Add BlackVolatilitySurfaceDelta class for FX options

QuantLib.vcxproj

@@ -1727,6 +1727,8 @@
     <ClInclude Include="ql\termstructures\volatility\equityfx\blackconstantvol.hpp" />
     <ClInclude Include="ql\termstructures\volatility\equityfx\blackvariancecurve.hpp" />
     <ClInclude Include="ql\termstructures\volatility\equityfx\blackvariancesurface.hpp" />
+    <ClInclude Include="ql\termstructures\volatility\equityfx\blackvariancetimeextrapolation.hpp" />
+    <ClInclude Include="ql\termstructures\volatility\equityfx\blackvolsurfacedelta.hpp" />
     <ClInclude Include="ql\termstructures\volatility\equityfx\blackvoltermstructure.hpp" />
     <ClInclude Include="ql\termstructures\volatility\equityfx\fixedlocalvolsurface.hpp" />
     <ClInclude Include="ql\termstructures\volatility\equityfx\gridmodellocalvolsurface.hpp" />
@@ -2753,6 +2755,7 @@
     <ClCompile Include="ql\termstructures\volatility\equityfx\andreasenhugevolatilityinterpl.cpp" />
     <ClCompile Include="ql\termstructures\volatility\equityfx\blackvariancecurve.cpp" />
     <ClCompile Include="ql\termstructures\volatility\equityfx\blackvariancesurface.cpp" />
+    <ClCompile Include="ql\termstructures\volatility\equityfx\blackvolsurfacedelta.cpp" />
     <ClCompile Include="ql\termstructures\volatility\equityfx\blackvoltermstructure.cpp" />
     <ClCompile Include="ql\termstructures\volatility\equityfx\fixedlocalvolsurface.cpp" />
     <ClCompile Include="ql\termstructures\volatility\equityfx\gridmodellocalvolsurface.cpp" />

QuantLib.vcxproj.filters

@@ -2049,6 +2049,12 @@
     <ClInclude Include="ql\termstructures\volatility\equityfx\blackvariancesurface.hpp">
       <Filter>termstructures\volatility\equityfx</Filter>
     </ClInclude>
+    <ClInclude Include="ql\termstructures\volatility\equityfx\blackvariancetimeextrapolation.hpp">
+      <Filter>termstructures\volatility\equityfx</Filter>
+    </ClInclude>
+    <ClInclude Include="ql\termstructures\volatility\equityfx\blackvolsurfacedelta.hpp">
+      <Filter>termstructures\volatility\equityfx</Filter>
+    </ClInclude>
     <ClInclude Include="ql\termstructures\volatility\equityfx\blackvoltermstructure.hpp">
       <Filter>termstructures\volatility\equityfx</Filter>
     </ClInclude>
@@ -5600,6 +5606,9 @@
     <ClCompile Include="ql\termstructures\volatility\equityfx\blackvariancesurface.cpp">
       <Filter>termstructures\volatility\equityfx</Filter>
     </ClCompile>
+    <ClCompile Include="ql\termstructures\volatility\equityfx\blackvolsurfacedelta.cpp">
+      <Filter>termstructures\volatility\equityfx</Filter>
+    </ClCompile>
     <ClCompile Include="ql\termstructures\volatility\equityfx\blackvoltermstructure.cpp">
       <Filter>termstructures\volatility\equityfx</Filter>
     </ClCompile>

ql/CMakeLists.txt

@@ -835,6 +835,7 @@ set(QL_SOURCES
     termstructures/volatility/equityfx/andreasenhugevolatilityinterpl.cpp
     termstructures/volatility/equityfx/blackvariancecurve.cpp
     termstructures/volatility/equityfx/blackvariancesurface.cpp
+    termstructures/volatility/equityfx/blackvolsurfacedelta.cpp
     termstructures/volatility/equityfx/blackvoltermstructure.cpp
     termstructures/volatility/equityfx/fixedlocalvolsurface.cpp
     termstructures/volatility/equityfx/gridmodellocalvolsurface.cpp
@@ -2103,6 +2104,8 @@ set(QL_HEADERS
     termstructures/volatility/equityfx/blackconstantvol.hpp
     termstructures/volatility/equityfx/blackvariancecurve.hpp
     termstructures/volatility/equityfx/blackvariancesurface.hpp
+    termstructures/volatility/equityfx/blackvariancetimeextrapolation.hpp
+    termstructures/volatility/equityfx/blackvolsurfacedelta.hpp
     termstructures/volatility/equityfx/blackvoltermstructure.hpp
     termstructures/volatility/equityfx/fixedlocalvolsurface.hpp
     termstructures/volatility/equityfx/gridmodellocalvolsurface.hpp

