Cash flow dependent on an index ratio. This cash flow is not a coupon, i.e., there's no accrual. The amount is either i(T)/i(0) or i(T)/i(0) - 1, depending on the growthOnly parameter. We expect this to be used inside an instrument that does all the date adjustment etc., so this takes just dates and does not change them. growthOnly = false means i(T)/i(0), which is a bond-type setting. growthOnly = true means i(T)/i(0) - 1, which is a swap-type setting.
Inheritance: CashFlow
        public double fairRate()
        {
            // What does this mean before or after trade date?
            // Always means that NPV is zero for _this_ instrument
            // if it was created with _this_ rate
            // _knowing_ the time from base to obs (etc).

            IndexedCashFlow icf = legs_[1][0] as IndexedCashFlow;

            if (icf == null)
            {
                throw new ApplicationException("failed to downcast to IndexedCashFlow in ::fairRate()");
            }

            // +1 because the IndexedCashFlow has growthOnly=true
            double growth = icf.amount() / icf.notional() + 1.0;
            double T      = Utils.inflationYearFraction(infIndex_.frequency(),
                                                        infIndex_.interpolated(),
                                                        dayCounter_, baseDate_, obsDate_);

            return(Math.Pow(growth, 1.0 / T) - 1.0);

            // we cannot use this simple definition because
            // it does not work for already-issued instruments
            // return infIndex_->zeroInflationTermStructure()->zeroRate(
            //      maturityDate(), observationLag(), infIndex_->interpolated());
        }
Exemple #2
0
        public double fairRate()
        {
            // What does this mean before or after trade date?
            // Always means that NPV is zero for _this_ instrument
            // if it was created with _this_ rate
            // _knowing_ the time from base to obs (etc).

            IndexedCashFlow icf = legs_[1][0] as IndexedCashFlow;

            Utils.QL_REQUIRE(icf != null, () => "failed to downcast to IndexedCashFlow in ::fairRate()");

            // +1 because the IndexedCashFlow has growthOnly=true
            double growth = icf.amount() / icf.notional() + 1.0;
            double T      = Utils.inflationYearFraction(infIndex_.frequency(),
                                                        infIndex_.interpolated(),
                                                        dayCounter_, baseDate_, obsDate_);

            return(Math.Pow(growth, 1.0 / T) - 1.0);
        }
Exemple #3
0
        public void testZeroTermStructure()
        {
            // Testing zero inflation term structure...

            SavedSettings backup = new SavedSettings();

            // try the Zero UK
            Calendar calendar = new UnitedKingdom();
            BusinessDayConvention bdc = BusinessDayConvention.ModifiedFollowing;
            Date evaluationDate = new Date( 13, Month.August, 2007 );
            evaluationDate = calendar.adjust( evaluationDate );
            Settings.setEvaluationDate( evaluationDate );

            // fixing data
            Date from = new Date( 1, Month.January, 2005 );
            Date to = new Date( 13, Month.August, 2007 );
            Schedule rpiSchedule = new MakeSchedule().from( from ).to( to )
                                          .withTenor( new Period( 1, TimeUnit.Months ) )
                                          .withCalendar( new UnitedKingdom() )
                                          .withConvention( BusinessDayConvention.ModifiedFollowing )
                                          .value();

            double[] fixData = { 189.9, 189.9, 189.6, 190.5, 191.6, 192.0,
                              192.2, 192.2, 192.6, 193.1, 193.3, 193.6,
                              194.1, 193.4, 194.2, 195.0, 196.5, 197.7,
                              198.5, 198.5, 199.2, 200.1, 200.4, 201.1,
                              202.7, 201.6, 203.1, 204.4, 205.4, 206.2,
                              207.3, 206.1,  -999.0 };

            RelinkableHandle<ZeroInflationTermStructure> hz = new RelinkableHandle<ZeroInflationTermStructure>();
            bool interp = false;
            UKRPI iiUKRPI = new UKRPI( interp, hz );
            for ( int i = 0; i < rpiSchedule.Count; i++ )
            {
                iiUKRPI.addFixing( rpiSchedule[i], fixData[i] );
            }

            ZeroInflationIndex ii = iiUKRPI as ZeroInflationIndex;
            YieldTermStructure nominalTS = nominalTermStructure();

