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 testDecomposition()
{
// Testing collared coupon against its decomposition...
CommonVars vars= new CommonVars();
double tolerance = 1e-10;
double npvVanilla,npvCappedLeg,npvFlooredLeg,npvCollaredLeg,npvCap,npvFloor,npvCollar;
double error;
double floorstrike = 0.05;
double capstrike = 0.10;
InitializedList<double> caps = new InitializedList<double>(vars.length,capstrike);
List<double> caps0 = new List<double>();
InitializedList<double> floors = new InitializedList<double>(vars.length,floorstrike);
List<double> floors0 = new List<double>();
double gearing_p = 0.5;
double spread_p = 0.002;
double gearing_n = -1.5;
double spread_n = 0.12;
// fixed leg with zero rate
List<CashFlow> fixedLeg = vars.makeFixedLeg(vars.startDate,vars.length);
// floating leg with gearing=1 and spread=0
List<CashFlow> floatLeg = vars.makeYoYLeg(vars.startDate,vars.length);
// floating leg with positive gearing (gearing_p) and spread<>0
List<CashFlow> floatLeg_p = vars.makeYoYLeg(vars.startDate,vars.length,gearing_p,spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
List<CashFlow> floatLeg_n = vars.makeYoYLeg(vars.startDate,vars.length,gearing_n,spread_n);
// Swap with null fixed leg and floating leg with gearing=1 and spread=0
Swap vanillaLeg = new Swap(fixedLeg,floatLeg);
// Swap with null fixed leg and floating leg with positive gearing and spread<>0
Swap vanillaLeg_p = new Swap(fixedLeg,floatLeg_p);
// Swap with null fixed leg and floating leg with negative gearing and spread<>0
Swap vanillaLeg_n = new Swap(fixedLeg,floatLeg_n);
IPricingEngine engine = new DiscountingSwapEngine(vars.nominalTS);
vanillaLeg.setPricingEngine(engine); // here use the autoset feature
vanillaLeg_p.setPricingEngine(engine);
vanillaLeg_n.setPricingEngine(engine);
// CAPPED coupon - Decomposition of payoff
// Payoff = Nom * Min(rate,strike) * accrualperiod =
// = Nom * [rate + Min(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod - Nom * Max(rate-strike,0) * accrualperiod =
// = VanillaFloatingLeg - Call
//
int whichPricer = 0;
// Case gearing = 1 and spread = 0
List<CashFlow> cappedLeg = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps,floors0,vars.volatility);
Swap capLeg = new Swap(fixedLeg,cappedLeg);
capLeg.setPricingEngine(engine);
YoYInflationCap cap = new YoYInflationCap(floatLeg, new List<double>(){capstrike});
cap.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance)
{
Assert.Fail("\nYoY Capped Leg: gearing=1, spread=0%, strike=" + capstrike*100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error );
}
// gearing = 1 and spread = 0
// FLOORED coupon - Decomposition of payoff
// Payoff = Nom * Max(rate,strike) * accrualperiod =
// = Nom * [rate + Max(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod + Nom * Max(strike-rate,0) * accrualperiod =
// = VanillaFloatingLeg + Put
//
List<CashFlow> flooredLeg = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps0,floors,vars.volatility);
Swap floorLeg = new Swap(fixedLeg,flooredLeg);
floorLeg.setPricingEngine(engine);
YoYInflationFloor floor= new YoYInflationFloor(floatLeg, new List<double>(){floorstrike});
floor.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = Math.Abs(npvFlooredLeg-(npvVanilla + npvFloor));
if (error>tolerance)
{
Assert.Fail("YoY Floored Leg: gearing=1, spread=0%, strike=" + floorstrike *100 +
"%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor) + "\n" +
" Diff: " + error );
}
// gearing = 1 and spread = 0
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(strikem,Max(rate,strikeM)) * accrualperiod =
// = VanillaFloatingLeg - Collar
//
List<CashFlow> collaredLeg = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps,floors,vars.volatility);
Swap collarLeg = new Swap(fixedLeg,collaredLeg);
collarLeg.setPricingEngine(engine);
YoYInflationCollar collar = new YoYInflationCollar(floatLeg,
new List<double>(){capstrike},
new List<double>(){floorstrike});
collar.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = Math.Abs(npvCollaredLeg -(npvVanilla - npvCollar));
if (error>tolerance)
{
Assert.Fail("\nYoY Collared Leg: gearing=1, spread=0%, strike=" +
