//! 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.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);
}
//! 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.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);
}
//! 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(List <CashFlow> leg, InterestRate y, Date settlementDate)
{
if (leg.Count == 0)
{
return(0.0);
}
double shift = 0.01;
double dirtyPrice = CashFlows.npv(leg, y, settlementDate);
double modifiedDuration = CashFlows.duration(leg, y, Duration.Type.Modified, settlementDate);
return((1.0 / (-dirtyPrice * modifiedDuration)) * shift);
}
public static double duration(Bond bond, InterestRate yield, Duration.Type type = Duration.Type.Modified,
Date settlementDate = null)
{
if (settlementDate == null)
{
settlementDate = bond.settlementDate();
}
Utils.QL_REQUIRE(BondFunctions.isTradable(bond, settlementDate), () =>
"non tradable at " + settlementDate +
" (maturity being " + bond.maturityDate() + ")");
return(CashFlows.duration(bond.cashflows(), yield, type, false, settlementDate));
}
// 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_,
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,
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);
}
//! Basis-point value
/*! Obtained by setting dy = 0.0001 in the 2nd-order Taylor
* series expansion.
*/
public static double basisPointValue(List <CashFlow> leg, InterestRate y, Date settlementDate)
{
if (leg.Count == 0)
{
return(0.0);
}
double shift = 0.0001;
double dirtyPrice = CashFlows.npv(leg, y, settlementDate);
double modifiedDuration = CashFlows.duration(leg, y, Duration.Type.Modified, settlementDate);
double convexity = CashFlows.convexity(leg, y, settlementDate);
double delta = -modifiedDuration * dirtyPrice;
double gamma = (convexity / 100.0) * dirtyPrice;
delta *= shift;
gamma *= shift * shift;
return(delta + 0.5 * gamma);
}