            // now build the zero inflation curve

            Datum[] zcData = {
               new Datum( new Date(13, Month.August, 2008), 2.93 ),
               new Datum( new Date(13, Month.August, 2009), 2.95 ),
               new Datum( new Date(13, Month.August, 2010), 2.965 ),
               new Datum( new Date(15, Month.August, 2011), 2.98 ),
               new Datum( new Date(13, Month.August, 2012), 3.0 ),
               new Datum( new Date(13, Month.August, 2014), 3.06 ),
               new Datum( new Date(13, Month.August, 2017), 3.175 ),
               new Datum( new Date(13, Month.August, 2019), 3.243 ),
               new Datum( new Date(15, Month.August, 2022), 3.293 ),
               new Datum( new Date(14, Month.August, 2027), 3.338 ),
               new Datum( new Date(13, Month.August, 2032), 3.348 ),
               new Datum( new Date(15, Month.August, 2037), 3.348 ),
               new Datum( new Date(13, Month.August, 2047), 3.308 ),
               new Datum( new Date(13, Month.August, 2057), 3.228 )};

            Period observationLag = new Period( 2, TimeUnit.Months );
            DayCounter dc = new Thirty360();
            Frequency frequency = Frequency.Monthly;
            List<BootstrapHelper<ZeroInflationTermStructure>> helpers =
                makeHelpers( zcData, zcData.Length, ii,
                                                observationLag,
                                                calendar, bdc, dc );

            double baseZeroRate = zcData[0].rate / 100.0;
            PiecewiseZeroInflationCurve<Linear> pZITS = new PiecewiseZeroInflationCurve<Linear>(
                                evaluationDate, calendar, dc, observationLag,
                                frequency, ii.interpolated(), baseZeroRate,
                                new Handle<YieldTermStructure>( nominalTS ), helpers );
            pZITS.recalculate();

            // first check that the zero rates on the curve match the data
            // and that the helpers give the correct impled rates
            const double eps = 0.00000001;
            bool forceLinearInterpolation = false;
            for ( int i = 0; i < zcData.Length; i++ )
            {
                Assert.IsTrue( Math.Abs( zcData[i].rate / 100.0
                - pZITS.zeroRate( zcData[i].date, observationLag, forceLinearInterpolation ) ) < eps,
                "ZITS zeroRate != instrument "
                + pZITS.zeroRate( zcData[i].date, observationLag, forceLinearInterpolation )
                + " vs " + zcData[i].rate / 100.0
                + " interpolation: " + ii.interpolated()
                + " forceLinearInterpolation " + forceLinearInterpolation );

                Assert.IsTrue( Math.Abs( helpers[i].impliedQuote()
                - zcData[i].rate / 100.0 ) < eps,
                "ZITS implied quote != instrument "
                + helpers[i].impliedQuote()
                + " vs " + zcData[i].rate / 100.0 );
            }

            // now test the forecasting capability of the index.
            hz.linkTo( pZITS );
            from = hz.link.baseDate();
            to = hz.link.maxDate() - new Period( 1, TimeUnit.Months ); // a bit of margin for adjustments
            Schedule testIndex = new MakeSchedule().from( from ).to( to )
                                            .withTenor( new Period( 1, TimeUnit.Months ) )
                                            .withCalendar( new UnitedKingdom() )
                                            .withConvention( BusinessDayConvention.ModifiedFollowing ).value();

            // we are testing UKRPI which is not interpolated
            Date bd = hz.link.baseDate();
            double bf = ii.fixing( bd );
            for ( int i = 0; i < testIndex.Count; i++ )
            {
                Date d = testIndex[i];
                double z = hz.link.zeroRate( d, new Period( 0, TimeUnit.Days ) );
                double t = hz.link.dayCounter().yearFraction( bd, d );
                if ( !ii.interpolated() ) // because fixing constant over period
                    t = hz.link.dayCounter().yearFraction( bd,
                     Utils.inflationPeriod( d, ii.frequency() ).Key );
                double calc = bf * Math.Pow( 1 + z, t );
                if ( t <= 0 )
                    calc = ii.fixing( d, false ); // still historical
                if ( Math.Abs( calc - ii.fixing( d, true ) ) / 10000.0 > eps )
                    Assert.Fail( "ZC index does not forecast correctly for date " + d
                                + " from base date " + bd
                                + " with fixing " + bf
                                + ", correct:  " + calc
                                + ", fix: " + ii.fixing( d, true )
                                + ", t " + t );
            }