floorstrike*100 + "% and " + capstrike*100 + "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg + "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar) + "\n" +
" Diff: " + error );
}
// gearing = a and spread = b
// CAPPED coupon - Decomposition of payoff
// Payoff
// = Nom * Min(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Min(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Min(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Call(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Min(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg + Put(|a|*rate+b,strike)
//
// Positive gearing
List<CashFlow> cappedLeg_p = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors0,
vars.volatility,gearing_p,spread_p);
Swap capLeg_p = new Swap(fixedLeg,cappedLeg_p);
capLeg_p.setPricingEngine(engine);
YoYInflationCap cap_p = new YoYInflationCap(floatLeg_p,new List<double>(){capstrike});
cap_p.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance)
{
Assert.Fail("\nYoY Capped Leg: gearing=" + gearing_p + ", " +
"spread= " + spread_p *100 +
"%, strike=" + capstrike*100 + "%, " +
"effective strike= " + (capstrike-spread_p)/gearing_p*100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Vanilla Leg NPV: " + npvVanilla + "\n" +
" Cap NPV: " + npvCap + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error );
}
// Negative gearing
List<CashFlow> cappedLeg_n = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors0,
vars.volatility,gearing_n,spread_n);
Swap capLeg_n = new Swap(fixedLeg,cappedLeg_n);
capLeg_n.setPricingEngine(engine);
YoYInflationFloor floor_n = new YoYInflationFloor(floatLeg,new List<double>(){(capstrike-spread_n)/gearing_n});
floor_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCappedLeg = capLeg_n.NPV();
npvFloor = floor_n.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla+ gearing_n*npvFloor));
if (error>tolerance)
{
Assert.Fail("\nYoY Capped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n *100 +
"%, strike=" + capstrike*100 + "%, " +
"effective strike= " + ((capstrike-spread_n)/gearing_n*100) +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" npv Vanilla: " + npvVanilla + "\n" +
" npvFloor: " + npvFloor + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla + gearing_n*npvFloor) + "\n" +
" Diff: " + error );
}
// gearing = a and spread = b
// FLOORED coupon - Decomposition of payoff
// Payoff
// = Nom * Max(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Max(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Max(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Put(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Max(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg - Call(|a|*rate+b,strike)
//
// Positive gearing
List<CashFlow> flooredLeg_p1 = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps0,floors,
vars.volatility,gearing_p,spread_p);
Swap floorLeg_p1 = new Swap(fixedLeg,flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
YoYInflationFloor floor_p1 = new YoYInflationFloor(floatLeg_p,new List<double>(){floorstrike});
floor_p1.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla+npvFloor));
if (error>tolerance)
{
Assert.Fail("\nYoY Floored Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p *100+ "%, strike=" + floorstrike *100 + "%, "
+ "effective strike= " + (floorstrike-spread_p)/gearing_p*100
+ "%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg
+ "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor)
+ "\n" +
" Diff: " + error );
}
// Negative gearing
List<CashFlow> flooredLeg_n = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps0,floors,
vars.volatility,gearing_n,spread_n);
Swap floorLeg_n = new Swap(fixedLeg,flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
YoYInflationCap cap_n = new YoYInflationCap(floatLeg,new List<double>(){(floorstrike-spread_n)/gearing_n});
cap_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvFlooredLeg = floorLeg_n.NPV();
npvCap = cap_n.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla - gearing_n*npvCap));
if (error>tolerance)
{
Assert.Fail("\nYoY Capped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n *100 +
"%, strike=" + floorstrike*100 + "%, " +
"effective strike= " + (floorstrike-spread_n)/gearing_n*100 +
"%\n" +
