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));
}
public static double macaulayDuration(List <CashFlow> cashflows, InterestRate y, Date settlementDate)
{
if (y.compounding() != Compounding.Compounded)
{
throw new ArgumentException("compounded rate required");
}
return((1.0 + y.rate() / (int)y.frequency()) * modifiedDuration(cashflows, y, settlementDate));
}
public static double modifiedDuration(List <CashFlow> cashflows, InterestRate y, Date settlementDate)
{
if (cashflows.Count == 0)
{
return(0.0);
}
double P = 0.0;
double dPdy = 0.0;
double r = y.rate();
int N = (int)y.frequency();
DayCounter dc = y.dayCounter();
foreach (CashFlow cf in cashflows.Where(cf => !cf.hasOccurred(settlementDate)))
{
double t = dc.yearFraction(settlementDate, cf.date());
double c = cf.amount();
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:
throw new ArgumentException("unknown compounding convention (" + y.compounding() + ")");
}
}
if (P == 0.0) // no cashflows
{
return(0.0);
}
return(-dPdy / P); // reverse derivative sign
}
// 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(List <CashFlow> cashflows, InterestRate irr, Date settlementDate = null)
{
if (settlementDate == null)
{
settlementDate = Settings.evaluationDate();
}
var flatRate = new FlatForward(settlementDate, irr.rate(), irr.dayCounter(), irr.compounding(), irr.frequency());
return(bps(cashflows, flatRate, settlementDate, settlementDate));
}
//! 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.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));
}
//! Cash-flow convexity
/*! The convexity of a string of cash flows is defined as
* \f[
* C = \frac{1}{P} \frac{\partial^2 P}{\partial y^2}
* \f]
* where \f$ P \f$ is the present value of the cash flows according to the given IRR \f$ y \f$.
*/
public static double convexity(List <CashFlow> cashflows, InterestRate rate, Date settlementDate = null)
{
if (cashflows.Count == 0)
{
return(0.0);
}
if (settlementDate == null)
{
settlementDate = Settings.evaluationDate();
}
DayCounter dayCounter = rate.dayCounter();
double P = 0;
double d2Pdy2 = 0;
double y = rate.rate();
int N = (int)rate.frequency();
foreach (CashFlow cashflow in cashflows.Where(cashflow => !cashflow.hasOccurred(settlementDate)))
{
double t = dayCounter.yearFraction(settlementDate, cashflow.date());
double c = cashflow.amount();
double B = rate.discountFactor(t);
P += c * B;
switch (rate.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 + y / N) * (1 + y / 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 + y / N) * (1 + y / N));
}
break;
default:
throw new ArgumentException("unknown compounding convention (" + rate.compounding() + ")");
}
}
// no cashflows
if (P == 0)
{
return(0);
}
return(d2Pdy2 / P);
}
public void testBrazilianCached()
{
//("Testing Brazilian public bond prices against cached values...");
CommonVars vars = new CommonVars();
double faceAmount = 1000.0;
double redemption = 100.0;
Date issueDate = new Date(1, Month.January, 2007);
Date today = new Date(6, Month.June, 2007);
Settings.setEvaluationDate(today);
// NTN-F maturity dates
InitializedList<Date> maturityDates = new InitializedList<Date>(6);
maturityDates[0] = new Date(1, Month.January, 2008);
maturityDates[1] = new Date(1, Month.January, 2010);
maturityDates[2] = new Date(1, Month.July, 2010);
