public void testParity()
{
// Testing yoy inflation cap/floor parity...
CommonVars vars = new CommonVars();
int[] lengths = { 1, 2, 3, 5, 7, 10, 15, 20 };
// vol is low ...
double[] strikes = { 0.0, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
// yoy inflation vol is generally very low
double[] vols = { 0.001, 0.005, 0.010, 0.015, 0.020 };
// cap-floor-swap parity is model-independent
for (int whichPricer = 0; whichPricer < 3; whichPricer++) {
for (int i=0; i<lengths.Length; i++) {
for (int j=0; j<strikes.Length; j++) {
for (int k=0; k<vols.Length; k++) {
List<CashFlow> leg = vars.makeYoYLeg(vars.evaluationDate,lengths[i]);
Instrument cap = vars.makeYoYCapFloor(CapFloorType.Cap,
leg, strikes[j], vols[k], whichPricer);
Instrument floor = vars.makeYoYCapFloor(CapFloorType.Floor,
leg, strikes[j], vols[k], whichPricer);
Date from = vars.nominalTS.link.referenceDate();
Date to = from+new Period(lengths[i],TimeUnit.Years);
Schedule yoySchedule = new MakeSchedule().from(from).to(to)
.withTenor(new Period(1,TimeUnit.Years))
.withConvention(BusinessDayConvention.Unadjusted)
.withCalendar(new UnitedKingdom()).backwards().value();
YearOnYearInflationSwap swap = new YearOnYearInflationSwap
(YearOnYearInflationSwap.Type.Payer,
1000000.0,
yoySchedule,//fixed schedule, but same as yoy
strikes[j],
vars.dc,
yoySchedule,
vars.iir,
vars.observationLag,
0.0, //spread on index
vars.dc,
new UnitedKingdom());
Handle<YieldTermStructure> hTS = new Handle<YieldTermStructure>(vars.nominalTS);
IPricingEngine sppe = new DiscountingSwapEngine(hTS);
swap.setPricingEngine(sppe);
// N.B. nominals are 10e6
if (Math.Abs((cap.NPV()-floor.NPV()) - swap.NPV()) > 1.0e-6) {
Assert.Fail(
"put/call parity violated:\n"
+ " length: " + lengths[i] + " years\n"
+ " volatility: " + vols[k] + "\n"
+ " strike: " + strikes[j] + "\n"
+ " cap value: " + cap.NPV() + "\n"
+ " floor value: " + floor.NPV() + "\n"
+ " swap value: " + swap.NPV());
}
}
}
}
}
// remove circular refernce
vars.hy.linkTo(new YoYInflationTermStructure());
}
public void testInstrumentEquality()
{
// Testing inflation capped/floored coupon against inflation capfloor instrument...
CommonVars vars = new CommonVars();
int[] lengths = { 1, 2, 3, 5, 7, 10, 15, 20 };
// vol is low ...
double[] strikes = { 0.01, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
// yoy inflation vol is generally very low
double[] vols = { 0.001, 0.005, 0.010, 0.015, 0.020 };
// this is model independent
// capped coupon = fwd - cap, and fwd = swap(0)
// floored coupon = fwd + floor
for (int whichPricer = 0; whichPricer < 3; whichPricer++)
{
for (int i = 0; i < lengths.Length; i++)
{
for (int j = 0; j < strikes.Length; j++)
{
for (int k = 0; k < vols.Length; k++)
{
List <CashFlow> leg = vars.makeYoYLeg(vars.evaluationDate, lengths[i]);
Instrument cap = vars.makeYoYCapFloor(CapFloorType.Cap,
leg, strikes[j], vols[k], whichPricer);
Instrument floor = vars.makeYoYCapFloor(CapFloorType.Floor,
leg, strikes[j], vols[k], whichPricer);
Date from = vars.nominalTS.link.referenceDate();
Date to = from + new Period(lengths[i], TimeUnit.Years);
Schedule yoySchedule = new MakeSchedule().from(from).to(to)
.withTenor(new Period(1, TimeUnit.Years))
.withCalendar(new UnitedKingdom())
.withConvention(BusinessDayConvention.Unadjusted)
.backwards().value();
YearOnYearInflationSwap swap = new YearOnYearInflationSwap(YearOnYearInflationSwap.Type.Payer,
1000000.0,
yoySchedule, //fixed schedule, but same as yoy
0.0, //strikes[j],
vars.dc,
yoySchedule,
vars.iir,
vars.observationLag,
0.0, //spread on index
vars.dc,
new UnitedKingdom());
Handle <YieldTermStructure> hTS = new Handle <YieldTermStructure>(vars.nominalTS);
