localvolsurface.cpp

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2003 Ferdinando Ametrano
 
 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.
*/
 
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/volatility/equityfx/blackvoltermstructure.hpp>
#include <ql/termstructures/volatility/equityfx/localvolsurface.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
 
namespace QuantLib {
 
 
    const Date& LocalVolSurface::referenceDate() const {
        return blackTS_->referenceDate();
    }
 
    DayCounter LocalVolSurface::dayCounter() const {
        return blackTS_->dayCounter();
    }
 
    Date LocalVolSurface::maxDate() const {
        return blackTS_->maxDate();
    }
 
    Real LocalVolSurface::minStrike() const {
        return blackTS_->minStrike();
    }
 
    Real LocalVolSurface::maxStrike() const {
        return blackTS_->maxStrike();
    }
 
    LocalVolSurface::LocalVolSurface(const Handle<BlackVolTermStructure>& blackTS,
                                     Handle<YieldTermStructure> riskFreeTS,
                                     Handle<YieldTermStructure> dividendTS,
                                     Handle<Quote> underlying)
    : LocalVolTermStructure(blackTS->businessDayConvention(), blackTS->dayCounter()),
      blackTS_(blackTS), riskFreeTS_(std::move(riskFreeTS)), dividendTS_(std::move(dividendTS)),
      underlying_(std::move(underlying)) {
        registerWith(blackTS_);
        registerWith(riskFreeTS_);
        registerWith(dividendTS_);
        registerWith(underlying_);
    }
 
    LocalVolSurface::LocalVolSurface(const Handle<BlackVolTermStructure>& blackTS,
                                     Handle<YieldTermStructure> riskFreeTS,
                                     Handle<YieldTermStructure> dividendTS,
                                     Real underlying)
    : LocalVolTermStructure(blackTS->businessDayConvention(), blackTS->dayCounter()),
      blackTS_(blackTS), riskFreeTS_(std::move(riskFreeTS)), dividendTS_(std::move(dividendTS)),
      underlying_(ext::shared_ptr<Quote>(new SimpleQuote(underlying))) {
        registerWith(blackTS_);
        registerWith(riskFreeTS_);
        registerWith(dividendTS_);
    }
 
    void LocalVolSurface::accept(AcyclicVisitor& v) {
        auto* v1 = dynamic_cast<Visitor<LocalVolSurface>*>(&v);
        if (v1 != nullptr)
            v1->visit(*this);
        else
            LocalVolTermStructure::accept(v);
    }
 
    Volatility LocalVolSurface::localVolImpl(Time t, Real underlyingLevel)
                                                                     const {
 
        DiscountFactor dr = riskFreeTS_->discount(t, true);
        DiscountFactor dq = dividendTS_->discount(t, true);
        Real forwardValue = underlying_->value()*dq/dr;
        
        // strike derivatives
        Real strike, y, dy, strikep, strikem;
        Real w, wp, wm, dwdy, d2wdy2;
        strike = underlyingLevel;
        y = std::log(strike/forwardValue);
        dy = ((std::fabs(y) > 0.001) ? Real(y*0.0001) : 0.000001);
        strikep=strike*std::exp(dy);
        strikem=strike/std::exp(dy);
        w  = blackTS_->blackVariance(t, strike,  true);
        wp = blackTS_->blackVariance(t, strikep, true);
        wm = blackTS_->blackVariance(t, strikem, true);
        dwdy = (wp-wm)/(2.0*dy);
        d2wdy2 = (wp-2.0*w+wm)/(dy*dy);
 
        // time derivative
        Real dt, wpt, wmt, dwdt;
        if (t==0.0) {
            dt = 0.0001;
            DiscountFactor drpt = riskFreeTS_->discount(t+dt, true);
            DiscountFactor dqpt = dividendTS_->discount(t+dt, true);           
            Real strikept = strike*dr*dqpt/(drpt*dq);
        
            wpt = blackTS_->blackVariance(t+dt, strikept, true);
            QL_ENSURE(wpt>=w,
                      "decreasing variance at strike " << strike
                      << " between time " << t << " and time " << t+dt);
            dwdt = (wpt-w)/dt;
        } else {
            dt = std::min<Time>(0.0001, t/2.0);
            DiscountFactor drpt = riskFreeTS_->discount(t+dt, true);
            DiscountFactor drmt = riskFreeTS_->discount(t-dt, true);
            DiscountFactor dqpt = dividendTS_->discount(t+dt, true);
            DiscountFactor dqmt = dividendTS_->discount(t-dt, true);
            
            Real strikept = strike*dr*dqpt/(drpt*dq);
            Real strikemt = strike*dr*dqmt/(drmt*dq);
            
            wpt = blackTS_->blackVariance(t+dt, strikept, true);
            wmt = blackTS_->blackVariance(t-dt, strikemt, true);
 
            QL_ENSURE(wpt>=w,
                      "decreasing variance at strike " << strike
                      << " between time " << t << " and time " << t+dt);
            QL_ENSURE(w>=wmt,
                      "decreasing variance at strike " << strike
                      << " between time " << t-dt << " and time " << t);
         
            dwdt = (wpt-wmt)/(2.0*dt);
        }
 
        if (dwdy==0.0 && d2wdy2==0.0) { // avoid /w where w might be 0.0
            return std::sqrt(dwdt);
        } else {
            Real den1 = 1.0 - y/w*dwdy;
            Real den2 = 0.25*(-0.25 - 1.0/w + y*y/w/w)*dwdy*dwdy;
            Real den3 = 0.5*d2wdy2;
            Real den = den1+den2+den3;
            Real result = dwdt / den;
 
            QL_ENSURE(result>=0.0,
                      "negative local vol^2 at strike " << strike
                      << " and time " << t
                      << "; the black vol surface is not smooth enough");
 
            return std::sqrt(result);
        }
    }
 
}