            //===========================================================================================
            // Test zero-inflation-indexed (i.e. cpi ratio) cashflow
            // just ordinary indexed cashflow with a zero inflation index

            Date baseDate = new Date( 1, Month.January, 2006 );
            Date fixDate = new Date( 1, Month.August, 2014 );
            Date payDate = new UnitedKingdom().adjust( fixDate + new Period( 3, TimeUnit.Months ), BusinessDayConvention.ModifiedFollowing );
            Index ind = ii as Index;
             Utils.QL_REQUIRE( ind != null, () => "dynamic_pointer_cast to Index from InflationIndex failed" );

            double notional = 1000000.0;//1m
            IndexedCashFlow iicf = new IndexedCashFlow( notional, ind, baseDate, fixDate, payDate );
            double correctIndexed = ii.fixing( iicf.fixingDate() ) / ii.fixing( iicf.baseDate() );
            double calculatedIndexed = iicf.amount() / iicf.notional();
            Assert.IsTrue( Math.Abs( correctIndexed - calculatedIndexed ) < eps,
                                  "IndexedCashFlow indexing wrong: " + calculatedIndexed + " vs correct = "
                                  + correctIndexed );

            //===========================================================================================
            // Test zero coupon swap

            // first make one ...

            ZeroInflationIndex zii = ii as ZeroInflationIndex;
             Utils.QL_REQUIRE( zii != null, () => "dynamic_pointer_cast to ZeroInflationIndex from UKRPI failed" );
            ZeroCouponInflationSwap nzcis =
                new ZeroCouponInflationSwap( ZeroCouponInflationSwap.Type.Payer,
                                                     1000000.0,
                                                     evaluationDate,
                                                     zcData[6].date,    // end date = maturity
                                                     calendar, bdc, dc, zcData[6].rate / 100.0, // fixed rate
                                                     zii, observationLag );

            // N.B. no coupon pricer because it is not a coupon, effect of inflation curve via
            //      inflation curve attached to the inflation index.
            Handle<YieldTermStructure> hTS = new Handle<YieldTermStructure>( nominalTS );
            IPricingEngine sppe = new DiscountingSwapEngine( hTS );
            nzcis.setPricingEngine( sppe );

            // ... and price it, should be zero
            Assert.IsTrue( Math.Abs( nzcis.NPV() ) < 0.00001, "ZCIS does not reprice to zero "
                              + nzcis.NPV()
                              + evaluationDate + " to " + zcData[6].date + " becoming " + nzcis.maturityDate()
                              + " rate " + zcData[6].rate
                              + " fixed leg " + nzcis.legNPV( 0 )
                              + " indexed-predicted inflated leg " + nzcis.legNPV( 1 )
                              + " discount " + nominalTS.discount( nzcis.maturityDate() ) );

            //===========================================================================================
            // Test multiplicative seasonality in price
            //

            //Seasonality factors NOT normalized
            //and UKRPI is not interpolated
            Date trueBaseDate = Utils.inflationPeriod( hz.link.baseDate(), ii.frequency() ).Value;
            Date seasonallityBaseDate = new Date( 31, Month.January, trueBaseDate.year() );
            List<double> seasonalityFactors = new List<double>( 12 );
            seasonalityFactors.Add( 1.003245 );
            seasonalityFactors.Add( 1.000000 );
            seasonalityFactors.Add( 0.999715 );
            seasonalityFactors.Add( 1.000495 );
            seasonalityFactors.Add( 1.000929 );
            seasonalityFactors.Add( 0.998687 );
            seasonalityFactors.Add( 0.995949 );
            seasonalityFactors.Add( 0.994682 );
            seasonalityFactors.Add( 0.995949 );
            seasonalityFactors.Add( 1.000519 );
            seasonalityFactors.Add( 1.003705 );
            seasonalityFactors.Add( 1.004186 );