IPricingEngine sppe = new DiscountingSwapEngine(hTS);
swap.setPricingEngine(sppe);
List <CashFlow> leg2 = vars.makeYoYCapFlooredLeg(whichPricer, from,
lengths[i],
new InitializedList <double>(lengths[i], strikes[j]), //cap
new List <double>(), //floor
vols[k],
1.0, // gearing
0.0); // spread
List <CashFlow> leg3 = vars.makeYoYCapFlooredLeg(whichPricer, from,
lengths[i],
new List <double>(), // cap
new InitializedList <double>(lengths[i], strikes[j]), //floor
vols[k],
1.0, // gearing
0.0); // spread
// N.B. nominals are 10e6
double capped = CashFlows.npv(leg2, vars.nominalTS, false);
if (Math.Abs(capped - (swap.NPV() - cap.NPV())) > 1.0e-6)
{
QAssert.Fail(
"capped coupon != swap(0) - cap:\n"
+ " length: " + lengths[i] + " years\n"
+ " volatility: " + vols[k] + "\n"
+ " strike: " + strikes[j] + "\n"
+ " cap value: " + cap.NPV() + "\n"
+ " swap value: " + swap.NPV() + "\n"
+ " capped coupon " + capped);
}
// N.B. nominals are 10e6
double floored = CashFlows.npv(leg3, vars.nominalTS, false);
if (Math.Abs(floored - (swap.NPV() + floor.NPV())) > 1.0e-6)
{
QAssert.Fail(
"floored coupon != swap(0) + floor :\n"
+ " length: " + lengths[i] + " years\n"
+ " volatility: " + vols[k] + "\n"
+ " strike: " + strikes[j] + "\n"
+ " floor value: " + floor.NPV() + "\n"
+ " swap value: " + swap.NPV() + "\n"
+ " floored coupon " + floored);
}
}
}
}
}
// remove circular refernce
vars.hy.linkTo(null);
}
public void testParity()
{
// Testing yoy inflation cap/floor parity...
CommonVars vars = new CommonVars();
int[] lengths = { 1, 2, 3, 5, 7, 10, 15, 20 };
// vol is low ...
double[] strikes = { 0.0, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
// yoy inflation vol is generally very low
double[] vols = { 0.001, 0.005, 0.010, 0.015, 0.020 };
// cap-floor-swap parity is model-independent
for (int whichPricer = 0; whichPricer < 3; whichPricer++)
{
for (int i = 0; i < lengths.Length; i++)
{
for (int j = 0; j < strikes.Length; j++)
{
for (int k = 0; k < vols.Length; k++)
{
List <CashFlow> leg = vars.makeYoYLeg(vars.evaluationDate, lengths[i]);
Instrument cap = vars.makeYoYCapFloor(CapFloorType.Cap,
leg, strikes[j], vols[k], whichPricer);
Instrument floor = vars.makeYoYCapFloor(CapFloorType.Floor,
leg, strikes[j], vols[k], whichPricer);
Date from = vars.nominalTS.link.referenceDate();
Date to = from + new Period(lengths[i], TimeUnit.Years);
Schedule yoySchedule = new MakeSchedule().from(from).to(to)
.withTenor(new Period(1, TimeUnit.Years))
.withConvention(BusinessDayConvention.Unadjusted)
.withCalendar(new UnitedKingdom()).backwards().value();
YearOnYearInflationSwap swap = new YearOnYearInflationSwap
(YearOnYearInflationSwap.Type.Payer,
1000000.0,
yoySchedule, //fixed schedule, but same as yoy
strikes[j],
vars.dc,
yoySchedule,
vars.iir,
vars.observationLag,
0.0, //spread on index
vars.dc,
new UnitedKingdom());
Handle <YieldTermStructure> hTS = new Handle <YieldTermStructure>(vars.nominalTS);
IPricingEngine sppe = new DiscountingSwapEngine(hTS);
swap.setPricingEngine(sppe);
// N.B. nominals are 10e6
if (Math.Abs((cap.NPV() - floor.NPV()) - swap.NPV()) > 1.0e-6)
{
Assert.Fail(
"put/call parity violated:\n"
+ " length: " + lengths[i] + " years\n"
+ " volatility: " + vols[k] + "\n"
+ " strike: " + strikes[j] + "\n"
+ " cap value: " + cap.NPV() + "\n"
+ " floor value: " + floor.NPV() + "\n"
+ " swap value: " + swap.NPV());
}
}
}
}
}
// remove circular refernce
vars.hy.linkTo(new YoYInflationTermStructure());
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(YearOnYearInflationSwap obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}
public void testYYTermStructure()
{
// Testing year-on-year inflation term structure...