" Capped Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - gearing_n*npvCap) + "\n" +
" Diff: " + error );
}
// gearing = a and spread = b
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(caprate,Max(a*rate+b,floorrate)) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Collar(a*rate+b, floorrate, caprate)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Collar(|a|*rate+b, caprate, floorrate)
//
// Positive gearing
List<CashFlow> collaredLeg_p = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors,
vars.volatility,gearing_p,spread_p);
Swap collarLeg_p1 = new Swap(fixedLeg,collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
YoYInflationCollar collar_p = new YoYInflationCollar(floatLeg_p,
new List<double>(){capstrike},
new List<double>(){floorstrike});
collar_p.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error>tolerance)
{
Assert.Fail("\nYoY Collared Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p*100 + "%, strike="
+ floorstrike*100 + "% and " + capstrike*100
+ "%, "
+ "effective strike=" + (floorstrike-spread_p)/gearing_p*100
+ "% and " + (capstrike-spread_p)/gearing_p*100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar)
+ "\n" +
" Diff: " + error );
}
// Negative gearing
List<CashFlow> collaredLeg_n = vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors,
vars.volatility,gearing_n,spread_n);
Swap collarLeg_n1 = new Swap(fixedLeg,collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
YoYInflationCollar collar_n = new YoYInflationCollar(floatLeg,
new List<double>(){(floorstrike-spread_n)/gearing_n},
new List<double>(){(capstrike-spread_n)/gearing_n});
collar_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCollaredLeg = collarLeg_n1.NPV();
npvCollar = collar_n.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - gearing_n*npvCollar));
if (error>tolerance)
{
Assert.Fail("\nYoY Collared Leg: gearing=" + gearing_n + ", "
+ "spread= " + spread_n*100 + "%, strike="
+ floorstrike*100 + "% and " + capstrike*100
+ "%, "
+ "effective strike=" + (floorstrike-spread_n)/gearing_n*100
+ "% and " + (capstrike-spread_n)/gearing_n*100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - gearing_n*npvCollar)
+ "\n" +
" Diff: " + error );
}
// remove circular refernce
vars.hy.linkTo(new YoYInflationTermStructure());
}
public void testDecomposition()
{
// Testing collared coupon against its decomposition...
CommonVars vars = new CommonVars();
double tolerance = 1e-10;
double npvVanilla, npvCappedLeg, npvFlooredLeg, npvCollaredLeg, npvCap, npvFloor, npvCollar;
double error;
double floorstrike = 0.05;
double capstrike = 0.10;
List <double> caps = new InitializedList <double>(vars.length, capstrike);
List <double> caps0 = new List <double>();
List <double> floors = new InitializedList <double>(vars.length, floorstrike);
List <double> floors0 = new List <double>();
double gearing_p = 0.5;
double spread_p = 0.002;
double gearing_n = -1.5;
double spread_n = 0.12;
// fixed leg with zero rate
List <CashFlow> fixedLeg = vars.makeFixedLeg(vars.startDate, vars.length);
// floating leg with gearing=1 and spread=0
List <CashFlow> floatLeg = vars.makeYoYLeg(vars.startDate, vars.length);
// floating leg with positive gearing (gearing_p) and spread<>0
List <CashFlow> floatLeg_p = vars.makeYoYLeg(vars.startDate, vars.length, gearing_p, spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
List <CashFlow> floatLeg_n = vars.makeYoYLeg(vars.startDate, vars.length, gearing_n, spread_n);
// Swap with null fixed leg and floating leg with gearing=1 and spread=0
Swap vanillaLeg = new Swap(fixedLeg, floatLeg);
// Swap with null fixed leg and floating leg with positive gearing and spread<>0
Swap vanillaLeg_p = new Swap(fixedLeg, floatLeg_p);
// Swap with null fixed leg and floating leg with negative gearing and spread<>0
Swap vanillaLeg_n = new Swap(fixedLeg, floatLeg_n);
IPricingEngine engine = new DiscountingSwapEngine(vars.nominalTS);
vanillaLeg.setPricingEngine(engine); // here use the autoset feature
vanillaLeg_p.setPricingEngine(engine);
vanillaLeg_n.setPricingEngine(engine);
// CAPPED coupon - Decomposition of payoff
// Payoff = Nom * Min(rate,strike) * accrualperiod =
// = Nom * [rate + Min(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod - Nom * Max(rate-strike,0) * accrualperiod =
