Package org.jquantlib.termstructures.volatilities

Examples of org.jquantlib.termstructures.volatilities.BlackConstantVol


        final Handle<YieldTermStructure> flatRiskFree = new Handle<YieldTermStructure>(
                new FlatForward(referenceDate, riskFreeRate, rfdc));
        final Handle<YieldTermStructure> flatDividends = new Handle <YieldTermStructure>(
                new FlatForward(referenceDate, q, divdc));
        final Handle<BlackVolTermStructure> flatVol = new Handle<BlackVolTermStructure>(
                new BlackConstantVol(referenceDate, volcal, v, voldc));

        QL.require(a.payoff != null, "non-plain payoff given");
        final PlainVanillaPayoff payoff = (PlainVanillaPayoff) a.payoff;
        final /*@Time*/ double maturity = rfdc.yearFraction(a.settlementDate, maturityDate);
        final GeneralizedBlackScholesProcess bs = new GeneralizedBlackScholesProcess(underlying, flatDividends, flatRiskFree, flatVol);
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        final Date referenceDate = process.riskFreeRate().currentLink().referenceDate();

        // binomial trees with constant coefficient
        final Handle<YieldTermStructure> flatRiskFree = new Handle<YieldTermStructure>(new FlatForward(referenceDate, rRate, rfdc));
        final Handle<YieldTermStructure> flatDividends = new Handle<YieldTermStructure>(new FlatForward(referenceDate, qRate, divdc));
        final Handle<BlackVolTermStructure> flatVol = new Handle<BlackVolTermStructure>(new BlackConstantVol(referenceDate, volcal, v, voldc));
        final PlainVanillaPayoff payoff = (PlainVanillaPayoff) a.payoff;
        QL.require(payoff!=null , "non-plain payoff given"); // QA:[RG]::verified // TODO: message

        final double maturity = rfdc.yearFraction(referenceDate, maturityDate);
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            // constant vol/rate assumption. It should be relaxed
            v = Math.sqrt((variance + i * jumpSquareVol) / t);
            r = riskFreeRate - process.jumpIntensity().currentLink().value() * k + i * muPlusHalfSquareVol / t;
            riskFreeTS.linkTo(new FlatForward(rateRefDate, r, voldc));
            volTS.linkTo(new BlackConstantVol(rateRefDate, volcal, v, voldc));

            baseArguments.validate();
            baseEngine.calculate();

            weight = p.op(i);
View Full Code Here

        // bootstrap the yield/dividend/volatility curves
        final Handle<Quote> underlyingH = new Handle<Quote>(new SimpleQuote(underlying));
        final Handle<YieldTermStructure> flatDividendTS = new Handle<YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
        final Handle<YieldTermStructure> flatTermStructure = new Handle<YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
        final Handle<BlackVolTermStructure> flatVolTS = new Handle<BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
        final Payoff payoff = new PlainVanillaPayoff(type, strike);

        // European Options
        final VanillaOption europeanOption = new EuropeanOption(payoff, europeanExercise);
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        final Handle<YieldTermStructure> dividendYield = process.dividendYield();
        final Handle<YieldTermStructure> riskFreeRate = process.riskFreeRate();

        final Handle<BlackVolTermStructure> blackVol = process.blackVolatility();
        final Handle<BlackVolTermStructure> volatility = new Handle<BlackVolTermStructure>(
                new BlackConstantVol(
                        blackVol.currentLink().referenceDate(),
                        blackVol.currentLink().calendar(),
                        new Handle<Quote>(volQuote),
                        blackVol.currentLink().dayCounter()));
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        final Handle<YieldTermStructure> flatRiskFree =
              new Handle<YieldTermStructure>(new FlatForward(referenceDate, riskFreeRate, rfdc));
        final Handle<YieldTermStructure> flatDividends =
              new Handle<YieldTermStructure>(new FlatForward(referenceDate, q, divdc));
        final Handle<BlackVolTermStructure> flatVol =
              new Handle<BlackVolTermStructure>(new BlackConstantVol(referenceDate, volcal, v, voldc));

        final PlainVanillaPayoff payoff = (PlainVanillaPayoff)(this.a.payoff);
        QL.require(payoff != null, "non-plain payoff given");

        final double maturity = rfdc.yearFraction(this.a.settlementDate, maturityDate);
View Full Code Here