SavedSettings backup = new SavedSettings();
//IndexHistoryCleaner cleaner;
// try the YY UK
Calendar calendar = new UnitedKingdom();
BusinessDayConvention bdc = BusinessDayConvention.ModifiedFollowing;
Date evaluationDate = new Date(13, Month.August, 2007);
evaluationDate = calendar.adjust(evaluationDate);
Settings.setEvaluationDate(evaluationDate);
// fixing data
Date from = new Date(1, Month.January, 2005);
Date to = new Date(13, Month.August, 2007);
Schedule rpiSchedule = new MakeSchedule().from(from).to(to)
.withTenor(new Period(1,TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(BusinessDayConvention.ModifiedFollowing).value();
double[] fixData = { 189.9, 189.9, 189.6, 190.5, 191.6, 192.0,
192.2, 192.2, 192.6, 193.1, 193.3, 193.6,
194.1, 193.4, 194.2, 195.0, 196.5, 197.7,
198.5, 198.5, 199.2, 200.1, 200.4, 201.1,
202.7, 201.6, 203.1, 204.4, 205.4, 206.2,
207.3 };
RelinkableHandle<YoYInflationTermStructure> hy = new RelinkableHandle<YoYInflationTermStructure>();
bool interp = false;
YYUKRPIr iir = new YYUKRPIr(interp, hy);
for (int i=0; i<fixData.Length; i++)
{
iir.addFixing(rpiSchedule[i], fixData[i]);
}
YieldTermStructure nominalTS = nominalTermStructure();
// now build the YoY inflation curve
Datum[] yyData = {
new Datum( new Date(13, Month.August, 2008), 2.95 ),
new Datum( new Date(13, Month.August, 2009), 2.95 ),
new Datum( new Date(13, Month.August, 2010), 2.93 ),
new Datum( new Date(15, Month.August, 2011), 2.955 ),
new Datum( new Date(13, Month.August, 2012), 2.945 ),
new Datum( new Date(13, Month.August, 2013), 2.985 ),
new Datum( new Date(13, Month.August, 2014), 3.01 ),
new Datum( new Date(13, Month.August, 2015), 3.035 ),
new Datum( new Date(13, Month.August, 2016), 3.055 ), // note that
new Datum( new Date(13, Month.August, 2017), 3.075 ), // some dates will be on
new Datum( new Date(13, Month.August, 2019), 3.105 ), // holidays but the payment
new Datum( new Date(15, Month.August, 2022), 3.135 ), // calendar will roll them
new Datum( new Date(13, Month.August, 2027), 3.155 ),
new Datum( new Date(13, Month.August, 2032), 3.145 ),
new Datum( new Date(13, Month.August, 2037), 3.145 )
};
Period observationLag = new Period(2,TimeUnit.Months);
DayCounter dc = new Thirty360();
// now build the helpers ...