maturityDates[3] = new Date(1, Month.January, 2012);
maturityDates[4] = new Date(1, Month.January, 2014);
maturityDates[5] = new Date(1, Month.January, 2017);
// NTN-F yields
InitializedList<double> yields = new InitializedList<double>(6);
yields[0] = 0.114614;
yields[1] = 0.105726;
yields[2] = 0.105328;
yields[3] = 0.104283;
yields[4] = 0.103218;
yields[5] = 0.102948;
// NTN-F prices
InitializedList<double> prices = new InitializedList<double>(6);
prices[0] = 1034.63031372;
prices[1] = 1030.09919487;
prices[2] = 1029.98307160;
prices[3] = 1028.13585068;
prices[4] = 1028.33383817;
prices[5] = 1026.19716497;
int settlementDays = 1;
vars.faceAmount = 1000.0;
// The tolerance is high because Andima truncate yields
double tolerance = 1.0e-4;
InitializedList<InterestRate> couponRates = new InitializedList<InterestRate>(1);
couponRates[0] = new InterestRate(0.1, new Thirty360(), Compounding.Compounded, Frequency.Annual);
for (int bondIndex = 0; bondIndex < maturityDates.Count; bondIndex++)
{
// plain
InterestRate yield = new InterestRate(yields[bondIndex], new Business252(new Brazil()),
Compounding.Compounded, Frequency.Annual);
Schedule schedule = new Schedule(new Date(1, Month.January, 2007),
maturityDates[bondIndex], new Period(Frequency.Semiannual),
new Brazil(Brazil.Market.Settlement),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Backward, false);
FixedRateBond bond = new FixedRateBond(settlementDays,
faceAmount,
schedule,
couponRates,
BusinessDayConvention.Following,
redemption,
issueDate);
double cachedPrice = prices[bondIndex];
double price = vars.faceAmount * (bond.cleanPrice(yield.rate(),
yield.dayCounter(),
yield.compounding(),
yield.frequency(),
today) + bond.accruedAmount(today)) / 100;
if (Math.Abs(price - cachedPrice) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice + "\n"
+ " error: " + (price - cachedPrice) + "\n"
);
}
}
}
public static double macaulayDuration(List<CashFlow> cashflows, InterestRate y, Date settlementDate)
{
if (y.compounding() != Compounding.Compounded) throw new ArgumentException("compounded rate required");
return (1.0 + y.rate() / (int)y.frequency()) * modifiedDuration(cashflows, y, settlementDate);
}
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);
}
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.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.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);
}
public static double modifiedDuration(List<CashFlow> cashflows, InterestRate y, Date settlementDate)
{
if (cashflows.Count == 0)
return 0.0;
double P = 0.0;
double dPdy = 0.0;
double r = y.rate();
int N = (int)y.frequency();
DayCounter dc = y.dayCounter();
foreach (CashFlow cf in cashflows.Where(cf => !cf.hasOccurred(settlementDate)))
{
double t = dc.yearFraction(settlementDate, cf.date());
double c = cf.amount();
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:
throw new ArgumentException("unknown compounding convention (" + y.compounding() + ")");
}
}
if (P == 0.0) // no cashflows
return 0.0;
return -dPdy / P; // reverse derivative sign
}
//! Cash-flow convexity
/*! The convexity of a string of cash flows is defined as
\f[
C = \frac{1}{P} \frac{\partial^2 P}{\partial y^2}
\f]
where \f$ P \f$ is the present value of the cash flows according to the given IRR \f$ y \f$.