ql/termstructures/volatility/equityfx/Makefile.am

@@ -10,6 +10,8 @@ this_include_HEADERS = \
     blackconstantvol.hpp \
     blackvariancecurve.hpp \
     blackvariancesurface.hpp \
+    blackvariancetimeextrapolation.hpp \
+    blackvolsurfacedelta.hpp \
     blackvoltermstructure.hpp \
     fixedlocalvolsurface.hpp \
     gridmodellocalvolsurface.hpp \
@@ -27,6 +29,7 @@ cpp_files = \
     andreasenhugevolatilityadapter.cpp \
     blackvariancecurve.cpp \
     blackvariancesurface.cpp \
+    blackvolsurfacedelta.cpp \
     blackvoltermstructure.cpp \
     fixedlocalvolsurface.cpp \
     gridmodellocalvolsurface.cpp \

ql/termstructures/volatility/equityfx/blackvariancecurve.cpp

@@ -20,6 +20,7 @@
 
 #include <ql/math/interpolations/linearinterpolation.hpp>
 #include <ql/termstructures/volatility/equityfx/blackvariancecurve.hpp>
+#include <ql/termstructures/volatility/equityfx/blackvariancetimeextrapolation.hpp>
 #include <utility>
 
 namespace QuantLib {
@@ -28,9 +29,10 @@ namespace QuantLib {
                                            const std::vector<Date>& dates,
                                            const std::vector<Volatility>& blackVolCurve,
                                            DayCounter dayCounter,
-                                           bool forceMonotoneVariance)
+                                           bool forceMonotoneVariance,
+                                           BlackVolTimeExtrapolation timeExtrapolation)
     : BlackVarianceTermStructure(referenceDate), dayCounter_(std::move(dayCounter)),
-      maxDate_(dates.back()) {
+      maxDate_(dates.back()), timeExtrapolation_(timeExtrapolation) {
 
         QL_REQUIRE(dates.size()==blackVolCurve.size(),
                    "mismatch between date vector and black vol vector");
@@ -62,11 +64,15 @@ namespace QuantLib {
     }
 
     Real BlackVarianceCurve::blackVarianceImpl(Time t, Real) const {
-        if (t<=times_.back()) {
-            return varianceCurve_(t, true);
-        } else {
+        if (t <= times_.back() || timeExtrapolation_ == BlackVolTimeExtrapolation::UseInterpolatorVariance) {
+            return std::max(varianceCurve_(t, true), 0.0);
+        } else if (timeExtrapolation_ == BlackVolTimeExtrapolation::FlatVolatility) {
             // extrapolate with flat vol
-            return varianceCurve_(times_.back(), true)*t/times_.back();
+            return timeExtrapolatationBlackVarianceFlat(t, times_, varianceCurve_);
+        } else if (timeExtrapolation_ == BlackVolTimeExtrapolation::UseInterpolatorVolatility) {
+            return timeExtrapolatationBlackVarianceInVolatility(t, times_, varianceCurve_);
+        } else {
+            QL_FAIL("Unknown time extrapolation method");
         }
     }
 

ql/termstructures/volatility/equityfx/blackvariancecurve.hpp

@@ -50,7 +50,8 @@ namespace QuantLib {
                            const std::vector<Date>& dates,
                            const std::vector<Volatility>& blackVolCurve,
                            DayCounter dayCounter,
-                           bool forceMonotoneVariance = true);
+                           bool forceMonotoneVariance = true,
+                           BlackVolTimeExtrapolation timeExtrapolation = BlackVolTimeExtrapolation::FlatVolatility);
         //! \name TermStructure interface
         //@{
         DayCounter dayCounter() const override { return dayCounter_; }
@@ -84,6 +85,7 @@ namespace QuantLib {
         std::vector<Time> times_;
         std::vector<Real> variances_;
         Interpolation varianceCurve_;
+        BlackVolTimeExtrapolation timeExtrapolation_;
     };
 
