public void testPutCallParity()
{
// Testing put-call parity for deltas
// Test for put call parity between put and call deltas.
SavedSettings backup = new SavedSettings();
/* The data below are from
* "Option pricing formulas", E.G. Haug, McGraw-Hill 1998
* pag 11-16
*/
EuropeanOptionData[] values =
{
// pag 2-8
// type, strike, spot, q, r, t, vol, value, tol
new EuropeanOptionData(Option.Type.Call, 65.00, 60.00, 0.00, 0.08, 0.25, 0.30, 2.1334, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 95.00, 100.00, 0.05, 0.10, 0.50, 0.20, 2.4648, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 19.00, 19.00, 0.10, 0.10, 0.75, 0.28, 1.7011, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 19.00, 19.00, 0.10, 0.10, 0.75, 0.28, 1.7011, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 1.60, 1.56, 0.08, 0.06, 0.50, 0.12, 0.0291, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 70.00, 75.00, 0.05, 0.10, 0.50, 0.35, 4.0870, 1.0e-4),
// pag 24
new EuropeanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 0.0205, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8734, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 9.9413, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 0.3150, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1217, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 10.3556, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 0.9474, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3693, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 11.1381, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 0.8069, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0232, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 10.5769, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 2.7026, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.6997, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 12.7857, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 4.9329, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.3679, 1.0e-4),
new EuropeanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 15.3086, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 9.9210, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8734, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 0.0408, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 10.2155, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1217, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 0.4551, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 10.8479, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3693, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 1.2376, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 10.3192, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0232, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 1.0646, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 12.2149, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.6997, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 3.2734, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 14.4452, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.3679, 1.0e-4),
new EuropeanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 5.7963, 1.0e-4),
// pag 27
new EuropeanOptionData(Option.Type.Call, 40.00, 42.00, 0.08, 0.04, 0.75, 0.35, 5.0975, 1.0e-4)
};
DayCounter dc = new Actual360();
Calendar calendar = new TARGET();
Date today = Date.Today;
double discFor = 0.0;
double discDom = 0.0;
double implVol = 0.0;
double deltaCall = 0.0;
double deltaPut = 0.0;
double expectedDiff = 0.0;
double calculatedDiff = 0.0;
double error = 0.0;
double forward = 0.0;
SimpleQuote spotQuote = new SimpleQuote(0.0);
SimpleQuote qQuote = new SimpleQuote(0.0);
Handle <Quote> qHandle = new Handle <Quote>(qQuote);
YieldTermStructure qTS = new FlatForward(today, qHandle, dc);
SimpleQuote rQuote = new SimpleQuote(0.0);
Handle <Quote> rHandle = new Handle <Quote>(qQuote);
YieldTermStructure rTS = new FlatForward(today, rHandle, dc);
SimpleQuote volQuote = new SimpleQuote(0.0);
Handle <Quote> volHandle = new Handle <Quote>(volQuote);
BlackVolTermStructure volTS = new BlackConstantVol(today, calendar, volHandle, dc);
StrikedTypePayoff payoff;
Date exDate;
Exercise exercise;
double tolerance = 1.0e-10;
for (int i = 0; i < values.Length; ++i)
{
payoff = new PlainVanillaPayoff(Option.Type.Call, values[i].strike);
exDate = today + timeToDays(values[i].t);
exercise = new EuropeanExercise(exDate);