List<BootstrapHelper<YoYInflationTermStructure>> helpers =
makeHelpers (yyData, yyData.Length, iir,observationLag, calendar, bdc, dc);
double baseYYRate = yyData[0].rate/100.0;
PiecewiseYoYInflationCurve<Linear> pYYTS = new PiecewiseYoYInflationCurve<Linear>(
evaluationDate, calendar, dc, observationLag,
iir.frequency(),iir.interpolated(), baseYYRate,
new Handle<YieldTermStructure>(nominalTS), helpers);
pYYTS.recalculate();
// validation
// yoy swaps should reprice to zero
// yy rates should not equal yySwap rates
double eps = 0.000001;
// usual swap engine
Handle<YieldTermStructure> hTS = new Handle<YieldTermStructure>(nominalTS);
IPricingEngine sppe = new DiscountingSwapEngine(hTS);
// make sure that the index has the latest yoy term structure
hy.linkTo(pYYTS);
for (int j = 1; j < yyData.Length; j++)
{
from = nominalTS.referenceDate();
to = yyData[j].date;
Schedule yoySchedule = new MakeSchedule().from(from).to(to)
.withConvention(BusinessDayConvention.Unadjusted) // fixed leg gets calendar from
.withCalendar(calendar) // schedule
.withTenor(new Period(1,TimeUnit.Years)).value(); // .back
YearOnYearInflationSwap yyS2 = new YearOnYearInflationSwap(
YearOnYearInflationSwap.Type.Payer,
1000000.0,
yoySchedule,//fixed schedule, but same as yoy
yyData[j].rate/100.0,
dc,
yoySchedule,
iir,
observationLag,
0.0, //spread on index
dc,
new UnitedKingdom());
yyS2.setPricingEngine(sppe);
Assert.IsTrue(Math.Abs(yyS2.NPV())<eps,"fresh yoy swap NPV!=0 from TS "
+"swap quote for pt " + j
+ ", is " + yyData[j].rate/100.0
+" vs YoY rate "+ pYYTS.yoyRate(yyData[j].date-observationLag)
+" at quote date "+(yyData[j].date-observationLag)
+", NPV of a fresh yoy swap is " + yyS2.NPV()
+"\n fair rate " + yyS2.fairRate()
+" payment "+yyS2.paymentConvention());
}
int jj=3;
for (int k = 0; k < 14; k++)
{
from = nominalTS.referenceDate() - new Period(k,TimeUnit.Months);
to = yyData[jj].date - new Period(k,TimeUnit.Months);
Schedule yoySchedule = new MakeSchedule().from(from).to(to)
.withConvention(BusinessDayConvention.Unadjusted) // fixed leg gets calendar from
.withCalendar(calendar) // schedule
.withTenor(new Period(1,TimeUnit.Years))
.value(); //backwards()
YearOnYearInflationSwap yyS3 = new YearOnYearInflationSwap(
YearOnYearInflationSwap.Type.Payer,
1000000.0,
yoySchedule,//fixed schedule, but same as yoy
yyData[jj].rate/100.0,
dc,
yoySchedule,
iir,
observationLag,
0.0, //spread on index
dc,
new UnitedKingdom());
yyS3.setPricingEngine(sppe);
Assert.IsTrue(Math.Abs(yyS3.NPV())< 20000.0,
"unexpected size of aged YoY swap, aged "
+ k +" months: YY aged NPV = " + yyS3.NPV()
+", legs "+ yyS3.legNPV(0) + " and " + yyS3.legNPV(1)
);
}
// remove circular refernce
hy.linkTo( new YoYInflationTermStructure());
}
public void testYYTermStructure()
{
// Testing year-on-year inflation term structure...
SavedSettings backup = new SavedSettings();
//IndexHistoryCleaner cleaner;
// try the YY UK
Calendar calendar = new UnitedKingdom();
BusinessDayConvention bdc = BusinessDayConvention.ModifiedFollowing;
Date evaluationDate = new Date(13, Month.August, 2007);
evaluationDate = calendar.adjust(evaluationDate);
Settings.setEvaluationDate(evaluationDate);
// fixing data
Date from = new Date(1, Month.January, 2005);
Date to = new Date(13, Month.August, 2007);
Schedule rpiSchedule = new MakeSchedule().from(from).to(to)
.withTenor(new Period(1, TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(BusinessDayConvention.ModifiedFollowing).value();
double[] fixData = { 189.9, 189.9, 189.6, 190.5, 191.6, 192.0,
192.2, 192.2, 192.6, 193.1, 193.3, 193.6,
194.1, 193.4, 194.2, 195.0, 196.5, 197.7,
198.5, 198.5, 199.2, 200.1, 200.4, 201.1,
202.7, 201.6, 203.1, 204.4, 205.4, 206.2,
207.3 };
RelinkableHandle <YoYInflationTermStructure> hy = new RelinkableHandle <YoYInflationTermStructure>();
bool interp = false;
YYUKRPIr iir = new YYUKRPIr(interp, hy);
for (int i = 0; i < fixData.Length; i++)
{
iir.addFixing(rpiSchedule[i], fixData[i]);
}
YieldTermStructure nominalTS = nominalTermStructure();
// now build the YoY inflation curve
Datum[] yyData =
{
new Datum(new Date(13, Month.August, 2008), 2.95),
new Datum(new Date(13, Month.August, 2009), 2.95),
new Datum(new Date(13, Month.August, 2010), 2.93),
new Datum(new Date(15, Month.August, 2011), 2.955),
new Datum(new Date(13, Month.August, 2012), 2.945),
new Datum(new Date(13, Month.August, 2013), 2.985),
new Datum(new Date(13, Month.August, 2014), 3.01),
new Datum(new Date(13, Month.August, 2015), 3.035),
new Datum(new Date(13, Month.August, 2016), 3.055), // note that
new Datum(new Date(13, Month.August, 2017), 3.075), // some dates will be on
new Datum(new Date(13, Month.August, 2019), 3.105), // holidays but the payment
new Datum(new Date(15, Month.August, 2022), 3.135), // calendar will roll them
new Datum(new Date(13, Month.August, 2027), 3.155),
new Datum(new Date(13, Month.August, 2032), 3.145),
new Datum(new Date(13, Month.August, 2037), 3.145)
};
Period observationLag = new Period(2, TimeUnit.Months);
DayCounter dc = new Thirty360();
// now build the helpers ...
