public void GetForwardVolga_TestCase_ViaDifferentialQuotientApproximation(ConstantVolatilityStandardEuropeanOptionConfiguration optionConfiguration)
{
var optionUnderTest = CreateOption(optionConfiguration.Strike, optionConfiguration.Forward, optionConfiguration.TimeToExpiry, optionConfiguration.DiscountFactor);
double actualVolga = optionUnderTest.GetVolga(optionConfiguration.Volatility);
double expectedVolga = DifferentialQuotientGreekApproximation.GetOptionVolga(optionConfiguration, (K, F, t, df, sigma) => CreateOption(K, F, t, df).GetValue(sigma));
Assert.That(actualVolga, Is.EqualTo(expectedVolga).Within(1E-4), optionUnderTest.ToString());
}
/// <summary>Gets the option kappa, i.e. strike-delta.
/// </summary>
/// <param name="optionParameters">The parameters of the option.</param>
/// <param name="getOptionValue">A delegate that calculates the value of the option for specified parameters.</param>
/// <returns>A approximation of the kappa.</returns>
public static double GetOptionKappa(ConstantVolatilityStandardEuropeanOptionConfiguration optionParameters, GetOptionValue getOptionValue)
{
double h = 0.0000001;
double value1 = getOptionValue(optionParameters.Strike + h, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility);
double value2 = getOptionValue(optionParameters.Strike, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility);
return((value1 - value2) / h);
}
/// <summary>Gets the Forward-Vanna of the option, i.e. the derivative \partial^2/ {\partial \sigma \partial F} of the option value.
/// </summary>
/// <param name="optionParameters">The parameters of the option.</param>
/// <param name="getOptionValue">A delegate that calculates the value of the option for specified parameters.</param>
/// <returns>A approximation of the gamma.</returns>
public static double GetOptionForwardVanna(ConstantVolatilityStandardEuropeanOptionConfiguration optionParameters, GetOptionValue getOptionValue)
{
double h = 0.00005; // should be not too small, otherwise one get numerical problems
double k = 0.00005;
double value = getOptionValue(optionParameters.Strike, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility);
double valuePlusHPlusK = getOptionValue(optionParameters.Strike, optionParameters.Forward + k, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility + h);
double valuePlusHMinusK = getOptionValue(optionParameters.Strike, optionParameters.Forward - k, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility + h);
double valueMinusHPlusK = getOptionValue(optionParameters.Strike, optionParameters.Forward + k, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility - h);
double valueMinusHMinusK = getOptionValue(optionParameters.Strike, optionParameters.Forward - k, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility - h);
return((valuePlusHPlusK - valuePlusHMinusK - valueMinusHPlusK + valueMinusHMinusK) / (4.0 * h * k));
}
public void TryGetImpliedVolatility_ComputedOptionValue_Volatility(ConstantVolatilityStandardEuropeanOptionConfiguration optionConfiguration)
{
var optionUnderTest = CreateOption(optionConfiguration.Strike, optionConfiguration.Forward, optionConfiguration.TimeToExpiry, optionConfiguration.DiscountFactor);
double optionValue = optionUnderTest.GetValue(optionConfiguration.Volatility);
Assume.That(IsVolatilityInvertibleOptionValue(optionValue, optionUnderTest) == true, String.Format("Option value {0} can not be inverted; intrinsic value {1}", optionValue, optionUnderTest.GetIntrinsicValue()));
double actualImpliedVolatility;
Assert.That(optionUnderTest.TryGetImpliedVolatility(optionValue, out actualImpliedVolatility), Is.EqualTo(ImpliedCalculationResultState.ProperResult), String.Format("Option value was: {0}, Intrinsic value: {1}.", optionValue, optionUnderTest.GetIntrinsicValue()));
Assert.That(actualImpliedVolatility, Is.EqualTo(optionConfiguration.Volatility).Within(1E-8), String.Format("Option value was: {0}, Intrinsic value: {1}", optionValue, optionUnderTest.GetIntrinsicValue()));
}
/// <summary>Gets the Volga of the option, i.e. the second derivative with respect to the volatilty.
/// </summary>
/// <param name="optionParameters">The parameters of the option.</param>
/// <param name="getOptionValue">A delegate that calculates the value of the option for specified parameters.</param>
/// <returns>A approximation of the volga.</returns>
public static double GetOptionVolga(ConstantVolatilityStandardEuropeanOptionConfiguration optionParameters, GetOptionValue getOptionValue)
{
double h = 0.00005; // should be not too small, otherwise one get numerical problems
double value = getOptionValue(optionParameters.Strike, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility);
double valueMinusH = getOptionValue(optionParameters.Strike, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility - h);
double valueMinus2H = getOptionValue(optionParameters.Strike, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility - 2.0 * h);
double valuePlusH = getOptionValue(optionParameters.Strike, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility + h);
double valuePlus2H = getOptionValue(optionParameters.Strike, optionParameters.Forward, optionParameters.TimeToExpiry, optionParameters.DiscountFactor, optionParameters.Volatility + 2.0 * h);
/* approximation of the second derivative: (Richardson's extrapolation)
* f''(x) \approx [-f(x-2h) + 16 * f(x-h) - 30 * f(x) + 16 * f(x+h) - f(x+2h)] / (12 * h^2)
*/
return((-valueMinus2H + 16.0 * valueMinusH - 30.0 * value + 16.0 * valuePlusH - valuePlus2H) / (12 * h * h));
}