 

ql/termstructures/volatility/equityfx/blackvariancetimeextrapolation.hpp

@@ -0,0 +1,102 @@
+/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+
+/*
+ Copyright (C) 2025 AcadiaSoft Inc.
+
+ 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 blackvariancetimeextrapolation.hpp
+    \brief Utility function for time extrapolation in Black volatility in black variance term structures
+*/
+#pragma once
+
+#include <array>
+#include <functional>
+#include <ql/math/comparison.hpp>
+#include <ql/math/interpolation.hpp>
+#include <ql/math/interpolations/interpolation2d.hpp>
+#include <ql/math/interpolations/linearinterpolation.hpp>
+
+namespace QuantLib {
+
+    namespace {
+        Real linearExtrapolation(const double t, const std::array<double, 2>& times, const std::array<double, 2>& variances);
+
+        inline Real linearExtrapolation(const double t, const std::array<double, 2>& times,
+                                        const std::array<double, 2>& variances) {
+            QL_REQUIRE(t > times[1], "t must be greater than times[1]");
+            QL_REQUIRE(times[1] > times[0], "times must be sorted");
+            QL_REQUIRE(variances[1] >= variances[0], "variances must be non-decreasing");
+            std::array<double, 2> vols;
+            vols[0] = close_enough(times[0], 0.0) ? 0.0 : std::sqrt(variances[0] / times[0]);
+            vols[1] = close_enough(times[1], 0.0) ? 0.0 : std::sqrt(variances[1] / times[1]);
+            LinearInterpolation interpolation(times.begin(), times.end(), vols.begin());
+            return std::max(interpolation(t, true), 0.0);
+        }
+    } // namespace
+
+
+
+    //! Extrapolate black variance using flat vol extrapolation in time direction
+    Real timeExtrapolatationBlackVarianceFlat(const Time t, const std::vector<double>& times,
+        const Interpolation& varianceCurve);
+
+    //! Extrapolate black variance using flat vol extrapolation in time direction
+    template <typename F>
+    Real timeExtrapolatationBlackVarianceFlat(const Time t, const Real strike, const std::vector<double>& times,
+                                            const F& varianceSurface) {
+        return std::max(varianceSurface(times.back(), strike, true), 0.0) / times.back() * t;
+    }
+
+
+    //! Extrapolate black variance in vol space and time direction using interpolation
+    //! Takes black variances convert them to volatilities and then linearly extrapolates
+    //! the volatilities in time direction
+    Real timeExtrapolatationBlackVarianceInVolatility(const Time t, const std::vector<double>& times,
+        const Interpolation& varianceCurve);
+
+    //! Extrapolate black variance in vol space and time direction using interpolation
+    //! Takes black variances convert them to volatilities and then linearly extrapolates
+    //! the volatilities in time direction
+    template <typename F>
+    Real timeExtrapolatationBlackVarianceInVolatility(const Time t, const Real strike, const std::vector<double>& times,
+                                                    const F& varianceSurface) {
+        Size ind1 = times.size() - 2;
+        Size ind2 = times.size() - 1;
+        std::array<Real, 2> xs{times[ind1], times[ind2]};
+        std::array<Real, 2> variances;
+        variances[0] = varianceSurface(xs[0], strike, true);
+        variances[1] = varianceSurface(xs[1], strike, true);
+        Real v = linearExtrapolation(t, xs, variances);
+        return v * v * t;
+    }
+
+    inline Real timeExtrapolatationBlackVarianceFlat(const Time t, const std::vector<double>& times,
+                                                    const Interpolation& varianceCurve) {
+        return std::max(varianceCurve(times.back(), true), 0.0) / times.back() * t;
+    }
+
+    inline Real timeExtrapolatationBlackVarianceInVolatility(const Time t, const std::vector<double>& times,
+                                                            const Interpolation& varianceCurve) {
+        Size ind1 = times.size() - 2;
+        Size ind2 = times.size() - 1;
+        std::array<Real, 2> xs{times[ind1], times[ind2]};
+        std::array<Real, 2> variances;
+        variances[0] = varianceCurve(xs[0], true);
+        variances[1] = varianceCurve(xs[1], true);
+        Real v = linearExtrapolation(t, xs, variances);
+        return v * v * t;
+    }
+} // namespace QuantLib