List <BootstrapHelper <YoYInflationTermStructure> > helpers =
makeHelpers(yyData, yyData.Length, iir, observationLag, calendar, bdc, dc);
double baseYYRate = yyData[0].rate / 100.0;
PiecewiseYoYInflationCurve <Linear> pYYTS = new PiecewiseYoYInflationCurve <Linear>(
evaluationDate, calendar, dc, observationLag,
iir.frequency(), iir.interpolated(), baseYYRate,
new Handle <YieldTermStructure>(nominalTS), helpers);
pYYTS.recalculate();
// validation
// yoy swaps should reprice to zero
// yy rates should not equal yySwap rates
double eps = 0.000001;
// usual swap engine
Handle <YieldTermStructure> hTS = new Handle <YieldTermStructure>(nominalTS);
IPricingEngine sppe = new DiscountingSwapEngine(hTS);
// make sure that the index has the latest yoy term structure
hy.linkTo(pYYTS);
for (int j = 1; j < yyData.Length; j++)
{
from = nominalTS.referenceDate();
to = yyData[j].date;
Schedule yoySchedule = new MakeSchedule().from(from).to(to)
.withConvention(BusinessDayConvention.Unadjusted) // fixed leg gets calendar from
.withCalendar(calendar) // schedule
.withTenor(new Period(1, TimeUnit.Years)).value(); // .back
YearOnYearInflationSwap yyS2 = new YearOnYearInflationSwap(
YearOnYearInflationSwap.Type.Payer,
1000000.0,
yoySchedule, //fixed schedule, but same as yoy
yyData[j].rate / 100.0,
dc,
yoySchedule,
iir,
observationLag,
0.0, //spread on index
dc,
new UnitedKingdom());
yyS2.setPricingEngine(sppe);
Assert.IsTrue(Math.Abs(yyS2.NPV()) < eps, "fresh yoy swap NPV!=0 from TS "
+ "swap quote for pt " + j
+ ", is " + yyData[j].rate / 100.0
+ " vs YoY rate " + pYYTS.yoyRate(yyData[j].date - observationLag)
+ " at quote date " + (yyData[j].date - observationLag)
+ ", NPV of a fresh yoy swap is " + yyS2.NPV()
+ "\n fair rate " + yyS2.fairRate()
+ " payment " + yyS2.paymentConvention());
}
int jj = 3;
for (int k = 0; k < 14; k++)
{
from = nominalTS.referenceDate() - new Period(k, TimeUnit.Months);
to = yyData[jj].date - new Period(k, TimeUnit.Months);
Schedule yoySchedule = new MakeSchedule().from(from).to(to)
.withConvention(BusinessDayConvention.Unadjusted) // fixed leg gets calendar from
.withCalendar(calendar) // schedule
.withTenor(new Period(1, TimeUnit.Years))
.value(); //backwards()
YearOnYearInflationSwap yyS3 = new YearOnYearInflationSwap(
YearOnYearInflationSwap.Type.Payer,
1000000.0,
yoySchedule, //fixed schedule, but same as yoy
yyData[jj].rate / 100.0,
dc,
yoySchedule,
iir,
observationLag,
0.0, //spread on index
dc,
new UnitedKingdom());
yyS3.setPricingEngine(sppe);
Assert.IsTrue(Math.Abs(yyS3.NPV()) < 20000.0,
"unexpected size of aged YoY swap, aged "
+ k + " months: YY aged NPV = " + yyS3.NPV()
+ ", legs " + yyS3.legNPV(0) + " and " + yyS3.legNPV(1)
);
}
// remove circular refernce
hy.linkTo(new YoYInflationTermStructure());
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(YearOnYearInflationSwap obj) {
return (obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr;
}
