public static double simpleDuration(Leg leg, InterestRate y, bool includeSettlementDateFlows,
Date settlementDate, Date npvDate)
{
if (leg.empty())
{
return(0.0);
}
if (settlementDate == null)
{
settlementDate = Settings.Instance.evaluationDate();
}
if (npvDate == null)
{
npvDate = settlementDate;
}
double P = 0.0;
double dPdy = 0.0;
double t = 0.0;
Date lastDate = npvDate;
DayCounter dc = y.dayCounter();
for (int i = 0; i < leg.Count; ++i)
{
if (leg[i].hasOccurred(settlementDate, includeSettlementDateFlows))
{
continue;
}
double c = leg[i].amount();
if (leg[i].tradingExCoupon(settlementDate))
{
c = 0.0;
}
t += getStepwiseDiscountTime(leg[i], dc, npvDate, lastDate);
double B = y.discountFactor(t);
P += c * B;
dPdy += t * c * B;
lastDate = leg[i].date();
}
if (P.IsEqual(0.0)) // no cashflows
{
return(0.0);
}
return(dPdy / P);
}
// NPV of the cash flows.
// The NPV is the sum of the cash flows, each discounted
// according to the given constant interest rate. The result
// is affected by the choice of the interest-rate compounding
// and the relative frequency and day counter.
public static double npv(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 = 0.0;
double discount = 1.0;
Date lastDate = npvDate;
DayCounter dc = yield.dayCounter();
for (int i = 0; i < leg.Count; ++i)
{
if (leg[i].hasOccurred(settlementDate, includeSettlementDateFlows))
{
continue;
}
double amount = leg[i].amount();
if (leg[i].tradingExCoupon(settlementDate))
{
amount = 0.0;
}
double b = yield.discountFactor(getStepwiseDiscountTime(leg[i], dc, npvDate, lastDate));
discount *= b;
lastDate = leg[i].date();
npv += amount * discount;
}
return(npv);
}
public static double modifiedDuration(Leg leg, InterestRate y, bool includeSettlementDateFlows,
Date settlementDate, Date npvDate)
{
if (leg.empty())
{
return(0.0);
}
if (settlementDate == null)
{
settlementDate = Settings.Instance.evaluationDate();
}
if (npvDate == null)
{
npvDate = settlementDate;
}
double P = 0.0;
double t = 0.0;
double dPdy = 0.0;
double r = y.rate();
int N = (int)y.frequency();
Date lastDate = npvDate;
DayCounter dc = y.dayCounter();
for (int i = 0; i < leg.Count; ++i)
{
if (leg[i].hasOccurred(settlementDate, includeSettlementDateFlows))
{
continue;
}
double c = leg[i].amount();
if (leg[i].tradingExCoupon(settlementDate))
{
c = 0.0;
}
t += getStepwiseDiscountTime(leg[i], dc, npvDate, lastDate);
double B = y.discountFactor(t);
P += c * B;
switch (y.compounding())
{
case Compounding.Simple:
dPdy -= c * B * B * t;
break;
case Compounding.Compounded:
dPdy -= c * t * B / (1 + r / N);
break;
case Compounding.Continuous:
dPdy -= c * B * t;
break;
case Compounding.SimpleThenCompounded:
if (t <= 1.0 / N)
{
dPdy -= c * B * B * t;
}
else
{
dPdy -= c * t * B / (1 + r / N);
}
break;
default:
Utils.QL_FAIL("unknown compounding convention (" + y.compounding() + ")");
break;
}
lastDate = leg[i].date();
}
if (P.IsEqual(0.0)) // no cashflows
{
return(0.0);
}
return(-dPdy / P); // reverse derivative sign
}
//! Cash-flow convexity
public static double convexity(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;
}
DayCounter dc = yield.dayCounter();
double P = 0.0;
double t = 0.0;
double d2Pdy2 = 0.0;
double r = yield.rate();
int N = (int)yield.frequency();
Date lastDate = npvDate;
for (int i = 0; i < leg.Count; ++i)
{
if (leg[i].hasOccurred(settlementDate, includeSettlementDateFlows))
{
continue;
}
double c = leg[i].amount();
if (leg[i].tradingExCoupon(settlementDate))
{
c = 0.0;
}
t += getStepwiseDiscountTime(leg[i], dc, npvDate, lastDate);
double B = yield.discountFactor(t);
P += c * B;
switch (yield.compounding())
{
case Compounding.Simple:
d2Pdy2 += c * 2.0 * B * B * B * t * t;
break;
case Compounding.Compounded:
d2Pdy2 += c * B * t * (N * t + 1) / (N * (1 + r / N) * (1 + r / N));
break;
case Compounding.Continuous:
d2Pdy2 += c * B * t * t;
break;
case Compounding.SimpleThenCompounded:
if (t <= 1.0 / N)
{
d2Pdy2 += c * 2.0 * B * B * B * t * t;
}
else
{
d2Pdy2 += c * B * t * (N * t + 1) / (N * (1 + r / N) * (1 + r / N));
}
break;
default:
Utils.QL_FAIL("unknown compounding convention (" + yield.compounding() + ")");
break;
}
lastDate = leg[i].date();
}
if (P.IsEqual(0.0))
{
// no cashflows
return(0.0);
}
return(d2Pdy2 / P);
}