        // bootstrap the yield/dividend/volatility curves
        final Handle<Quote> underlyingH = new Handle<Quote>(new SimpleQuote(underlying));
        final Handle<YieldTermStructure> flatDividendTS = new Handle<YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
        final Handle<YieldTermStructure> flatTermStructure = new Handle<YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
        final Handle<BlackVolTermStructure> flatVolTS = new Handle<BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
        final Payoff payoff = new PlainVanillaPayoff(type, strike);

        final BlackScholesMertonProcess bsmProcess = new BlackScholesMertonProcess(underlyingH, flatDividendTS, flatTermStructure, flatVolTS);

        // European Options
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            final Class<? extends BlackVolTermStructure> klass = blackVolatility.currentLink().getClass();

            // constant Black vol?
            if (BlackConstantVol.class.isAssignableFrom(klass)) {
                // ok, the local volatility is constant too.
                final BlackConstantVol constVol = (BlackConstantVol) blackVolatility.currentLink();
                localVolatility.linkTo(new LocalConstantVol(
                        constVol.referenceDate(),
                        constVol.blackVol(/*@Time*/0.0, /*@Real*/x0.currentLink().value()), constVol.dayCounter()));
                updated = true;
                return localVolatility;
            }

            // ok, so it's not constant. Maybe it's strike-independent?
View Full Code Here

        //Let's explore BlackConstantVolatility by calculating blackVolatility,blackForwardVolatility,blackVariance and blackForwardVariance
        //Following example explains that when volatility is assumed to be constant BlackConstantVol termstructure can be used to represent
        //such a volatility termstructure.
        final SimpleQuote volatilityQuote = new SimpleQuote(0.3);
        final RelinkableHandle<Quote>  handleToVolatilityQuote = new RelinkableHandle<Quote>(volatilityQuote);
        BlackVolatilityTermStructure constantVolatility = new BlackConstantVol(2,new UnitedStates(Market.NYSE),handleToVolatilityQuote, new Actual365Fixed());

        //Calculating blackVolatility using maturity as 10 days after today and strike as 20
        Double volatility1 = constantVolatility.blackVol(date10.clone(), 20);
        System.out.println("BlackVolatility = "+volatility1);

        //Calculating blackVolatility using maturity as 20 days after today and strike as 30
        Double volatility2 = constantVolatility.blackVol(date20.clone(), 30);
        System.out.println("BlackVolatility = "+volatility2);

        //Calculating blackVolatility using maturity as 30 days after today and strike as 40
        Double volatility3 = constantVolatility.blackVol(date30.clone(), 40);
        System.out.println("BlackVolatility = "+volatility3);

        //The volatilities calculated above are same as it's constant volatility termstructure
        if(volatility1.equals(volatility2) && volatility2.equals(volatility3)){
            System.out.println("All the volatilities calculated above are same and = "+volatility1);
        }

        //Calculating blackForwardVolatility between 10 days after today and 15 days after today with strike as 20
        Double forwardVolatility1 = constantVolatility.blackForwardVol(date10.clone(), date15.clone(), 20, true);
        System.out.println("BlackForwardVolatility = "+forwardVolatility1);

        //Calculating blackForwardVolatility between 20 days after today and 25 days after today with strike as 40
        Double forwardVolatility2 = constantVolatility.blackForwardVol(date10.clone(), date15.clone(), 20, true);
        System.out.println("BlackForwardVolatility = "+forwardVolatility2);

        //Calculating blackForwardVolatility between 27 days after today and 35 days after today with strike as 60
        Double forwardVolatility3 = constantVolatility.blackForwardVol(date27.clone(), date35.clone(), 60, true);
        System.out.println("BlackForwardVolatility = "+forwardVolatility3);

