private void AssertStandDevEqualsVolSquRootTimeToMaturity(MultiFactorSpotSimResults <Day> simResults)
{
for (int i = 0; i < simResults.NumSteps; i++)
{
ReadOnlyMemory <double> simulatedSpotPrices =
simResults.SpotPricesForStepIndex(i);
Day period = simResults.SimulatedPeriods[i];
double factorVolForPeriod = _singleNonMeanRevertingFactorParams.Factors.Single().Volatility[period];
double timeToMaturity = TimeFunctions.Act365(_currentDate, period.Start);
double expectedLogStanDev = factorVolForPeriod * Math.Sqrt(timeToMaturity);
double simulatedLogStanDev = LogStandardDeviation(simulatedSpotPrices.Span);
double percentageError = Math.Abs((simulatedLogStanDev - expectedLogStanDev) / expectedLogStanDev);
Assert.LessOrEqual(percentageError, 0.001);
}
}
public void Simulate_ZeroVolatility_PricesEqualForwardCurve()
{
MultiFactorSpotSimResults <Day> simResults = SimulateForZeroVolatility();
IReadOnlyList <Day> simulatedPeriods = simResults.SimulatedPeriods;
for (int periodIndex = 0; periodIndex < simulatedPeriods.Count; periodIndex++)
{
double forwardPrice = _dailyForwardCurve[simulatedPeriods[periodIndex]];
ReadOnlyMemory <double> simulatedSpotPrices = simResults.SpotPricesForStepIndex(periodIndex);
for (int simIndex = 0; simIndex < simulatedSpotPrices.Length; simIndex++)
{
Assert.AreEqual(forwardPrice, simulatedSpotPrices.Span[simIndex]);
}
}
}
private static void MeanRevertingFactorsAverageWithin3StanDevsOfZero(MultiFactorSpotSimResults <Day> simResults)
{
AssertWithin3StanDevsOfExpectedValueValue(
simResults.MarkovFactorsForStepIndex(0, 1).Span, 0.0);
AssertWithin3StanDevsOfExpectedValueValue(
simResults.MarkovFactorsForStepIndex(0, 2).Span, 0.0);
AssertWithin3StanDevsOfExpectedValueValue(
simResults.MarkovFactorsForStepIndex(1, 1).Span, 0.0);
AssertWithin3StanDevsOfExpectedValueValue(
simResults.MarkovFactorsForStepIndex(1, 2).Span, 0.0);
AssertWithin3StanDevsOfExpectedValueValue(
simResults.MarkovFactorsForPeriod(new Day(2021, 07, 30), 1).Span, 0.0);
AssertWithin3StanDevsOfExpectedValueValue(
simResults.MarkovFactorsForPeriod(new Day(2021, 07, 30), 2).Span, 0.0);
}
public MultiFactorSpotPriceSimulatorTest()
{
_seed = 12;
_currentDate = new DateTime(2020, 07, 27);
_dailyForwardCurve = new Dictionary <Day, double>
{
{ new Day(2020, 08, 01), 56.85 },
{ new Day(2021, 01, 15), 59.08 },
{ new Day(2021, 07, 30), 62.453 }
};
_meanAndNonMeanRevertingFactorsResultsAntithetic = SimulateForMeanAndNonMeanRevertingFactors(true);
_meanAndNonMeanRevertingFactorsResultsNotAntithetic = SimulateForMeanAndNonMeanRevertingFactors(false);
_twoNonMeanRevertingFactorsResultsAntithetic = SimulateForTwoNonMeanRevertingFactors(true);
_twoNonMeanRevertingFactorsResultsNotAntithetic = SimulateForTwoNonMeanRevertingFactors(false);
_singleNonMeanRevertingFactorResultsAntithetic = SimulateForSingleNonMeanRevertingFactor(true);
_singleNonMeanRevertingFactorResultsNotAntithetic = SimulateForSingleNonMeanRevertingFactor(false);
}
private static void AssertAverageSimSpotPricesWithin3StanDevsOfForwardPrice <T>(MultiFactorSpotSimResults <T> simResults, Dictionary <T, double> forwardCurve)
where T : ITimePeriod <T>
{
IReadOnlyList <T> simulatedPeriods = simResults.SimulatedPeriods;
for (int periodIndex = 0; periodIndex < simulatedPeriods.Count; periodIndex++)
{
double forwardPrice = forwardCurve[simulatedPeriods[periodIndex]];
ReadOnlyMemory <double> simulatedSpotPrices = simResults.SpotPricesForStepIndex(periodIndex);
AssertWithin3StanDevsOfExpectedValueValue(simulatedSpotPrices.Span, forwardPrice);
}
}
