/// <summary>
/// AreaSpread describes areas that should be placed on the map
/// </summary>
/// <param name="id">Mapped tile id</param>
/// <param name="flag">Tile flags</param>
/// <param name="percentage">Percentage of map space covered by this flag</param>
/// <param name="minSizeInMeter">Minimum size of area in meter</param>
/// <param name="maxSizeInMeter">Maximum size of area in meter</param>
/// <param name="useEdgeNoise">Can be used to add aliasing to avoid symmetric areas</param>
/// <param name="connectEqualFlags">Areas with the same flags will be connected, all free tiles within a give distance will be set to the flag value</param>
/// <param name="connectDistance">Maximum distance between two areas with the same flag</param>
/// <param name="spreadType">Geometrical form of the area</param>
/// <param name="layer">Dicides which generation algorithm will be used</param>
public AreaSpread(ushort id, byte flag, float percentage, int minSizeInMeter, int maxSizeInMeter, bool useEdgeNoise, bool connectEqualFlags, int connectDistance, SpreadOption spreadType, LayerType layer)
{
Id = id;
Flag = flag;
Percentage = percentage;
MinSizeInMeter = minSizeInMeter;
MaxSizeInMeter = maxSizeInMeter;
UseEdgeNoise = useEdgeNoise;
SpreadType = spreadType;
Layer = layer;
ConnectEqualFlags = connectEqualFlags;
ConnectDistance = connectDistance;
}
private void SpreadOptionBjerksundCalc(string spreadType = "TwoAssetsSpread", Boolean isCall = true, string ValuationDate = "2017-12-26", double vol1 = 0.28, double spot1 = 1.0, double vol2 = 0.30, double spot2 = 2.0,
double vol3 = 0.28, double spot3 = 1.0, double vol4 = 0.28, double spot4 = 1.0, double strike = 1.03, double tol = 1e-8)
{
var valuationDate = DateFromStr(ValuationDate);
var maturityDate = new Term("176D").Next(valuationDate);
var calendar = CalendarImpl.Get("chn");
var asset1 = "asset1";
var asset2 = "asset2";
var asset3 = "asset3";
var asset4 = "asset4";
var option = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: (isCall) ? OptionType.Call : OptionType.Put,
spreadType: ToSpreadType(spreadType),
strike: strike,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var market = TestMarket(referenceDate: ValuationDate, vol1: vol1, vol2: vol2, vol3: vol3, vol4: vol4, spot1: spot1, spot2: spot2, spot3: spot3, spot4: spot4,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
var analyticalEngine = new AnalyticalSpreadOptionBjerksundEngine();
var analyticalResult = analyticalEngine.Calculate(option, market, PricingRequest.All);
var Engine = new AnalyticalSpreadOptionKirkEngine();
var Result = Engine.Calculate(option, market, PricingRequest.All);
Assert.AreEqual(analyticalResult.Pv, Result.Pv, tol);
}
private void SpreadOptionGreekCalc(double ExpectedPv, string spreadType = "TwoAssetsSpread", string ValuationDate = "2017-12-26")
{
var valuationDate = DateFromStr(ValuationDate);
var maturityDate = new Term("176D").Next(valuationDate);
var calendar = CalendarImpl.Get("chn");
var asset1 = "asset1";
var asset2 = "asset2";
var asset3 = "asset3";
var asset4 = "asset4";
var option = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: OptionType.Call,
spreadType: ToSpreadType(spreadType),
strike: 1.03,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var market = TestMarket(referenceDate: ValuationDate, asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
//var analyticalEngine = new AnalyticalSpreadOptionEngine();
//var analyticalResult = analyticalEngine.Calculate(option, market, PricingRequest.All);
var Engine = new AnalyticalSpreadOptionKirkEngine();
var Result = Engine.Calculate(option, market, PricingRequest.All);
//Assert.AreEqual(ExpectedPv, analyticalResult.Pv, 1e-8);
Assert.AreEqual(ExpectedPv, Result.Pv, 1e-8);
}
private void SpreadOptionGreekTest(double vol1 = 0.28, double vol2 = 0.30, double vol3 = 0.40, double spot1 = 4900, double spot2 = 1500, double spot3 = 1500,
