public override double value(double zSpread)
{
zSpread_.setValue(zSpread);
double NPV = CashFlows.npv(leg_, curve_, includeSettlementDateFlows_, settlementDate_, npvDate_);
return(npv_ - NPV);
}
//! Yield value of a basis point
/*! The yield value of a one basis point change in price is
* the derivative of the yield with respect to the price
* multiplied by 0.01
*/
public static double yieldValueBasisPoint(Leg leg, InterestRate yield, bool includeSettlementDateFlows,
Date settlementDate = null, Date npvDate = null)
{
if (leg.empty())
{
return(0.0);
}
if (settlementDate == null)
{
settlementDate = Settings.Instance.evaluationDate();
}
if (npvDate == null)
{
npvDate = settlementDate;
}
double npv = CashFlows.npv(leg, yield, includeSettlementDateFlows, settlementDate, npvDate);
double modifiedDuration = CashFlows.duration(leg, yield, Duration.Type.Modified, includeSettlementDateFlows,
settlementDate, npvDate);
double shift = 0.01;
return((1.0 / (-npv * modifiedDuration)) * shift);
}
public override double value(double y)
{
InterestRate yield = new InterestRate(y, dayCounter_, compounding_, frequency_);
double NPV = CashFlows.npv(leg_, yield, includeSettlementDateFlows_, settlementDate_, npvDate_);
return(npv_ - NPV);
}
//! Basis-point value
/*! Obtained by setting dy = 0.0001 in the 2nd-order Taylor
* series expansion.
*/
public static double basisPointValue(Leg leg, InterestRate yield, bool includeSettlementDateFlows,
Date settlementDate = null, Date npvDate = null)
{
if (leg.empty())
{
return(0.0);
}
if (settlementDate == null)
{
settlementDate = Settings.Instance.evaluationDate();
}
if (npvDate == null)
{
npvDate = settlementDate;
}
double npv = CashFlows.npv(leg, yield, includeSettlementDateFlows, settlementDate, npvDate);
double modifiedDuration = CashFlows.duration(leg, yield, Duration.Type.Modified, includeSettlementDateFlows,
settlementDate, npvDate);
double convexity = CashFlows.convexity(leg, yield, includeSettlementDateFlows, settlementDate, npvDate);
double delta = -modifiedDuration * npv;
double gamma = (convexity / 100.0) * npv;
double shift = 0.0001;
delta *= shift;
gamma *= shift * shift;
return(delta + 0.5 * gamma);
}
// converts the yield volatility into a forward price volatility
private double forwardPriceVolatility()
{
Date bondMaturity = arguments_.redemptionDate;
Date exerciseDate = arguments_.callabilityDates[0];
List <CashFlow> fixedLeg = arguments_.cashflows;
// value of bond cash flows at option maturity
double fwdNpv = CashFlows.npv(fixedLeg, discountCurve_, false, exerciseDate);
DayCounter dayCounter = arguments_.paymentDayCounter;
Frequency frequency = arguments_.frequency;
// adjust if zero coupon bond (see also bond.cpp)
if (frequency == Frequency.NoFrequency || frequency == Frequency.Once)
{
frequency = Frequency.Annual;
}
double fwdYtm = CashFlows.yield(fixedLeg,
fwdNpv,
dayCounter,
Compounding.Compounded,
frequency,
false,
exerciseDate);
InterestRate fwdRate = new InterestRate(fwdYtm, dayCounter, Compounding.Compounded, frequency);
double fwdDur = CashFlows.duration(fixedLeg,
fwdRate,
Duration.Type.Modified, false,
exerciseDate);
double cashStrike = arguments_.callabilityPrices[0];
dayCounter = volatility_.link.dayCounter();
Date referenceDate = volatility_.link.referenceDate();
double exerciseTime = dayCounter.yearFraction(referenceDate,
exerciseDate);
double maturityTime = dayCounter.yearFraction(referenceDate,
bondMaturity);
double yieldVol = volatility_.link.volatility(exerciseTime,
maturityTime - exerciseTime,
cashStrike);
double fwdPriceVol = yieldVol * fwdDur * fwdYtm;
return(fwdPriceVol);
}
public static double dirtyPrice(Bond bond, InterestRate yield, Date settlementDate = null)
{
if (settlementDate == null)
{
settlementDate = bond.settlementDate();
}
Utils.QL_REQUIRE(BondFunctions.isTradable(bond, settlementDate), () =>
"non tradable at " + settlementDate +
" (maturity being " + bond.maturityDate() + ")",
QLNetExceptionEnum.NotTradableException);
double dirtyPrice = CashFlows.npv(bond.cashflows(), yield, false, settlementDate) *
100.0 / bond.notional(settlementDate);
return(dirtyPrice);
}
public override void calculate()
{
// validate args for Black engine
Utils.QL_REQUIRE(arguments_.putCallSchedule.Count == 1, () => "Must have exactly one call/put date to use Black Engine");
Date settle = arguments_.settlementDate;
Date exerciseDate = arguments_.callabilityDates[0];
Utils.QL_REQUIRE(exerciseDate >= settle, () => "must have exercise Date >= settlement Date");
List <CashFlow> fixedLeg = arguments_.cashflows;
double value = CashFlows.npv(fixedLeg, discountCurve_, false, settle);
double npv = CashFlows.npv(fixedLeg, discountCurve_, false, discountCurve_.link.referenceDate());
double fwdCashPrice = (value - spotIncome()) /
discountCurve_.link.discount(exerciseDate);
double cashStrike = arguments_.callabilityPrices[0];
Option.Type type = (arguments_.putCallSchedule[0].type() ==
Callability.Type.Call ? Option.Type.Call : Option.Type.Put);
double priceVol = forwardPriceVolatility();
double exerciseTime = volatility_.link.dayCounter().yearFraction(
volatility_.link.referenceDate(),
exerciseDate);
double embeddedOptionValue = Utils.blackFormula(type,
cashStrike,
fwdCashPrice,
priceVol * Math.Sqrt(exerciseTime));
if (type == Option.Type.Call)
{
results_.value = npv - embeddedOptionValue;
results_.settlementValue = value - embeddedOptionValue;
}
else
{
results_.value = npv + embeddedOptionValue;
results_.settlementValue = value + embeddedOptionValue;
}
}
public static double cleanPrice(Bond bond, YieldTermStructure discount, double zSpread, DayCounter dayCounter, Compounding compounding,
Frequency frequency, Date settlementDate = null)
{
if (settlementDate == null)
{
settlementDate = bond.settlementDate();
}
Utils.QL_REQUIRE(BondFunctions.isTradable(bond, settlementDate), () =>
"non tradable at " + settlementDate +
" (maturity being " + bond.maturityDate() + ")",
QLNetExceptionEnum.NotTradableException);
double dirtyPrice = CashFlows.npv(bond.cashflows(), discount, zSpread, dayCounter, compounding, frequency, false, settlementDate) *
100.0 / bond.notional(settlementDate);
return(dirtyPrice - bond.accruedAmount(settlementDate));
}