spotQuote.setValue(values[i].s);
volQuote.setValue(values[i].v);
rQuote.setValue(values[i].r);
qQuote.setValue(values[i].q);
discDom = rTS.discount(exDate);
discFor = qTS.discount(exDate);
implVol = Math.Sqrt(volTS.blackVariance(exDate, 0.0));
forward = spotQuote.value() * discFor / discDom;
BlackDeltaCalculator myCalc = new BlackDeltaCalculator(Option.Type.Call, DeltaVolQuote.DeltaType.Spot,
spotQuote.value(), discDom, discFor, implVol);
deltaCall = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Put);
deltaPut = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Call);
expectedDiff = discFor;
calculatedDiff = deltaCall - deltaPut;
error = Math.Abs(expectedDiff - calculatedDiff);
if (error > tolerance)
{
QAssert.Fail("\n Put-call parity failed for spot delta. \n"
+ "Calculated Call Delta: " + deltaCall + "\n"
+ "Calculated Put Delta: " + deltaPut + "\n"
+ "Expected Difference: " + expectedDiff + "\n"
+ "Calculated Difference: " + calculatedDiff);
}
myCalc.setDeltaType(DeltaVolQuote.DeltaType.Fwd);
deltaCall = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Put);
deltaPut = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Call);
expectedDiff = 1.0;
calculatedDiff = deltaCall - deltaPut;
error = Math.Abs(expectedDiff - calculatedDiff);
if (error > tolerance)
{
QAssert.Fail("\n Put-call parity failed for forward delta. \n"
+ "Calculated Call Delta: " + deltaCall + "\n"
+ "Calculated Put Delta: " + deltaPut + "\n"
+ "Expected Difference: " + expectedDiff + "\n"
+ "Calculated Difference: " + calculatedDiff);
}
myCalc.setDeltaType(DeltaVolQuote.DeltaType.PaSpot);
deltaCall = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Put);
deltaPut = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Call);
expectedDiff = discFor * values[i].strike / forward;
calculatedDiff = deltaCall - deltaPut;
error = Math.Abs(expectedDiff - calculatedDiff);
if (error > tolerance)
{
QAssert.Fail("\n Put-call parity failed for premium-adjusted spot delta. \n"
+ "Calculated Call Delta: " + deltaCall + "\n"
+ "Calculated Put Delta: " + deltaPut + "\n"
+ "Expected Difference: " + expectedDiff + "\n"
+ "Calculated Difference: " + calculatedDiff);
}
myCalc.setDeltaType(DeltaVolQuote.DeltaType.PaFwd);
deltaCall = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Put);
deltaPut = myCalc.deltaFromStrike(values[i].strike);
myCalc.setOptionType(Option.Type.Call);
expectedDiff = values[i].strike / forward;
calculatedDiff = deltaCall - deltaPut;
error = Math.Abs(expectedDiff - calculatedDiff);
if (error > tolerance)
{
QAssert.Fail("\n Put-call parity failed for premium-adjusted forward delta. \n"
+ "Calculated Call Delta: " + deltaCall + "\n"
+ "Calculated Put Delta: " + deltaPut + "\n"
+ "Expected Difference: " + expectedDiff + "\n"
+ "Calculated Difference: " + calculatedDiff);
}
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(BlackConstantVol obj) {
return (obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr;
}
public void testDeltaPriceConsistency()
{
// Testing premium-adjusted delta price consistency
// This function tests for price consistencies with the standard
// Black Scholes calculator, since premium adjusted deltas can be calculated
// from spot deltas by adding/subtracting the premium.
SavedSettings backup = new SavedSettings();
// actually, value and tol won't be needed for testing
EuropeanOptionData[] values =
{
// type, strike, spot, rd, rf, t, vol, value, tol
new EuropeanOptionData(Option.Type.Call, 0.9123, 1.2212, 0.0231, 0.0000, 0.25, 0.301, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 0.9234, 1.2212, 0.0231, 0.0000, 0.35, 0.111, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 0.9783, 1.2212, 0.0231, 0.0000, 0.45, 0.071, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 1.0000, 1.2212, 0.0231, 0.0000, 0.55, 0.082, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 1.1230, 1.2212, 0.0231, 0.0000, 0.65, 0.012, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 1.2212, 1.2212, 0.0231, 0.0000, 0.75, 0.129, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 1.3212, 1.2212, 0.0231, 0.0000, 0.85, 0.034, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 1.3923, 1.2212, 0.0131, 0.2344, 0.95, 0.001, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Call, 1.3455, 1.2212, 0.0000, 0.0000, 1.00, 0.127, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 0.9123, 1.2212, 0.0231, 0.0000, 0.25, 0.301, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 0.9234, 1.2212, 0.0231, 0.0000, 0.35, 0.111, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 0.9783, 1.2212, 0.0231, 0.0000, 0.45, 0.071, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 1.0000, 1.2212, 0.0231, 0.0000, 0.55, 0.082, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 1.1230, 1.2212, 0.0231, 0.0000, 0.65, 0.012, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 1.2212, 1.2212, 0.0231, 0.0000, 0.75, 0.129, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 1.3212, 1.2212, 0.0231, 0.0000, 0.85, 0.034, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 1.3923, 1.2212, 0.0131, 0.2344, 0.95, 0.001, 0.0, 0.0),