string spreadType = "TwoAssetsSpread", string t0 = "2017-12-26", string t1 = "2017-12-27", double volMove = 0.10, double mktMove = 1e-4, double toleranceInPct = 2)
{
var valuationDate = DateFromStr(t0);
var maturityDate = new Term("176D").Next(valuationDate);
var calendar = CalendarImpl.Get("chn");
var spot1New = spot1 + spot1 * mktMove;
var spot2New = spot2 + spot2 * mktMove;
var spot3New = spot3 + spot3 * mktMove;
var vol1New = vol1 + volMove;
var vol2New = vol2 + volMove;
var vol3New = vol3 + volMove;
var T0 = DateFromStr(t0);
var T1 = DateFromStr(t1);
var valuationDay = t0;
var valuationDayNew = t1;
var asset1 = "asset1";
var asset2 = "asset2";
var asset3 = "asset3";
var asset4 = "asset4";
var option = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: OptionType.Call,
spreadType: ToSpreadType(spreadType),
strike: 1000,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var market = TestMarket(referenceDate: t0, vol1: vol1, vol2: vol2, vol3: vol3, spot1: spot1, spot2: spot2, spot3: spot3,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
var marketNew = TestMarket(referenceDate: t1, vol1: vol1New, vol2: vol2New, vol3: vol3New, spot1: spot1New, spot2: spot2New, spot3: spot3New,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
var marketPI = TestMarket(referenceDate: t0, vol1: vol1, vol2: vol2, vol3: vol3, spot1: spot1New, spot2: spot2New, spot3: spot3New,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
var marketVI = TestMarket(referenceDate: t0, vol1: vol1New, vol2: vol2New, vol3: vol3New, spot1: spot1, spot2: spot2, spot3: spot3,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
var marketPVC = TestMarket(referenceDate: t0, vol1: vol1New, vol2: vol2New, vol3: vol3New, spot1: spot1New, spot2: spot2New, spot3: spot3New,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
var engine = new AnalyticalSpreadOptionKirkEngine();
var result = engine.Calculate(option, market, PricingRequest.All);
var resultNew = engine.Calculate(option, marketNew, PricingRequest.All);
var resultPI = engine.Calculate(option, marketPI, PricingRequest.All);
var resultVI = engine.Calculate(option, marketVI, PricingRequest.All);
var resultPVC = engine.Calculate(option, marketPVC, PricingRequest.All);
var actualPL = resultNew.Pv - result.Pv;
//price Impact
//PI = PV(t-1, priceNew) - Pv(t-1)
var basePv = result.Pv;
var PI = resultPI.Pv - basePv;
var thetapl = result.Theta * (T1 - T0);
//vol impact
//VI = PV(t-1. volNew) - Pv (t-1)
var VI = resultVI.Pv - basePv;
//price vol cross impact
//PVC = PV(t-1. volNew, PriceNew) - Pv (t-1) - (PI+VI)
var PVC = resultPVC.Pv - basePv - PI - VI;
var newEstimate = PI + VI + PVC + thetapl;
var newUnexplained = actualPL - newEstimate;
//Time impact
//TI = PV(t, all OldInfo) - Pv(t-1)
//TODO:
//Time/ price cross Impact
//TPC = PV(t, priceNew) - pv(t-1) - (TI +PI)
//Time/vol cross impact
//TVC = PV(t, volNew) - pv(t-1) -(TI+VI)
//TODO:
//in case of big move ( vol and spot), we need high order risk to explain pnl
//var diff = actualPL - esimstatedPL;
//Assert.AreEqual(true, Math.Abs(diff / actualPL) * 100.0 < toleranceInPct); //pnl well explained in not too extreme moves
Assert.AreEqual(true, Math.Abs(newUnexplained / actualPL) * 100.0 < toleranceInPct);
}
private void SpreadVanillaCalc(string spreadType = "TwoAssetsSpread", string ValuationDate = "2017-12-26",
double spot1 = 4500, double spot2 = 2500, double strike = 2000, double vol1 = 0.5, double vol2 = 0.5, double rho12 = 0.5)
{
var valuationDate = DateFromStr(ValuationDate);
var maturityDate = new Term("176D").Next(valuationDate);
var calendar = CalendarImpl.Get("chn");
var asset1 = "asset1";
var asset2 = "asset2";
var asset3 = "asset3";
var asset4 = "asset4";
var option = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: OptionType.Call,
spreadType: ToSpreadType(spreadType),
strike: strike,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var option1 = new VanillaOption(
valuationDate,
maturityDate,
OptionExercise.European,