// = VanillaFloatingLeg - Call
//
int whichPricer = 0;
// Case gearing = 1 and spread = 0
List <CashFlow> cappedLeg = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length,
caps, floors0, vars.volatility);
Swap capLeg = new Swap(fixedLeg, cappedLeg);
capLeg.setPricingEngine(engine);
YoYInflationCap cap = new YoYInflationCap(floatLeg, new List <double>()
{
capstrike
});
cap.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=1, spread=0%, strike=" + capstrike * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error);
}
// gearing = 1 and spread = 0
// FLOORED coupon - Decomposition of payoff
// Payoff = Nom * Max(rate,strike) * accrualperiod =
// = Nom * [rate + Max(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod + Nom * Max(strike-rate,0) * accrualperiod =
// = VanillaFloatingLeg + Put
//
List <CashFlow> flooredLeg = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length,
caps0, floors, vars.volatility);
Swap floorLeg = new Swap(fixedLeg, flooredLeg);
floorLeg.setPricingEngine(engine);
YoYInflationFloor floor = new YoYInflationFloor(floatLeg, new List <double>()
{
floorstrike
});
floor.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("YoY Floored Leg: gearing=1, spread=0%, strike=" + floorstrike * 100 +
"%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor) + "\n" +
" Diff: " + error);
}
// gearing = 1 and spread = 0
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(strikem,Max(rate,strikeM)) * accrualperiod =
// = VanillaFloatingLeg - Collar
//
List <CashFlow> collaredLeg = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length,
caps, floors, vars.volatility);
Swap collarLeg = new Swap(fixedLeg, collaredLeg);
collarLeg.setPricingEngine(engine);
YoYInflationCollar collar = new YoYInflationCollar(floatLeg,
new List <double>()
{
capstrike
},
new List <double>()
{
floorstrike
});
collar.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nYoY Collared Leg: gearing=1, spread=0%, strike=" +
floorstrike * 100 + "% and " + capstrike * 100 + "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg + "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar) + "\n" +
" Diff: " + error);
}
// gearing = a and spread = b
// CAPPED coupon - Decomposition of payoff
// Payoff
// = Nom * Min(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Min(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Min(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Call(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Min(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg + Put(|a|*rate+b,strike)
//
// Positive gearing
List <CashFlow> cappedLeg_p = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_p, spread_p);
Swap capLeg_p = new Swap(fixedLeg, cappedLeg_p);
capLeg_p.setPricingEngine(engine);
YoYInflationCap cap_p = new YoYInflationCap(floatLeg_p, new List <double>()
{
capstrike
});
cap_p.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=" + gearing_p + ", " +
"spread= " + spread_p * 100 +
"%, strike=" + capstrike * 100 + "%, " +
"effective strike= " + (capstrike - spread_p) / gearing_p * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Vanilla Leg NPV: " + npvVanilla + "\n" +
" Cap NPV: " + npvCap + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> cappedLeg_n = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_n, spread_n);
Swap capLeg_n = new Swap(fixedLeg, cappedLeg_n);
capLeg_n.setPricingEngine(engine);
YoYInflationFloor floor_n = new YoYInflationFloor(floatLeg, new List <double>()
{
(capstrike - spread_n) / gearing_n
});
floor_n.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCappedLeg = capLeg_n.NPV();
npvFloor = floor_n.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla + gearing_n * npvFloor));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n * 100 +
"%, strike=" + capstrike * 100 + "%, " +
"effective strike= " + ((capstrike - spread_n) / gearing_n * 100) +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" npv Vanilla: " + npvVanilla + "\n" +
" npvFloor: " + npvFloor + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla + gearing_n * npvFloor) + "\n" +
" Diff: " + error);
}
// gearing = a and spread = b