        //The volatilities calculated above are same as it's constant volatility termstructure
        if(forwardVolatility1.equals(forwardVolatility2) && forwardVolatility2.equals(forwardVolatility3)){
            System.out.println("All the forward volatilities calculated above are same and = "+forwardVolatility1);
        }else{
            System.out.println("The forward volatilities may not be constant");
        }

        //Calculating blackVariance
        System.out.println("BlackVariance = "+constantVolatility.blackVariance(date10.clone(), 20));

        //Calculating blackForwardVariance
        System.out.println("BlackForwardVariance = "+constantVolatility.blackForwardVariance(date10.clone(), date15.clone(), 20, true));

        //As BlackConstantVol termstructure has been initialized using relinkable handle so lets change the observable SimpleQuote of this handle
        //and see the change getting reflected to all the calculations done above.
        volatilityQuote.setValue(0.04) ;
        constantVolatility = new BlackConstantVol(2,new UnitedStates(Market.NYSE),handleToVolatilityQuote, new Actual365Fixed());

        //Calculating blackVolatility using maturity as 10 days after today and strike as 20
        volatility1 = constantVolatility.blackVol(date10.clone(), 20);
        System.out.println("BlackVolatility = "+volatility1);

        //Calculating blackVolatility using maturity as 20 days after today and strike as 30
        volatility2 = constantVolatility.blackVol(date20.clone(), 30);
        System.out.println("BlackVolatility = "+volatility2);

        volatility3 = constantVolatility.blackVol(date30.clone(), 40);
        System.out.println("BlackVolatility = "+volatility3);

        //The volatilities calculated above are same as it's constant volatility termstructure
        if(volatility1.equals(volatility2) && volatility2.equals(volatility3)){
            System.out.println("All the volatilities calculated above are same and = "+volatility1);
        }

        //Calculating blackForwardVolatility between 10 days after today and 15 days after today with strike as 20
        forwardVolatility1 = constantVolatility.blackForwardVol(date10.clone(), date15.clone(), 20, true);
        System.out.println("BlackForwardVolatility = "+forwardVolatility1);

        //Calculating blackForwardVolatility between 20 days after today and 25 days after today with strike as 40
        forwardVolatility2 = constantVolatility.blackForwardVol(date10.clone(), date15.clone(), 20, true);
        System.out.println("BlackForwardVolatility = "+forwardVolatility2);

        //Calculating blackForwardVolatility between 27 days after today and 35 days after today with strike as 60
        forwardVolatility3 = constantVolatility.blackForwardVol(date27.clone(), date35.clone(), 60, true);
        System.out.println("BlackForwardVolatility = "+forwardVolatility3);

        //The volatilities calculated above are same as it's constant volatility termstructure
        if(forwardVolatility1.equals(forwardVolatility2) && forwardVolatility2.equals(forwardVolatility3)){
            System.out.println("All the volatilities calculated above are same and = "+forwardVolatility1);
        }else{
            System.out.println("The forward volatilities may not be constant");
        }

        //Calculating blackVariance
        System.out.println("BlackVariance = "+constantVolatility.blackVariance(date10.clone(), 20));

        //Calculating blackForwardVariance
        System.out.println("BlackForwardVariance = "+constantVolatility.blackForwardVariance(date10.clone(), date15.clone(), 20, true));

        System.out.println("//===============================BlackVarianceCurve================================");

        //Let's create black variance curve and calculate volatilities/variances by interpolating on
        //the created curve for a given strike.

        //-- Date today = DateFactory.getFactory().getTodaysDate();

        //Following is the time axis
        final Date[] dates = {date10.clone(), date15.clone(), date20.clone(), date25.clone(), date30.clone(), date40.clone() };

        //Following is the volatility axis
        final double[] volatilities = {0.1,0.2,0.3,0.4,0.5,0.6};

        //Following is the curve
        final BlackVarianceTermStructure varianceCurve = new BlackVarianceCurve(today,dates,volatilities, new Actual365Fixed(), false);
        ((BlackVarianceCurve)varianceCurve).setInterpolation();

        //Calculating blackVolatility using maturity as 12 days after today and strike as 20
        volatility1 = varianceCurve.blackVol(date12.clone(), 20);
        System.out.println("Interpolated BlackVolatility on BlackVarianceCurve = "+volatility1);