OptionType.Call,
2.0 * strike,
InstrumentType.EquityIndex,
calendar,
new Act365(),
CurrencyCode.CNY,
CurrencyCode.CNY,
new[] { maturityDate },
new[] { maturityDate }
);
var option2 = new VanillaOption(
valuationDate,
maturityDate,
OptionExercise.European,
OptionType.Put,
strike,
InstrumentType.EquityIndex,
calendar,
new Act365(),
CurrencyCode.CNY,
CurrencyCode.CNY,
new[] { maturityDate },
new[] { maturityDate }
);
var market = TestMarket(referenceDate: ValuationDate, vol1: vol1, vol2: vol2, vol3: 0.0, spot1: spot1, spot2: spot2, spot3: 0.0,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4, rho12: rho12, rho23: 0.0, rho13: 0.0);
var market1 = GetMarket(referenceDate: ValuationDate, vol: vol1, spot: spot1);
var market2 = GetMarket(referenceDate: ValuationDate, vol: vol2, spot: spot2);
var analyticalEngine = new AnalyticalSpreadOptionKirkEngine();
var analyticalEngine2 = new AnalyticalVanillaEuropeanOptionEngine();
var result = analyticalEngine.Calculate(option, market, PricingRequest.All);
var result1 = analyticalEngine2.Calculate(option1, market1, PricingRequest.All);
var result2 = analyticalEngine2.Calculate(option2, market2, PricingRequest.All);
Assert.AreEqual(true, result1.Pv + result2.Pv - result.Pv > 0);
}
private void SpreadOptionParity(string ValuationDate = "2017-12-26", double vol1 = 0.28, double spot1 = 1.0, double vol2 = 0.30, double spot2 = 2.0, double vol3 = 0.30, double spot3 = 2.0, double strike = 1.03)
{
var valuationDate = DateFromStr(ValuationDate);
var maturityDate = new Term("176D").Next(valuationDate);
var calendar = CalendarImpl.Get("chn");
var asset1 = "asset1";
var asset2 = "asset2";
var asset3 = "asset3";
var asset4 = "asset4";
var option1 = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: OptionType.Call,
spreadType: SpreadType.ThreeAssetsSpread,
strike: strike,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var option2 = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: OptionType.Call,
spreadType: SpreadType.FourAssetsSpread,
strike: strike,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var option3 = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: OptionType.Call,
spreadType: SpreadType.ThreeAssetsSpreadBasket,
strike: strike,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var option4 = new SpreadOption(
startDate: valuationDate,
maturityDate: maturityDate,
exercise: OptionExercise.European,
optionType: OptionType.Call,
spreadType: SpreadType.FourAssetsSpreadBasketType1,
strike: strike,
weights: new double[] { 1.0, 1.0, 1.0, 1.0 },
underlyingInstrumentType: InstrumentType.EquityIndex,
calendar: calendar,
dayCount: new Act365(),
payoffCcy: CurrencyCode.CNY,
settlementCcy: CurrencyCode.CNY,
exerciseDates: new[] { maturityDate },
observationDates: new[] { maturityDate },
underlyingTickers: new[] { asset1, asset2, asset3, asset4 }
)
{
UnderlyingTickers = new string[] { asset1, asset2, asset3, asset4 }
};
var market = TestMarket(referenceDate: ValuationDate, vol1: vol1, vol2: vol2, vol3: vol3, spot1: spot1, spot2: spot2, spot3: spot3,
asset1: asset1, asset2: asset2, asset3: asset3, asset4: asset4);
var analyticalEngine = new AnalyticalSpreadOptionKirkEngine();
var result1 = analyticalEngine.Calculate(option1, market, PricingRequest.All);
var result2 = analyticalEngine.Calculate(option2, market, PricingRequest.All);
var result3 = analyticalEngine.Calculate(option3, market, PricingRequest.All);
var result4 = analyticalEngine.Calculate(option4, market, PricingRequest.All);
var Engine = new AnalyticalSpreadOptionBjerksundEngine();
var result5 = Engine.Calculate(option1, market, PricingRequest.All);
var result6 = Engine.Calculate(option2, market, PricingRequest.All);
var result7 = Engine.Calculate(option3, market, PricingRequest.All);
var result8 = Engine.Calculate(option4, market, PricingRequest.All);
Assert.AreEqual(result1.Pv, result2.Pv, 1.0e-8);
Assert.AreEqual(result3.Pv, result4.Pv, 1.0e-8);