// FLOORED coupon - Decomposition of payoff
// Payoff
// = Nom * Max(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Max(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Max(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Put(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Max(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg - Call(|a|*rate+b,strike)
//
// Positive gearing
List <CashFlow> flooredLeg_p1 = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_p, spread_p);
Swap floorLeg_p1 = new Swap(fixedLeg, flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
YoYInflationFloor floor_p1 = new YoYInflationFloor(floatLeg_p, new List <double>()
{
floorstrike
});
floor_p1.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("\nYoY Floored Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p * 100 + "%, strike=" + floorstrike * 100 + "%, "
+ "effective strike= " + (floorstrike - spread_p) / gearing_p * 100
+ "%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg
+ "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor)
+ "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> flooredLeg_n = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_n, spread_n);
Swap floorLeg_n = new Swap(fixedLeg, flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
YoYInflationCap cap_n = new YoYInflationCap(floatLeg, new List <double>()
{
(floorstrike - spread_n) / gearing_n
});
cap_n.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvFlooredLeg = floorLeg_n.NPV();
npvCap = cap_n.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla - gearing_n * npvCap));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n * 100 +
"%, strike=" + floorstrike * 100 + "%, " +
"effective strike= " + (floorstrike - spread_n) / gearing_n * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - gearing_n * npvCap) + "\n" +
" Diff: " + error);
}
// gearing = a and spread = b
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(caprate,Max(a*rate+b,floorrate)) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Collar(a*rate+b, floorrate, caprate)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Collar(|a|*rate+b, caprate, floorrate)
//
// Positive gearing
List <CashFlow> collaredLeg_p = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_p, spread_p);
Swap collarLeg_p1 = new Swap(fixedLeg, collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
YoYInflationCollar collar_p = new YoYInflationCollar(floatLeg_p,
new List <double>()
{
capstrike
},
new List <double>()
{
floorstrike
});
collar_p.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nYoY Collared Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p * 100 + "%, strike="
+ floorstrike * 100 + "% and " + capstrike * 100
+ "%, "
+ "effective strike=" + (floorstrike - spread_p) / gearing_p * 100
+ "% and " + (capstrike - spread_p) / gearing_p * 100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar)
+ "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> collaredLeg_n = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_n, spread_n);
Swap collarLeg_n1 = new Swap(fixedLeg, collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
YoYInflationCollar collar_n = new YoYInflationCollar(floatLeg,
new List <double>()
{
(floorstrike - spread_n) / gearing_n
},
new List <double>()
{
(capstrike - spread_n) / gearing_n
});
collar_n.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCollaredLeg = collarLeg_n1.NPV();
npvCollar = collar_n.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - gearing_n * npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nYoY Collared Leg: gearing=" + gearing_n + ", "
+ "spread= " + spread_n * 100 + "%, strike="
+ floorstrike * 100 + "% and " + capstrike * 100
+ "%, "
+ "effective strike=" + (floorstrike - spread_n) / gearing_n * 100
+ "% and " + (capstrike - spread_n) / gearing_n * 100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - gearing_n * npvCollar)
+ "\n" +
" Diff: " + error);
}
// remove circular refernce
vars.hy.linkTo(null);
}
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)
{
Assert.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)
{
Assert.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(new YoYInflationTermStructure());
}