        //Calculating blackVolatility using maturity as 22 days after today and strike as 30
        volatility2 = varianceCurve.blackVol(date22.clone(), 30);
        System.out.println("Interpolated BlackVolatility on BlackVarianceCurve = "+volatility2);

        //Calculating blackVolatility using maturity as 32 days after today and strike as 40
        volatility3 = varianceCurve.blackVol(date32.clone(), 40);
        System.out.println("Interpolated BlackVolatility on BlackVarianceCurve = "+volatility3);


        //Calculating blackForwardVolatility between 12 days after today and 16 days after today with strike as 20
        forwardVolatility1 = varianceCurve.blackForwardVol(date12.clone(), date16.clone(), 20, true);
        System.out.println("Interpolated BlackForwardVolatility on BlackVarianceCurve = "+forwardVolatility1);

        //Calculating blackForwardVolatility between 22 days after today and 26 days after today with strike as 40
        forwardVolatility2 = varianceCurve.blackForwardVol(date22.clone(), date26.clone(), 40, true);
        System.out.println("Interpolated BlackForwardVolatility on BlackVarianceCurve = "+forwardVolatility2);

        //Calculating blackForwardVolatility between 27 days after today and 35 days after today with strike as 60
        forwardVolatility3 = varianceCurve.blackForwardVol(date27.clone(), date35.clone(), 60, true);
        System.out.println("Interpolated BlackForwardVolatility on BlackVarianceCurve = "+forwardVolatility3);


        //Calculating blackVariance using maturity as 12 days after today and strike as 20
        System.out.println("Interpolated BlackVariance on BlackVarianceCurve = "+varianceCurve.blackVariance(date12.clone(), 20));

        //Calculating blackForwardVariance between 12 days after today and 16 days after today with strike as 20
        System.out.println("Interpolated BlackForwardVariance on BlackVarianceCurve = "+varianceCurve.blackForwardVariance(date12.clone(), date16.clone(), 20, true));

        System.out.println("//===============================BlackVarianceSurface================================");

        //Let's create black variance surface and calculate volatilities/variances by interpolating on
        //the created curve for a given strike.

        //-- today = DateFactory.getFactory().getTodaysDate();

        //Following is the time axis
        final Date[] datesAxis = {date10.clone(), date15.clone(), date20.clone(), date25.clone(), date30.clone(), date40.clone() };

        final Array strikeAxis = new Array(new double[] {10,20,35,40,56,60});

        //Following is the volatility surface on which interpolations will be done
        final Matrix volatilityMatrix = new Matrix(new double[][] {
                {0.01,0.02,0.03,0.04,0.05,0.06},
                {0.02,0.03,0.04,0.05,0.06,0.07},
                {0.03,0.04,0.05,0.06,0.07,0.08},
                {0.3,0.5,0.6,0.7,0.8,0.9},
                {0.1,0.4,0.6,0.7,0.8,0.9},
                {0.2,0.5,0.6,0.7,0.8,0.9}
        });


        //Following is the variance surface where variance = f(strike,maturity) and f = function
        final BlackVarianceTermStructure varianceSurface = new BlackVarianceSurface(
                today, datesAxis,
                strikeAxis, volatilityMatrix, new Actual365Fixed(),
                Extrapolation.InterpolatorDefaultExtrapolation,
                Extrapolation.InterpolatorDefaultExtrapolation);
        ((BlackVarianceSurface)varianceSurface).setInterpolation(null);

        //As the surface has been set up to do interpolations so let's start calculating the volatilities for strikes
        //and maturities lying between the points as mentioned by strikesAxis and dateAxis.
        //Calculating blackVolatility using maturity as 12 days after today and strike as 18
        volatility1 = varianceSurface.blackVol(date12.clone(), 18);
        System.out.println("Interpolated BlackVolatility on BlackVarianceSurface = "+volatility1);

        //Calculating blackVolatility using maturity as 22 days after today and strike as 33
        volatility2 = varianceSurface.blackVol(date22.clone(), 33);
        System.out.println("Interpolated BlackVolatility on BlackVarianceSurface = "+volatility2);

