public static double macaulayDuration(Leg leg, InterestRate y, bool includeSettlementDateFlows,
Date settlementDate, Date npvDate)
{
Utils.QL_REQUIRE(y.compounding() == Compounding.Compounded, () => "compounded rate required");
return((1.0 + y.rate() / (int)y.frequency()) *
modifiedDuration(leg, y, includeSettlementDateFlows, settlementDate, npvDate));
}
//! Basis-point sensitivity of the cash flows.
// The result is the change in NPV due to a uniform
// 1-basis-point change in the rate paid by the cash
// flows. The change for each coupon is 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 bps(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;
}
FlatForward flatRate = new FlatForward(settlementDate, yield.rate(), yield.dayCounter(),
yield.compounding(), yield.frequency());
return(bps(leg, flatRate, includeSettlementDateFlows, settlementDate, npvDate));
}
// creator
public override List <CashFlow> value()
{
if (couponRates_.Count == 0)
{
throw new ArgumentException("no coupon rates given");
}
if (notionals_.Count == 0)
{
throw new ArgumentException("no nominals given");
}
List <CashFlow> leg = new List <CashFlow>();
Calendar schCalendar = schedule_.calendar();
// first period might be short or long
Date start = schedule_[0], end = schedule_[1];
Date paymentDate = calendar_.adjust(end, paymentAdjustment_);
Date exCouponDate = null;
InterestRate rate = couponRates_[0];
double nominal = notionals_[0];
if (exCouponPeriod_ != null)
{
exCouponDate = exCouponCalendar_.advance(paymentDate,
-exCouponPeriod_,
exCouponAdjustment_,
exCouponEndOfMonth_);
}
if (schedule_.isRegular(1))
{
if (!(firstPeriodDC_ == null || firstPeriodDC_ == rate.dayCounter()))
{
throw new ArgumentException("regular first coupon does not allow a first-period day count");
}
leg.Add(new FixedRateCoupon(paymentDate, nominal, rate, start, end, start, end, exCouponDate));
}
else
{
Date refer = end - schedule_.tenor();
refer = schCalendar.adjust(refer, schedule_.businessDayConvention());
InterestRate r = new InterestRate(rate.rate(),
(firstPeriodDC_ == null || firstPeriodDC_.empty()) ? rate.dayCounter() : firstPeriodDC_,
rate.compounding(), rate.frequency());
leg.Add(new FixedRateCoupon(paymentDate, nominal, r, start, end, refer, end, exCouponDate));
}
// regular periods
for (int i = 2; i < schedule_.Count - 1; ++i)
{
start = end; end = schedule_[i];
paymentDate = calendar_.adjust(end, paymentAdjustment_);
if (exCouponPeriod_ != null)
{
exCouponDate = exCouponCalendar_.advance(paymentDate,
-exCouponPeriod_,
exCouponAdjustment_,
exCouponEndOfMonth_);
}
if ((i - 1) < couponRates_.Count)
{
rate = couponRates_[i - 1];
}
else
{
rate = couponRates_.Last();
}
if ((i - 1) < notionals_.Count)
{
nominal = notionals_[i - 1];
}
else
{
nominal = notionals_.Last();
}
leg.Add(new FixedRateCoupon(paymentDate, nominal, rate, start, end, start, end, exCouponDate));
}
if (schedule_.Count > 2)
{
// last period might be short or long
int N = schedule_.Count;
start = end; end = schedule_[N - 1];
paymentDate = calendar_.adjust(end, paymentAdjustment_);
if (exCouponPeriod_ != null)
{
exCouponDate = exCouponCalendar_.advance(paymentDate,
-exCouponPeriod_,
exCouponAdjustment_,
exCouponEndOfMonth_);
}
if ((N - 2) < couponRates_.Count)
{
rate = couponRates_[N - 2];
}
else
{
rate = couponRates_.Last();
}
if ((N - 2) < notionals_.Count)
{
nominal = notionals_[N - 2];
}
else
{
nominal = notionals_.Last();
}
InterestRate r = new InterestRate(rate.rate(),
lastPeriodDC_ == null ? rate.dayCounter() : lastPeriodDC_, rate.compounding(), rate.frequency());
if (schedule_.isRegular(N - 1))
{
leg.Add(new FixedRateCoupon(paymentDate, nominal, r, start, end, start, end, exCouponDate));
}
else
{
Date refer = start + schedule_.tenor();
refer = schCalendar.adjust(refer, schedule_.businessDayConvention());
leg.Add(new FixedRateCoupon(paymentDate, nominal, r, start, end, start, refer, exCouponDate));
}
}
return(leg);
}
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);
}