/// <summary>
/// Compute the SABR implied volatility at a user defined asset price,
/// exercise time and strike.
/// </summary>
/// <param name="assetPrice">Price of the relevant asset.
/// Precondition: assetPrice > 0.0.</param>
/// <param name="exerciseTime">Time to option exercise.
/// Precondition: exerciseTime > 0.0.</param>
/// <param name="strike">Option strike price.
/// Precondition: strike > 0.0.</param>
/// <param name="errorMessage">Container for any possible error
/// message.</param>
/// <param name="result">Container to store the result(SABR implied
/// volatility.</param>
/// <param name="checkImpliedVolParameters">If set to <c>true</c> then
/// a check of the implied volatility parameters is performed.</param>
/// <returns>
/// True if SABR implied volatility computed, else
/// false.
/// </returns>
public bool SABRInterpolatedVolatility(double assetPrice,
double exerciseTime,
double strike,
ref string errorMessage,
ref double result,
bool checkImpliedVolParameters)
{
// Declare and initialise the return variable.
var success = false;
// Ensure that asset parameters are checked only if required.
var areAssetParametersValid = true;
if (checkImpliedVolParameters)
{
areAssetParametersValid =
ImpliedVolatilityParameters.CheckImpliedVolatilityParameters(
assetPrice, exerciseTime, strike, ref errorMessage);
}
if (areAssetParametersValid)
{
// Valid asset parameters: compute the SABR interpolated
// volatility.
var z = ComputeZ(assetPrice, strike);
var x = ComputeX(z);
result = ComputeSigma(assetPrice, exerciseTime, strike, x, z);
// Update the return variable to indicate successful completion.
success = true;
errorMessage = "";
}
return(success);
}
/// <summary>
/// Tests the static method CheckExerciseTime.
/// </summary>
public void TestCheckExerciseTime()
{
_exerciseTime = -5.0d;
_isValidImpliedVolatilityParameter =
ImpliedVolatilityParameters.CheckExerciseTime(_exerciseTime,
ref _errorMessage);
const string expected = "Exercise time cannot be negative.";
Assert.IsFalse(_isValidImpliedVolatilityParameter);
Assert.AreEqual(expected, _errorMessage);
}
public void TestCheckStrike()
{
_strike = 0.0d;
_isValidImpliedVolatilityParameter =
ImpliedVolatilityParameters.CheckStrike(_strike,
ref _errorMessage);
const string expected = "Strike must be positive.";
Assert.IsFalse(_isValidImpliedVolatilityParameter);
Assert.AreEqual(expected, _errorMessage);
}
public void TestCheckAssetPrice()
{
_assetPrice = -3.98d / 100.0d;
_isValidImpliedVolatilityParameter =
ImpliedVolatilityParameters.CheckAssetPrice(_assetPrice,
ref _errorMessage);
const string expected = "Asset price must be positive.";
Assert.IsFalse(_isValidImpliedVolatilityParameter);
Assert.AreEqual(expected, _errorMessage);
}
