,
                  maturityTime, eps_, scalingFactor_,
                  std::make_pair(payoff->strike(), 0.1));
  
          const Real lowerBound = cevMesher->locations().front();
          const Real upperBound = cevMesher->locations().back();
  
          const ext::shared_ptr<FdmMesher> mesher =
             ext::make_shared<FdmMesherComposite>(cevMesher);
  
          // 2. Calculator
          const ext::shared_ptr<FdmInnerValueCalculator> calculator =
              ext::make_shared<FdmCellAveragingInnerValue>(payoff, mesher, 0);
  
          // 3. Step conditions
          const ext::shared_ptr<FdmStepConditionComposite> conditions =
              FdmStepConditionComposite::vanillaComposite(
                  DividendSchedule(), arguments_.exercise,
                  mesher, calculator,
                  referenceDate, dc);
  
          // 4. Boundary conditions
          FdmBoundaryConditionSet boundaries;
  
          const PriceAtBoundary upperBoundPrice(
              maturityTime, payoff, rTS,
              ext::make_shared<CEVCalculator>(upperBound, alpha_, beta_));
  
          boundaries.push_back(ext::make_shared<FdmTimeDepDirichletBoundary>(
              mesher, ext::function<Real (Real)>(upperBoundPrice),
              0, FdmTimeDepDirichletBoundary::Upper));
  
          const Real delta = (1-2*beta_)/(1-beta_);
          if (delta < 2.0) {
              const Real terminalCashFlow = (*payoff)(lowerBound);
  
              boundaries.push_back(
                  ext::make_shared<FdmDiscountDirichletBoundary>(
                      mesher, rTS, maturityTime, terminalCashFlow,
                      0, FdmTimeDepDirichletBoundary::Lower));
          }
  
          // 5. Solver
          const FdmSolverDesc solverDesc = {
              mesher, boundaries, conditions,
              calculator, maturityTime, tGrid_, dampingSteps_
          };
  
          const ext::shared_ptr<FdmLinearOpComposite> op =
              ext::make_shared<FdmCEVOp>(
                 mesher, discountCurve_.currentLink(), f0_, alpha_, beta_, 0);
  
          const ext::shared_ptr<Fdm1DimSolver> solver =
              ext::make_shared<Fdm1DimSolver>(solverDesc, schemeDesc_, op);
  
          results_.value = solver->interpolateAt(f0_);
          results_.delta = solver->derivativeX(f0_);
          results_.gamma = solver->derivativeXX(f0_);
          results_.theta = solver->thetaAt(f0_);
      }
  }
  