*/
public static double convexity(List<CashFlow> cashflows, InterestRate rate, Date settlementDate = null)
{
if (cashflows.Count == 0)
return 0.0;
if (settlementDate == null) settlementDate = Settings.evaluationDate();
DayCounter dayCounter = rate.dayCounter();
double P = 0;
double d2Pdy2 = 0;
double y = rate.rate();
int N = (int)rate.frequency();
foreach (CashFlow cashflow in cashflows.Where(cashflow => !cashflow.hasOccurred(settlementDate)))
{
double t = dayCounter.yearFraction(settlementDate, cashflow.date());
double c = cashflow.amount();
double B = rate.discountFactor(t);
P += c * B;
switch (rate.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 + y / N) * (1 + y / 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 + y / N) * (1 + y / N));
break;
default:
throw new ArgumentException("unknown compounding convention (" + rate.compounding() + ")");
}
}
// no cashflows
if (P == 0) return 0;
return d2Pdy2 / P;
}
// 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(List<CashFlow> cashflows, InterestRate irr, Date settlementDate = null) {
if (settlementDate == null)
settlementDate = Settings.evaluationDate();
var flatRate = new FlatForward(settlementDate, irr.rate(), irr.dayCounter(), irr.compounding(), irr.frequency());
return bps(cashflows, flatRate, settlementDate, settlementDate);
}
public void testConversions()
{
InterestRateData[] cases = {
// data from "Option Pricing Formulas", Haug, pag.181-182
// Rate,Compounding, Frequency, Time, Compounding2, Frequency2, Rate2, precision
new InterestRateData(0.0800, Compounding.Compounded, Frequency.Quarterly, 1.00, Compounding.Continuous, Frequency.Annual, 0.0792, 4),
new InterestRateData(0.1200, Compounding.Continuous, Frequency.Annual, 1.00, Compounding.Compounded, Frequency.Annual, 0.1275, 4),
new InterestRateData(0.0800, Compounding.Compounded, Frequency.Quarterly, 1.00, Compounding.Compounded, Frequency.Annual, 0.0824, 4),
new InterestRateData(0.0700, Compounding.Compounded, Frequency.Quarterly, 1.00, Compounding.Compounded, Frequency.Semiannual, 0.0706, 4),
// undocumented, but reasonable :)
new InterestRateData(0.0100, Compounding.Compounded, Frequency.Annual, 1.00, Compounding.Simple, Frequency.Annual, 0.0100, 4),
new InterestRateData(0.0200, Compounding.Simple, Frequency.Annual, 1.00, Compounding.Compounded, Frequency.Annual, 0.0200, 4),
new InterestRateData(0.0300, Compounding.Compounded, Frequency.Semiannual, 0.50, Compounding.Simple, Frequency.Annual, 0.0300, 4),
new InterestRateData(0.0400, Compounding.Simple, Frequency.Annual, 0.50, Compounding.Compounded, Frequency.Semiannual, 0.0400, 4),
new InterestRateData(0.0500, Compounding.Compounded, Frequency.EveryFourthMonth, 1.0/3, Compounding.Simple, Frequency.Annual, 0.0500, 4),
new InterestRateData(0.0600, Compounding.Simple, Frequency.Annual, 1.0/3, Compounding.Compounded, Frequency.EveryFourthMonth, 0.0600, 4),
new InterestRateData(0.0500, Compounding.Compounded, Frequency.Quarterly, 0.25, Compounding.Simple, Frequency.Annual, 0.0500, 4),
new InterestRateData(0.0600, Compounding.Simple, Frequency.Annual, 0.25, Compounding.Compounded, Frequency.Quarterly, 0.0600, 4),
new InterestRateData(0.0700, Compounding.Compounded, Frequency.Bimonthly, 1.0/6, Compounding.Simple, Frequency.Annual, 0.0700, 4),
new InterestRateData(0.0800, Compounding.Simple, Frequency.Annual, 1.0/6, Compounding.Compounded, Frequency.Bimonthly, 0.0800, 4),
new InterestRateData(0.0900, Compounding.Compounded, Frequency.Monthly, 1.0/12, Compounding.Simple, Frequency.Annual, 0.0900, 4),
new InterestRateData(0.1000, Compounding.Simple, Frequency.Annual, 1.0/12, Compounding.Compounded, Frequency.Monthly, 0.1000, 4),
new InterestRateData(0.0300, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.25, Compounding.Simple, Frequency.Annual, 0.0300, 4),