        //Calculating blackVolatility using maturity as 32 days after today and strike as 45
        volatility3 = varianceSurface.blackVol(date32.clone(), 45);
        System.out.println("Interpolated BlackVolatility on BlackVarianceSurface = "+volatility3);


        //Calculating blackForwardVolatility between 12 days after today and 16 days after today with strike as 20
        forwardVolatility1 = varianceSurface.blackForwardVol(date12.clone(), date16.clone(), 20, true);
        System.out.println("Interpolated BlackForwardVolatility on BlackVarianceSurface = "+forwardVolatility1);

        //Calculating blackForwardVolatility between 22 days after today and 26 days after today with strike as 40
        forwardVolatility2 = varianceSurface.blackForwardVol(date22.clone(), date26.clone(), 40, true);
        System.out.println("Interpolated BlackForwardVolatility on BlackVarianceSurface = "+forwardVolatility2);

        //Calculating blackForwardVolatility between 27 days after today and 35 days after today with strike as 50
        forwardVolatility3 = varianceSurface.blackForwardVol(date27.clone(), date35.clone(), 50, true);
        System.out.println("Interpolated BlackForwardVolatility on BlackVarianceSurface = "+forwardVolatility3);


        //Calculating blackVariance using maturity as 12 days after today and strike as 20
        System.out.println("Interpolated BlackVariance on BlackVarianceSurface = "+varianceSurface.blackVariance(date12.clone(), 20));

        //Calculating blackForwardVariance between 12 days after today and 16 days after today with strike as 20
        System.out.println("Interpolated BlackForwardVariance on BlackVarianceSurface = "+varianceSurface.blackForwardVariance(date12.clone(), date16.clone(), 20, true));

        System.out.println("//================================ImpliedVolTermStructure=============================");

        //As mentioned in the java docs the implied volatility termstructure remains linked to
        //the underlying termstructure and changes to same are linked to ImpliedVolTermStructure
        //as well.

        //Lets use underlying as varianceCurve defined above by creating a relinkable handle as shown below
        final RelinkableHandle<BlackVolTermStructure> varianceCurveHandle = new RelinkableHandle<BlackVolTermStructure>(varianceCurve);
        final BlackVarianceTermStructure impliedVolTermStructure = new ImpliedVolTermStructure(varianceCurveHandle, today);

        //Calculating blackVolatility using maturity as 12 days after today and strike as 20
        volatility1 = varianceCurve.blackVol(date12.clone(), 20);
        final double impliedVolatility1 = impliedVolTermStructure.blackVol(date12.clone(), 20);

        if(volatility1 == impliedVolatility1){
            System.out.println("Interpolated BlackVolatility on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+volatility1);
        }

        //Calculating blackVolatility using maturity as 22 days after today and strike as 30
        volatility2 = varianceCurve.blackVol(date22.clone(), 30);
        final double impliedVolatility2 = impliedVolTermStructure.blackVol(date22.clone(), 30);
        if(volatility2 == impliedVolatility2){
            System.out.println("Interpolated BlackVolatility on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+volatility2);
        }

        //Calculating blackVolatility using maturity as 32 days after today and strike as 40
        volatility3 = varianceCurve.blackVol(date32.clone(), 40);
        final double impliedVolatility3 = impliedVolTermStructure.blackVol(date32.clone(), 40);
        if(volatility3 == impliedVolatility3){
            System.out.println("Interpolated BlackVolatility on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+volatility3);
        }


        //Calculating blackForwardVolatility between 12 days after today and 16 days after today with strike as 20
        forwardVolatility1 = varianceCurve.blackForwardVol(date12.clone(), date16.clone(), 20, true);
        final double impliedForwardVolatility1 = impliedVolTermStructure.blackForwardVol(date12.clone(), date16.clone(), 20, true);
        if(forwardVolatility1 == impliedForwardVolatility1){
            System.out.println("Interpolated BlackForwardVolatility on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+forwardVolatility1);
        }