            //Creating two different seasonality objects
            //
            MultiplicativePriceSeasonality seasonality_1 = new MultiplicativePriceSeasonality();
            InitializedList<double> seasonalityFactors_1 = new InitializedList<double>( 12, 1.0 );
            seasonality_1.set( seasonallityBaseDate, Frequency.Monthly, seasonalityFactors_1 );

            MultiplicativePriceSeasonality seasonality_real =
                new MultiplicativePriceSeasonality( seasonallityBaseDate, Frequency.Monthly, seasonalityFactors );
            //Testing seasonality correction when seasonality factors are = 1
            //
            double[] fixing = {
            ii.fixing(new Date(14,Month.January  ,2013),true),
            ii.fixing(new Date(14,Month.February ,2013),true),
            ii.fixing(new Date(14,Month.March    ,2013),true),
            ii.fixing(new Date(14,Month.April    ,2013),true),
            ii.fixing(new Date(14,Month.May      ,2013),true),
            ii.fixing(new Date(14,Month.June     ,2013),true),
            ii.fixing(new Date(14,Month.July     ,2013),true),
            ii.fixing(new Date(14,Month.August   ,2013),true),
            ii.fixing(new Date(14,Month.September,2013),true),
            ii.fixing(new Date(14,Month.October  ,2013),true),
            ii.fixing(new Date(14,Month.November ,2013),true),
            ii.fixing(new Date(14,Month.December ,2013),true)
             };

            hz.link.setSeasonality( seasonality_1 );
             Utils.QL_REQUIRE( hz.link.hasSeasonality(), () => "[44] incorrectly believes NO seasonality correction" );

            double[] seasonalityFixing_1 = {
            ii.fixing(new Date(14,Month.January  ,2013),true),
            ii.fixing(new Date(14,Month.February ,2013),true),
            ii.fixing(new Date(14,Month.March    ,2013),true),
            ii.fixing(new Date(14,Month.April    ,2013),true),
            ii.fixing(new Date(14,Month.May      ,2013),true),
            ii.fixing(new Date(14,Month.June     ,2013),true),
            ii.fixing(new Date(14,Month.July     ,2013),true),
            ii.fixing(new Date(14,Month.August   ,2013),true),
            ii.fixing(new Date(14,Month.September,2013),true),
            ii.fixing(new Date(14,Month.October  ,2013),true),
            ii.fixing(new Date(14,Month.November ,2013),true),
            ii.fixing(new Date(14,Month.December ,2013),true)
             };

            for ( int i = 0; i < 12; i++ )
            {
                if ( Math.Abs( fixing[i] - seasonalityFixing_1[i] ) > eps )
                {
                    Assert.Fail( "Seasonality doesn't work correctly when seasonality factors are set = 1" );
                }
            }

            //Testing seasonality correction when seasonality factors are different from 1
            //
            //0.998687 is the seasonality factor corresponding to June (the base CPI curve month)
            //
            double[] expectedFixing = {
            ii.fixing(new Date(14,Month.January  ,2013),true) * 1.003245/0.998687,
            ii.fixing(new Date(14,Month.February ,2013),true) * 1.000000/0.998687,
            ii.fixing(new Date(14,Month.March    ,2013),true) * 0.999715/0.998687,
            ii.fixing(new Date(14,Month.April    ,2013),true) * 1.000495/0.998687,
            ii.fixing(new Date(14,Month.May      ,2013),true) * 1.000929/0.998687,
            ii.fixing(new Date(14,Month.June     ,2013),true) * 0.998687/0.998687,
            ii.fixing(new Date(14,Month.July     ,2013),true) * 0.995949/0.998687,
            ii.fixing(new Date(14,Month.August   ,2013),true) * 0.994682/0.998687,
            ii.fixing(new Date(14,Month.September,2013),true) * 0.995949/0.998687,
            ii.fixing(new Date(14,Month.October  ,2013),true) * 1.000519/0.998687,
            ii.fixing(new Date(14,Month.November ,2013),true) * 1.003705/0.998687,
            ii.fixing(new Date(14,Month.December ,2013),true) * 1.004186/0.998687
             };

            hz.link.setSeasonality( seasonality_real );