new InterestRateData(0.0300, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.25, Compounding.Simple, Frequency.Semiannual, 0.0300, 4),
new InterestRateData(0.0300, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.25, Compounding.Simple, Frequency.Quarterly, 0.0300, 4),
new InterestRateData(0.0300, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.50, Compounding.Simple, Frequency.Annual, 0.0300, 4),
new InterestRateData(0.0300, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.50, Compounding.Simple, Frequency.Semiannual, 0.0300, 4),
new InterestRateData(0.0300, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.75, Compounding.Compounded, Frequency.Semiannual, 0.0300, 4),
new InterestRateData(0.0400, Compounding.Simple, Frequency.Semiannual, 0.25, Compounding.SimpleThenCompounded, Frequency.Quarterly, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Simple, Frequency.Semiannual, 0.25, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Simple, Frequency.Semiannual, 0.25, Compounding.SimpleThenCompounded, Frequency.Annual, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Compounded, Frequency.Quarterly, 0.50, Compounding.SimpleThenCompounded, Frequency.Quarterly, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Simple, Frequency.Semiannual, 0.50, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Simple, Frequency.Semiannual, 0.50, Compounding.SimpleThenCompounded, Frequency.Annual, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Compounded, Frequency.Quarterly, 0.75, Compounding.SimpleThenCompounded, Frequency.Quarterly, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Compounded, Frequency.Semiannual, 0.75, Compounding.SimpleThenCompounded, Frequency.Semiannual, 0.0400, 4),
new InterestRateData(0.0400, Compounding.Simple, Frequency.Semiannual, 0.75, Compounding.SimpleThenCompounded, Frequency.Annual, 0.0400, 4)
};
Rounding roundingPrecision;
double r3;
double r2;
Date d1 = Date.Today;
Date d2;
InterestRate ir;
InterestRate ir2;
InterestRate ir3;
InterestRate expectedIR;
double compoundf;
double error;
double disc;
for (int i = 0; i < cases.Length-1 ; i++)
{
ir = new InterestRate(cases[i].r, new Actual360(), cases[i].comp, cases[i].freq);
d2 = d1 + new Period((int)(360 * cases[i].t + 0.5) ,TimeUnit.Days);
roundingPrecision = new Rounding(cases[i].precision);
// check that the compound factor is the inverse of the discount factor
compoundf = ir.compoundFactor(d1, d2);
disc = ir.discountFactor(d1, d2);
error = Math.Abs(disc - 1.0 / compoundf);
if (error > 1e-15)
Assert.Fail(ir + " 1.0/compound_factor: " + 1.0 / compoundf);
// check that the equivalent InterestRate with *same* daycounter,
// compounding, and frequency is the *same* InterestRate
ir2 = ir.equivalentRate(d1, d2, ir.dayCounter(), ir.compounding(), ir.frequency());
error = Math.Abs(ir.rate() - ir2.rate());
if (error > 1e-15)
Assert.Fail("original interest rate: " + ir + " equivalent interest rate: " + ir2 + " rate error: " + error);
if (ir.dayCounter() != ir2.dayCounter())
Assert.Fail("day counter error original interest rate: " + ir + " equivalent interest rate: " + ir2);
if (ir.compounding() != ir2.compounding())
Assert.Fail("compounding error original interest rate: " + ir + " equivalent interest rate: " + ir2);
if (ir.frequency() != ir2.frequency())
Assert.Fail("frequency error original interest rate: " + ir + " equivalent interest rate: " + ir2);
// check that the equivalent rate with *same* daycounter,
// compounding, and frequency is the *same* rate
r2 = ir.equivalentRate(d1, d2, ir.dayCounter(), ir.compounding(), ir.frequency()).rate();
error = Math.Abs(ir.rate() - r2);
if (error > 1e-15)
Assert.Fail("original rate: " + ir + " equivalent rate: " + r2 + " error: " + error);
// check that the equivalent InterestRate with *different*