        //Calculating blackForwardVolatility between 22 days after today and 26 days after today with strike as 40
        forwardVolatility2 = varianceCurve.blackForwardVol(date22.clone(), date26.clone(), 40, true);
        final double impliedForwardVolatility2 = impliedVolTermStructure.blackForwardVol(date22.clone(), date26.clone(), 40, true);
        if(forwardVolatility2 == impliedForwardVolatility2){
            System.out.println("Interpolated BlackForwardVolatility on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+forwardVolatility2);
        }

        //Calculating blackForwardVolatility between 27 days after today and 35 days after today with strike as 60
        forwardVolatility3 = varianceCurve.blackForwardVol(date27.clone(), date35.clone(), 60, true);
        final double impliedForwardVolatility3 = impliedVolTermStructure.blackForwardVol(date27.clone(), date35.clone(), 60, true);
        if(forwardVolatility3 == impliedForwardVolatility3){
            System.out.println("Interpolated BlackForwardVolatility on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+forwardVolatility3);
        }


        //Calculating blackVariance using maturity as 12 days after today and strike as 20
        final double variance = varianceCurve.blackVariance(date12.clone(), 20);
        final double impliedVariance = impliedVolTermStructure.blackVariance(date12.clone(), 20);
        if(variance == impliedVariance){
            System.out.println("Interpolated BlackVariance on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+varianceCurve.blackVariance(date12.clone(), 20));
        }

        //Calculating blackForwardVariance between 12 days after today and 16 days after today with strike as 20
        final double forwardVariance = varianceCurve.blackForwardVariance(date12.clone(), date16.clone(), 20, true);
        final double impliedForwardVariance = impliedVolTermStructure.blackForwardVariance(date12.clone(), date16.clone(), 20, true);
        if(forwardVariance == impliedForwardVariance){
            System.out.println("Interpolated BlackForwardVariance on BlackVarianceCurve is same for varianceCurve and ImpliedVolTermStructure derived on it and = "+varianceCurve.blackForwardVariance(date12.clone(), date16.clone(), 20, true));
        }

        System.out.println("//================================LocalConstantVol=======================================");

        //LocalConstantVolatility is essentially same as BlackConstantVol and is a local volatility version of BlackConstantVol

        //Let's set the quoteValue = 0.05 and use the constantVolatility a BlackConstantVol
        volatilityQuote.setValue(0.05);
        final LocalVolTermStructure localConstantVolatility = new LocalConstantVol(2,new UnitedStates(Market.NYSE),handleToVolatilityQuote, new Actual365Fixed());

        //Calculating blackVolatility using maturity as 10 days after today and strike as 20
        if(constantVolatility.blackVol(date10.clone(), 20) == localConstantVolatility.localVol(date10.clone(), 20,true)){
            System.out.println("BlackVolatility and LocalVolatility are same and are = "+localConstantVolatility.localVol(date10.clone(), 20,true));
        }

        //Calculating blackVolatility using maturity as 20 days after today and strike as 30
        if(constantVolatility.blackVol(date20.clone(), 30) == localConstantVolatility.localVol(date20.clone(), 30,true)){
            System.out.println("BlackVolatility and LocalVolatility are same and are = "+localConstantVolatility.localVol(date20.clone(), 30,true));
        }

        //Calculating blackVolatility using maturity as 30 days after today and strike as 40
        if(constantVolatility.blackVol(date30.clone(), 40) == localConstantVolatility.localVol(date30.clone(), 40,true)){
            System.out.println("BlackVolatility and LocalVolatility are same and are = "+localConstantVolatility.localVol(date30.clone(), 40,true));
        }

        System.out.println("//================================LocalVolCurve==========================================");
View Full Code Here

            // constant vol/rate assumption. It should be relaxed
            v = Math.sqrt((variance + i * jumpSquareVol) / t);
            r = riskFreeRate - process.jumpIntensity().currentLink().value() * k + i * muPlusHalfSquareVol / t;
            riskFreeTS.linkTo(new FlatForward(rateRefDate, r, voldc));
            volTS.linkTo(new BlackConstantVol(rateRefDate, volcal, v, voldc));

            baseArguments.validate();
            baseEngine.calculate();

            weight = p.op(i);
View Full Code Here

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