new EuropeanOptionData(Option.Type.Put, 1.3455, 1.2212, 0.0000, 0.0000, 1.00, 0.127, 0.0, 0.0),
// extreme case: zero vol
new EuropeanOptionData(Option.Type.Put, 1.3455, 1.2212, 0.0000, 0.0000, 0.50, 0.000, 0.0, 0.0),
// extreme case: zero strike
new EuropeanOptionData(Option.Type.Put, 0.0000, 1.2212, 0.0000, 0.0000, 1.50, 0.133, 0.0, 0.0),
// extreme case: zero strike+zero vol
new EuropeanOptionData(Option.Type.Put, 0.0000, 1.2212, 0.0000, 0.0000, 1.00, 0.133, 0.0, 0.0),
};
DayCounter dc = new Actual360();
Calendar calendar = new TARGET();
Date today = Date.Today;
// Start setup of market data
double discFor = 0.0;
double discDom = 0.0;
double implVol = 0.0;
double expectedVal = 0.0;
double calculatedVal = 0.0;
double error = 0.0;
SimpleQuote spotQuote = new SimpleQuote(0.0);
Handle <Quote> spotHandle = new Handle <Quote>(spotQuote);
SimpleQuote qQuote = new SimpleQuote(0.0);
Handle <Quote> qHandle = new Handle <Quote>(qQuote);
YieldTermStructure qTS = new FlatForward(today, qHandle, dc);
SimpleQuote rQuote = new SimpleQuote(0.0);
Handle <Quote> rHandle = new Handle <Quote>(qQuote);
YieldTermStructure rTS = new FlatForward(today, rHandle, dc);
SimpleQuote volQuote = new SimpleQuote(0.0);
Handle <Quote> volHandle = new Handle <Quote>(volQuote);
BlackVolTermStructure volTS = new BlackConstantVol(today, calendar, volHandle, dc);
BlackScholesMertonProcess stochProcess;
IPricingEngine engine;
StrikedTypePayoff payoff;
Date exDate;
Exercise exercise;
// Setup of market data finished
double tolerance = 1.0e-10;
for (int i = 0; i < values.Length; ++i)
{
payoff = new PlainVanillaPayoff(values[i].type, values[i].strike);
exDate = today + timeToDays(values[i].t);
exercise = new EuropeanExercise(exDate);
spotQuote.setValue(values[i].s);
volQuote.setValue(values[i].v);
rQuote.setValue(values[i].r);
qQuote.setValue(values[i].q);
discDom = rTS.discount(exDate);
discFor = qTS.discount(exDate);
implVol = Math.Sqrt(volTS.blackVariance(exDate, 0.0));
BlackDeltaCalculator myCalc = new BlackDeltaCalculator(values[i].type, DeltaVolQuote.DeltaType.PaSpot,
spotQuote.value(), discDom, discFor, implVol);
stochProcess = new BlackScholesMertonProcess(spotHandle,
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
engine = new AnalyticEuropeanEngine(stochProcess);
EuropeanOption option = new EuropeanOption(payoff, exercise);
option.setPricingEngine(engine);
calculatedVal = myCalc.deltaFromStrike(values[i].strike);
expectedVal = option.delta() - option.NPV() / spotQuote.value();
error = Math.Abs(expectedVal - calculatedVal);
if (error > tolerance)
{
QAssert.Fail("\n Premium-adjusted spot delta test failed. \n"
+ "Calculated Delta: " + calculatedVal + "\n"
+ "Expected Value: " + expectedVal + "\n"
+ "Error: " + error);
}
myCalc.setDeltaType(DeltaVolQuote.DeltaType.PaFwd);
calculatedVal = myCalc.deltaFromStrike(values[i].strike);
expectedVal = expectedVal / discFor; // Premium adjusted Fwd Delta is PA spot without discount
error = Math.Abs(expectedVal - calculatedVal);
if (error > tolerance)
{
QAssert.Fail("\n Premium-adjusted forward delta test failed. \n"
+ "Calculated Delta: " + calculatedVal + "\n"
+ "Expected Value: " + expectedVal + "\n"
+ "Error: " + error);
}
// Test consistency with BlackScholes Calculator for Spot Delta
myCalc.setDeltaType(DeltaVolQuote.DeltaType.Spot);
calculatedVal = myCalc.deltaFromStrike(values[i].strike);
expectedVal = option.delta();
error = Math.Abs(calculatedVal - expectedVal);
if (error > tolerance)
{
QAssert.Fail("\n spot delta in BlackDeltaCalculator differs from delta in BlackScholesCalculator. \n"
+ "Calculated Value: " + calculatedVal + "\n"
+ "Expected Value: " + expectedVal + "\n"
+ "Error: " + error);
}
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(BlackConstantVol obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}