            double[] seasonalityFixing_real = {
            ii.fixing(new Date(14,Month.January  ,2013),true),
            ii.fixing(new Date(14,Month.February ,2013),true),
            ii.fixing(new Date(14,Month.March    ,2013),true),
            ii.fixing(new Date(14,Month.April    ,2013),true),
            ii.fixing(new Date(14,Month.May      ,2013),true),
            ii.fixing(new Date(14,Month.June     ,2013),true),
            ii.fixing(new Date(14,Month.July     ,2013),true),
            ii.fixing(new Date(14,Month.August   ,2013),true),
            ii.fixing(new Date(14,Month.September,2013),true),
            ii.fixing(new Date(14,Month.October  ,2013),true),
            ii.fixing(new Date(14,Month.November ,2013),true),
            ii.fixing(new Date(14,Month.December ,2013),true)
             };

            for ( int i = 0; i < 12; i++ )
            {
                if ( Math.Abs( expectedFixing[i] - seasonalityFixing_real[i] ) > 0.01 )
                {
                    Assert.Fail( "Seasonality doesn't work correctly when considering seasonality factors != 1 "
                                    + expectedFixing[i] + " vs " + seasonalityFixing_real[i] );
                }
            }

            //Testing Unset function
            //
             Utils.QL_REQUIRE( hz.link.hasSeasonality(), () => "[4] incorrectly believes NO seasonality correction" );
            hz.link.setSeasonality();
             Utils.QL_REQUIRE( !hz.link.hasSeasonality(), () => "[5] incorrectly believes HAS seasonality correction" );

            double[] seasonalityFixing_unset = {
            ii.fixing(new Date(14,Month.January  ,2013),true),
            ii.fixing(new Date(14,Month.February ,2013),true),
            ii.fixing(new Date(14,Month.March    ,2013),true),
            ii.fixing(new Date(14,Month.April    ,2013),true),
            ii.fixing(new Date(14,Month.May      ,2013),true),
            ii.fixing(new Date(14,Month.June     ,2013),true),
            ii.fixing(new Date(14,Month.July     ,2013),true),
            ii.fixing(new Date(14,Month.August   ,2013),true),
            ii.fixing(new Date(14,Month.September,2013),true),
            ii.fixing(new Date(14,Month.October  ,2013),true),
            ii.fixing(new Date(14,Month.November ,2013),true),
            ii.fixing(new Date(14,Month.December ,2013),true)
             };

            for ( int i = 0; i < 12; i++ )
            {
                if ( Math.Abs( seasonalityFixing_unset[i] - seasonalityFixing_1[i] ) > eps )
                {
                    Assert.Fail( "UnsetSeasonality doesn't work correctly "
                                    + seasonalityFixing_unset[i] + " vs " + seasonalityFixing_1[i] );
                }
            }

            //==============================================================================
            // now do an INTERPOLATED index, i.e. repeat everything on a fake version of
            // UKRPI (to save making another term structure)

            bool interpYES = true;
            UKRPI iiUKRPIyes = new UKRPI( interpYES, hz );
            for ( int i = 0; i < fixData.Length; i++ )
            {
                iiUKRPIyes.addFixing( rpiSchedule[i], fixData[i] );
            }

            ZeroInflationIndex iiyes = iiUKRPIyes as ZeroInflationIndex;

            // now build the zero inflation curve
            // same data, bigger lag or it will be a self-contradiction
            Period observationLagyes = new Period( 3, TimeUnit.Months );
            List<BootstrapHelper<ZeroInflationTermStructure>> helpersyes =
                makeHelpers( zcData, zcData.Length,
                iiyes, observationLagyes, calendar, bdc, dc );

            PiecewiseZeroInflationCurve<Linear> pZITSyes =
                    new PiecewiseZeroInflationCurve<Linear>(
                    evaluationDate, calendar, dc, observationLagyes,
                    frequency, iiyes.interpolated(), baseZeroRate,
                    new Handle<YieldTermStructure>( nominalTS ), helpersyes );
            pZITSyes.recalculate();

