public void testCapletPricing()
{
//"Testing caplet pricing...";
//SavedSettings backup;
const int size = 10;
#if QL_USE_INDEXED_COUPON
const double tolerance = 1e-5;
#else
const double tolerance = 1e-12;
#endif
IborIndex index = makeIndex();
LiborForwardModelProcess process = new LiborForwardModelProcess(size, index);
// set-up pricing engine
OptionletVolatilityStructure capVolCurve = makeCapVolCurve(Settings.evaluationDate());
Vector variances = new LfmHullWhiteParameterization(process, capVolCurve).covariance(0.0, null).diagonal();
LmVolatilityModel volaModel = new LmFixedVolatilityModel(Vector.Sqrt(variances), process.fixingTimes());
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.3);
IAffineModel model = (IAffineModel)(new LiborForwardModel(process, volaModel, corrModel));
Handle <YieldTermStructure> termStructure = process.index().forwardingTermStructure();
AnalyticCapFloorEngine engine1 = new AnalyticCapFloorEngine(model, termStructure);
Cap cap1 = new Cap(process.cashFlows(),
new InitializedList <double>(size, 0.04));
cap1.setPricingEngine(engine1);
const double expected = 0.015853935178;
double calculated = cap1.NPV();
if (Math.Abs(expected - calculated) > tolerance)
{
Assert.Fail("Failed to reproduce npv"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
}
public void testDecomposition()
{
// Testing collared coupon against its decomposition
CommonVars vars = new CommonVars();
double tolerance = 1e-12;
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.makeFloatingLeg(vars.startDate, vars.length);
// floating leg with positive gearing (gearing_p) and spread<>0
List <CashFlow> floatLeg_p = vars.makeFloatingLeg(vars.startDate, vars.length, gearing_p, spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
List <CashFlow> floatLeg_n = vars.makeFloatingLeg(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.termStructure);
vanillaLeg.setPricingEngine(engine);
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
*/
// Case gearing = 1 and spread = 0
List <CashFlow> cappedLeg = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors0, vars.volatility);
Swap capLeg = new Swap(fixedLeg, cappedLeg);
capLeg.setPricingEngine(engine);
Cap cap = new Cap(floatLeg, new InitializedList <double>(1, capstrike));
cap.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nCapped 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.makeCapFlooredLeg(vars.startDate, vars.length, caps0, floors, vars.volatility);
Swap floorLeg = new Swap(fixedLeg, flooredLeg);
floorLeg.setPricingEngine(engine);
Floor floor = new Floor(floatLeg, new InitializedList <double>(1, floorstrike));
floor.setPricingEngine(vars.makeEngine(vars.volatility));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("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.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors, vars.volatility);
Swap collarLeg = new Swap(fixedLeg, collaredLeg);
collarLeg.setPricingEngine(engine);
Collar collar = new Collar(floatLeg, new InitializedList <double>(1, capstrike),
new InitializedList <double>(1, floorstrike));
collar.setPricingEngine(vars.makeEngine(vars.volatility));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nCollared 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.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_p, spread_p);
Swap capLeg_p = new Swap(fixedLeg, cappedLeg_p);
capLeg_p.setPricingEngine(engine);
Cap cap_p = new Cap(floatLeg_p, new InitializedList <double>(1, capstrike));
cap_p.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nCapped 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.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_n, spread_n);
Swap capLeg_n = new Swap(fixedLeg, cappedLeg_n);
capLeg_n.setPricingEngine(engine);
Floor floor_n = new Floor(floatLeg, new InitializedList <double>(1, (capstrike - spread_n) / gearing_n));
floor_n.setPricingEngine(vars.makeEngine(vars.volatility));
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("\nCapped 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.makeCapFlooredLeg(vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_p, spread_p);
Swap floorLeg_p1 = new Swap(fixedLeg, flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
Floor floor_p1 = new Floor(floatLeg_p, new InitializedList <double>(1, floorstrike));
floor_p1.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("\nFloored 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.makeCapFlooredLeg(vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_n, spread_n);
Swap floorLeg_n = new Swap(fixedLeg, flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
Cap cap_n = new Cap(floatLeg, new InitializedList <double>(1, (floorstrike - spread_n) / gearing_n));
cap_n.setPricingEngine(vars.makeEngine(vars.volatility));
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("\nCapped 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.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_p, spread_p);
Swap collarLeg_p1 = new Swap(fixedLeg, collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
Collar collar_p = new Collar(floatLeg_p, new InitializedList <double>(1, capstrike),
new InitializedList <double>(1, floorstrike));
collar_p.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nCollared 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.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_n, spread_n);
Swap collarLeg_n1 = new Swap(fixedLeg, collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
Collar collar_n = new Collar(floatLeg, new InitializedList <double>(1, (floorstrike - spread_n) / gearing_n),
new InitializedList <double>(1, (capstrike - spread_n) / gearing_n));
collar_n.setPricingEngine(vars.makeEngine(vars.volatility));
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("\nCollared 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);
}
}
public void testCapletPricing()
{
//"Testing caplet pricing...";
//SavedSettings backup;
const int size = 10;
#if QL_USE_INDEXED_COUPON
const double tolerance = 1e-5;
#else
const double tolerance = 1e-12;
#endif
IborIndex index = makeIndex();
LiborForwardModelProcess process=new LiborForwardModelProcess(size, index);
// set-up pricing engine
OptionletVolatilityStructure capVolCurve = makeCapVolCurve(Settings.evaluationDate());
Vector variances = new LfmHullWhiteParameterization(process, capVolCurve).covariance(0.0,null).diagonal();
LmVolatilityModel volaModel = new LmFixedVolatilityModel(Vector.Sqrt(variances),process.fixingTimes());
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.3);
IAffineModel model = (IAffineModel)(new LiborForwardModel(process, volaModel, corrModel));
Handle<YieldTermStructure> termStructure = process.index().forwardingTermStructure();
AnalyticCapFloorEngine engine1 = new AnalyticCapFloorEngine(model, termStructure);
Cap cap1 = new Cap( process.cashFlows(),
new InitializedList<double>(size, 0.04));
cap1.setPricingEngine(engine1);
const double expected = 0.015853935178;
double calculated = cap1.NPV();
if (Math.Abs(expected - calculated) > tolerance)
Assert.Fail("Failed to reproduce npv"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}