// compounding, and frequency is the *expected* InterestRate
ir3 = ir.equivalentRate(d1, d2, ir.dayCounter(), cases[i].comp2, cases[i].freq2);
expectedIR = new InterestRate(cases[i].expected, ir.dayCounter(), cases[i].comp2, cases[i].freq2);
r3 = roundingPrecision.Round(ir3.rate());
error = Math.Abs(r3 - expectedIR.rate());
if (error > 1.0e-17)
Assert.Fail("original interest rate: " + ir + " calculated equivalent interest rate: " + ir3 + " truncated equivalent rate: " + r3 + " expected equivalent interest rate: " + expectedIR + " rate error: " + error);
if (ir3.dayCounter() != expectedIR.dayCounter())
Assert.Fail("day counter error original interest rate: " + ir3 + " equivalent interest rate: " + expectedIR);
if (ir3.compounding() != expectedIR.compounding())
Assert.Fail("compounding error original interest rate: " + ir3 + " equivalent interest rate: " + expectedIR);
if (ir3.frequency() != expectedIR.frequency())
Assert.Fail("frequency error original interest rate: " + ir3 + " equivalent interest rate: " + expectedIR);
// check that the equivalent rate with *different*
// compounding, and frequency is the *expected* rate
r3 = ir.equivalentRate(d1, d2, ir.dayCounter(), cases[i].comp2, cases[i].freq2).rate();
r3 = roundingPrecision.Round(r3);
error = Math.Abs(r3 - cases[i].expected);
if (error > 1.0e-17)
Assert.Fail("calculated equivalent rate: " + r3 + " expected equivalent rate: " + cases[i].expected + " error: " + error);
}
}
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.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;
Date refStartDate, refEndDate;
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;
}
Date couponDate = leg[i].date();
Coupon coupon = leg[i] as Coupon;
if (coupon != null)
{
refStartDate = coupon.refPeriodStart;
refEndDate = coupon.refPeriodEnd;
}
else
{
if (lastDate == npvDate)
{
// we don't have a previous coupon date,
// so we fake it
refStartDate = couponDate - new Period(1,TimeUnit.Years);
}
else
{
refStartDate = lastDate;
}
refEndDate = couponDate;
}
t += dc.yearFraction(lastDate, couponDate, refStartDate, refEndDate);
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 = couponDate;
}
if (P == 0.0) // no cashflows
return 0.0;
return -dPdy/P; // reverse derivative sign
}
// 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(nominal, paymentDate, 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(nominal, paymentDate, 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(nominal, paymentDate, 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();
}
if (schedule_.isRegular(N - 1))
{
leg.Add(new FixedRateCoupon(nominal, paymentDate, rate, start, end, start, end, exCouponDate));
}
else
{
Date refer = start + schedule_.tenor();
refer = schCalendar.adjust(refer, schedule_.businessDayConvention());
leg.Add(new FixedRateCoupon(nominal, paymentDate, rate, start, end, start, refer, exCouponDate));
}
}
return(leg);
}
//! 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.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);
}
static void Main(string[] args)
{
// boost::timer timer;
Date today = new Date(16,Month.October,2007);
Settings.setEvaluationDate(today);
Console.WriteLine();
Console.WriteLine("Pricing a callable fixed rate bond using");
Console.WriteLine("Hull White model w/ reversion parameter = 0.03");
Console.WriteLine("BAC4.65 09/15/12 ISIN: US06060WBJ36");
Console.WriteLine("roughly five year tenor, ");
Console.WriteLine("quarterly coupon and call dates");
Console.WriteLine("reference date is : " + today );
/* Bloomberg OAS1: "N" model (Hull White)
varying volatility parameter
The curve entered into Bloomberg OAS1 is a flat curve,
at constant yield = 5.5%, semiannual compounding.
Assume here OAS1 curve uses an ACT/ACT day counter,
as documented in PFC1 as a "default" in the latter case.