            // first check that the zero rates on the curve match the data
            // and that the helpers give the correct impled rates
            forceLinearInterpolation = false;   // still
            for ( int i = 0; i < zcData.Length; i++ )
            {
                Assert.IsTrue( Math.Abs( zcData[i].rate / 100.0
                                - pZITSyes.zeroRate( zcData[i].date, observationLagyes, forceLinearInterpolation ) ) < eps,
                                "ZITS INTERPOLATED zeroRate != instrument "
                                + pZITSyes.zeroRate( zcData[i].date, observationLagyes, forceLinearInterpolation )
                                + " date " + zcData[i].date + " observationLagyes " + observationLagyes
                                + " vs " + zcData[i].rate / 100.0
                                + " interpolation: " + iiyes.interpolated()
                                + " forceLinearInterpolation " + forceLinearInterpolation );
                Assert.IsTrue( Math.Abs( helpersyes[i].impliedQuote()
                                    - zcData[i].rate / 100.0 ) < eps,
                                "ZITS INTERPOLATED implied quote != instrument "
                                + helpersyes[i].impliedQuote()
                                + " vs " + zcData[i].rate / 100.0 );
            }

            //======================================================================================
            // now test the forecasting capability of the index.
            hz.linkTo( pZITSyes );
            from = hz.link.baseDate() + new Period( 1, TimeUnit.Months ); // to avoid historical linear bit for rest of base month
            to = hz.link.maxDate() - new Period( 1, TimeUnit.Months ); // a bit of margin for adjustments
            testIndex = new MakeSchedule().from( from ).to( to )
            .withTenor( new Period( 1, TimeUnit.Months ) )
            .withCalendar( new UnitedKingdom() )
            .withConvention( BusinessDayConvention.ModifiedFollowing ).value();

            // we are testing UKRPI which is FAKE interpolated for testing here
            bd = hz.link.baseDate();
            bf = iiyes.fixing( bd );
            for ( int i = 0; i < testIndex.Count; i++ )
            {
                Date d = testIndex[i];
                double z = hz.link.zeroRate( d, new Period( 0, TimeUnit.Days ) );
                double t = hz.link.dayCounter().yearFraction( bd, d );
                double calc = bf * Math.Pow( 1 + z, t );
                if ( t <= 0 ) calc = iiyes.fixing( d ); // still historical
                if ( Math.Abs( calc - iiyes.fixing( d ) ) > eps )
                    Assert.Fail( "ZC INTERPOLATED index does not forecast correctly for date " + d
                                    + " from base date " + bd
                                    + " with fixing " + bf
                                    + ", correct:  " + calc
                                    + ", fix: " + iiyes.fixing( d )
                                    + ", t " + t
                                    + ", zero " + z );
            }

            //===========================================================================================
            // Test zero coupon swap

            ZeroInflationIndex ziiyes = iiyes as ZeroInflationIndex;
             Utils.QL_REQUIRE( ziiyes != null, () => "dynamic_pointer_cast to ZeroInflationIndex from UKRPI-I failed" );
            ZeroCouponInflationSwap nzcisyes = new ZeroCouponInflationSwap( ZeroCouponInflationSwap.Type.Payer,
                                                              1000000.0,
                                                              evaluationDate,
                                                              zcData[6].date,    // end date = maturity
                                                              calendar, bdc, dc, zcData[6].rate / 100.0, // fixed rate
                                                              ziiyes, observationLagyes );

            // N.B. no coupon pricer because it is not a coupon, effect of inflation curve via
            //      inflation curve attached to the inflation index.
            nzcisyes.setPricingEngine( sppe );

            // ... and price it, should be zero
            Assert.IsTrue( Math.Abs( nzcisyes.NPV() ) < 0.00001, "ZCIS-I does not reprice to zero "
                                    + nzcisyes.NPV()
                                    + evaluationDate + " to " + zcData[6].date + " becoming " + nzcisyes.maturityDate()
                                    + " rate " + zcData[6].rate
                                    + " fixed leg " + nzcisyes.legNPV( 0 )
                                    + " indexed-predicted inflated leg " + nzcisyes.legNPV( 1 )
                                    + " discount " + nominalTS.discount( nzcisyes.maturityDate() )
                                    );

            // remove circular refernce
            hz.linkTo( new ZeroInflationTermStructure() );
        }