//Assert.AreEqual(result5.Pv, result6.Pv, 1.0e-8);
Assert.AreEqual(result7.Pv, result8.Pv, 1.0e-8);
}
public void testKirkEngine()
{
// Testing Kirk approximation for spread options
/* The example data below are from "complete guide to option
* pricing formulas", Espen Gaarder Haug, p 60
*
* Expected values of option theta were calculated using automatic
* differentiation of the pricing function. The engine uses closed-form
* formula */
Case[] cases =
{
new Case(28.0, 20.0, 7.0, 0.05, 0.29, 0.36, 0.42, 90, 2.1670, 3.0431),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.20, -0.5, 36, 4.7530, 25.5905),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.20, 0.0, 36, 3.7970, 20.8841),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.20, 0.5, 36, 2.5537, 14.7260),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.20, -0.5, 180, 10.7517, 10.0847),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.20, 0.0, 180, 8.7020, 8.2619),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.20, 0.5, 180, 6.0257, 5.8661),
new Case(122.0, 120.0, 3.0, 0.10, 0.25, 0.20, -0.5, 36, 5.4275, 28.9013),
new Case(122.0, 120.0, 3.0, 0.10, 0.25, 0.20, 0.0, 36, 4.3712, 23.7133),
new Case(122.0, 120.0, 3.0, 0.10, 0.25, 0.20, 0.5, 36, 3.0086, 16.9864),
new Case(122.0, 120.0, 3.0, 0.10, 0.25, 0.20, -0.5, 180, 12.1941, 11.3603),
new Case(122.0, 120.0, 3.0, 0.10, 0.25, 0.20, 0.0, 180, 9.9340, 9.3589),
new Case(122.0, 120.0, 3.0, 0.10, 0.25, 0.20, 0.5, 180, 7.0067, 6.7463),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.25, -0.5, 36, 5.4061, 28.7963),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.25, 0.0, 36, 4.3451, 23.5848),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.25, 0.5, 36, 2.9723, 16.8060),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.25, -0.5, 180, 12.1483, 11.3200),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.25, 0.0, 180, 9.8780, 9.3091),
new Case(122.0, 120.0, 3.0, 0.10, 0.20, 0.25, 0.5, 180, 6.9284, 6.6761)
};
for (int i = 0; i < cases.Length; ++i)
{
// First step: preparing the test values
// Useful dates
DayCounter dc = new Actual360();
Date today = Date.Today;
Date exerciseDate = today + cases[i].length;
// Futures values
SimpleQuote F1 = new SimpleQuote(cases[i].F1);
SimpleQuote F2 = new SimpleQuote(cases[i].F2);
// Risk-free interest rate
double riskFreeRate = cases[i].r;
YieldTermStructure forwardRate = Utilities.flatRate(today, riskFreeRate, dc);
// Correlation
Quote rho = new SimpleQuote(cases[i].rho);
// Volatilities
double vol1 = cases[i].sigma1;
double vol2 = cases[i].sigma2;
BlackVolTermStructure volTS1 = Utilities.flatVol(today, vol1, dc);
BlackVolTermStructure volTS2 = Utilities.flatVol(today, vol2, dc);
// Black-Scholes Processes
// The BlackProcess is the relevant class for futures contracts
BlackProcess stochProcess1 = new BlackProcess(new Handle <Quote>(F1),
new Handle <YieldTermStructure>(forwardRate),
new Handle <BlackVolTermStructure>(volTS1));
BlackProcess stochProcess2 = new BlackProcess(new Handle <Quote>(F2),
new Handle <YieldTermStructure>(forwardRate),
new Handle <BlackVolTermStructure>(volTS2));
// Creating the pricing engine
IPricingEngine engine = new KirkSpreadOptionEngine(stochProcess1,
stochProcess2, new Handle <Quote>(rho));
// Finally, create the option:
Option.Type type = Option.Type.Call;
double strike = cases[i].X;
PlainVanillaPayoff payoff = new PlainVanillaPayoff(type, strike);
Exercise exercise = new EuropeanExercise(exerciseDate);
SpreadOption option = new SpreadOption(payoff, exercise);
option.setPricingEngine(engine);
// And test the data
double value = option.NPV();
double theta = option.theta();
double tolerance = 1e-4;
if (Math.Abs(value - cases[i].value) > tolerance)
{
REPORT_FAILURE("value",
payoff, exercise,
cases[i].value, value, tolerance, today);
}
if (Math.Abs(theta - cases[i].theta) > tolerance)
{
REPORT_FAILURE("theta",
payoff, exercise,
cases[i].theta, theta, tolerance, today);
}
}
}