*/
// set up a flat curve corresponding to Bloomberg flat curve
double bbCurveRate = 0.055;
DayCounter bbDayCounter = new ActualActual(ActualActual.Convention.Bond);
InterestRate bbIR = new InterestRate(bbCurveRate,bbDayCounter,Compounding.Compounded ,Frequency.Semiannual);
Handle<YieldTermStructure> termStructure = new Handle<YieldTermStructure>(flatRate( today,
bbIR.rate(),
bbIR.dayCounter(),
bbIR.compounding(),
bbIR.frequency()));
// set up the call schedule
CallabilitySchedule callSchedule = new CallabilitySchedule();
double callPrice = 100.0;
int numberOfCallDates = 24;
Date callDate = new Date(15,Month.September,2006);
for (int i=0; i< numberOfCallDates; i++)
{
Calendar nullCalendar = new NullCalendar();
Callability.Price myPrice = new Callability.Price(callPrice, Callability.Price.Type.Clean);
callSchedule.Add( new Callability(myPrice,Callability.Type.Call, callDate ));
callDate = nullCalendar.advance(callDate, 3, TimeUnit.Months);
}
// set up the callable bond
Date dated = new Date(16,Month.September,2004);
Date issue = dated;
Date maturity = new Date(15,Month.September,2012);
int settlementDays = 3; // Bloomberg OAS1 settle is Oct 19, 2007
Calendar bondCalendar = new UnitedStates(UnitedStates.Market.GovernmentBond);
double coupon = .0465;
Frequency frequency = Frequency.Quarterly;
double redemption = 100.0;
double faceAmount = 100.0;
/* The 30/360 day counter Bloomberg uses for this bond cannot
reproduce the US Bond/ISMA (constant) cashflows used in PFC1.
Therefore use ActAct(Bond)
*/
DayCounter bondDayCounter = new ActualActual(ActualActual.Convention.Bond);
// PFC1 shows no indication dates are being adjusted
// for weekends/holidays for vanilla bonds
BusinessDayConvention accrualConvention = BusinessDayConvention.Unadjusted;
BusinessDayConvention paymentConvention = BusinessDayConvention.Unadjusted;
Schedule sch = new Schedule( dated, maturity, new Period(frequency), bondCalendar,
accrualConvention, accrualConvention,
DateGeneration.Rule.Backward, false);
int maxIterations = 1000;
double accuracy = 1e-8;
int gridIntervals = 40;
double reversionParameter = .03;
// output price/yield results for varying volatility parameter
double sigma = Const.QL_Epsilon; // core dumps if zero on Cygwin
ShortRateModel hw0 = new HullWhite(termStructure,reversionParameter,sigma);
IPricingEngine engine0 = new TreeCallableFixedRateBondEngine(hw0, gridIntervals, termStructure);
CallableFixedRateBond callableBond = new CallableFixedRateBond( settlementDays, faceAmount, sch,
new InitializedList<double>(1, coupon),
bondDayCounter, paymentConvention,
redemption, issue, callSchedule);
callableBond.setPricingEngine(engine0);
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine( "{0:0.00} / {1:0.00} ", callableBond.cleanPrice() ,
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("96.50 / 5.47");
//
sigma = .01;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw1 = new HullWhite(termStructure,reversionParameter,sigma);
IPricingEngine engine1 = new TreeCallableFixedRateBondEngine(hw1,gridIntervals,termStructure);
callableBond.setPricingEngine(engine1);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine( "{0:0.00} / {1:0.00} ", callableBond.cleanPrice() ,
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("95.68 / 5.66");
//
sigma = .03;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw2 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine2 = new TreeCallableFixedRateBondEngine(hw2, gridIntervals, termStructure);
callableBond.setPricingEngine(engine2);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("92.34 / 6.49");
//
sigma = .06;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw3 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine3 = new TreeCallableFixedRateBondEngine(hw3, gridIntervals, termStructure);
callableBond.setPricingEngine(engine3);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("87.16 / 7.83");
//
sigma = .12;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw4 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine4 = new TreeCallableFixedRateBondEngine(hw4, gridIntervals, termStructure);
callableBond.setPricingEngine(engine4);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("77.31 / 10.65");
}