/// <summary>
/// Values at.
/// </summary>
/// <param name="axisValue">The axis value.</param>
/// <param name="extrapolation">if set to <c>true</c> [extrapolation].</param>
/// <returns></returns>
public double ValueAt(double axisValue, bool extrapolation)
{
string engineHandle = SettingsHandle;
decimal time = Convert.ToDecimal(ExpiryTime);
const decimal tenor = 0;
var calibrationEngine =
new SABRCalibrationEngine(engineHandle,
CalibrationSettings,
EngineHandles,
AtmVolatility,
AssetPrice,
time,
tenor
);
calibrationEngine.CalibrateInterpSABRModel();
var sabrParameters = new SABRParameters(calibrationEngine.GetSABRParameters.Alpha,
calibrationEngine.GetSABRParameters.Beta,
calibrationEngine.GetSABRParameters.Nu,
calibrationEngine.GetSABRParameters.Rho);
var sabrImpliedVol = new SABRImpliedVolatility(sabrParameters, false);
var value = Convert.ToDecimal(axisValue) * AssetPrice;
string errMsg = "Error interpolating";
decimal result = 0.0m;
sabrImpliedVol.SABRInterpolatedVolatility(AssetPrice, time, value, ref errMsg, ref result, true);
return(Convert.ToDouble(result));
}
/// <summary>
/// Computes the Caplet volatility smile at a particular Caplet expiry.
/// Exception: ArgumentException, System.Exception
/// </summary>
/// <param name="logger">The logger.</param>
/// <param name="cache">The cache.</param>
/// <param name="nameSpace">The clients namespace</param>
/// <param name="expiry">Caplet expiry.</param>
/// <param name="strikes">List of strikes for which to compute the
/// implied volatility.</param>
/// <returns>List that contains the implied volatility computed
/// at each strike.</returns>
public List <decimal> ComputeVolatilitySmile
(ILogger logger, ICoreCache cache, string nameSpace, DateTime expiry, List <decimal> strikes)
{
// Check that the list of strikes is not empty.
if (strikes.Count == 0)
{
throw new ArgumentException("Empty list of strikes found by Caplet smile", nameof(strikes));
}
CalibrateSABREngine(logger, cache, nameSpace, expiry);
// Compute the Caplet volatility at each strike.
var volatilities = new List <decimal>(); // answers
var impliedVolObj
= new SABRImpliedVolatility(_sabrEngine.GetSABRParameters, false);
var errorMessage = "";
var result = -1.0m;
foreach (var strike in strikes)
{
var success = impliedVolObj.SABRInterpolatedVolatility
(_assetPrice,
_excerciseTime,
strike,
ref errorMessage,
ref result,
true);
if (!success)
{
throw new Exception(errorMessage);
}
// Volatility was successfully computed: store result.
volatilities.Add(result);
}
return(volatilities);
}
public void TestSABRImpliedVolatility()
{
SABRImpliedVolatility impliedVolObj =
new SABRImpliedVolatility(_sabrParameters,
_checkSABRParameters);
Assert.IsNotNull(impliedVolObj);
}
/// <summary>
/// Calculate the SABR implied volatility for the strike value.
/// This method uses the calibration engine indexed by the exerciseTime/assetCode pair
/// When an ATM engine is used then the assetCode is ignored.
/// </summary>
/// <param name="engineHandle">The CalibrationEngine to use</param>
/// <param name="exerciseTime">Option Expiry index</param>
/// <param name="assetCode">Swap Tenor index</param>
/// <param name="strikes">The strikes to calculate Volatility for</param>
/// <returns></returns>
public decimal[] SABRInterpolateVolatilities(string engineHandle, string exerciseTime, string assetCode,
decimal[] strikes)
{
// Only process if the engine object holder holds the engine for this exercise/asset key
if (!_sabrEngines.ContainsKey(engineHandle))
{
throw new System.Exception("Calibration Engine " + engineHandle + " not found.");
}
// Extract the information we need from this engine holder
SortedDictionary <SABRKey, SABRCalibrationEngine> engine = _sabrEngines[engineHandle];
var key = new SABRKey(GenerateTenorLabel(exerciseTime), GenerateTenorLabel(assetCode));
// Check that the engine for this exercise/asset key exists
if (!engine.ContainsKey(key))
{
throw new System.Exception("The Calibration Engine with Key(" + exerciseTime + "," + assetCode + ") not found.");
}
SABRCalibrationEngine calibrationEngine = engine[key];
if (!calibrationEngine.IsSABRModelCalibrated)
{
throw new ArgumentException(string.Format(CultureInfo.CurrentCulture,
"SABR Engine with key: {0}:{1} is not calibrated",
new object[] { key.Expiry, key.Tenor }));
}
// Create SABRImpliedVolatility parameters
decimal assetPrice = _engineRatesGrid.ContainsKey(engineHandle)
? _engineRatesGrid[engineHandle].GetAssetPrice(exerciseTime, assetCode)
: calibrationEngine.AssetPrice;
decimal expiry = GenerateDayValue(exerciseTime, 365.0m);
// build an ImpliedVolatility object
SABRParameters parameters = calibrationEngine.GetSABRParameters;
var vol = new SABRImpliedVolatility(parameters, true);
// value the strike (interpolate as necessary)
var results = new List <decimal>(strikes.Length);
foreach (decimal strike in strikes)
{
string errmsg = "";
decimal result = 0;
if (!vol.SABRInterpolatedVolatility(assetPrice, expiry, strike, ref errmsg, ref result, true))
{
throw new System.Exception(errmsg);
}
results.Add(result);
}
return(results.ToArray());
}
/// <summary>
/// Calculate the SABR implied volatility for the strike value.
/// This method uses the calibration engine indexed by the exerciseTime/assetCode pair
/// When an ATM engine is used then the assetCode is ignored.
/// </summary>
/// <param name="engineHandle">The CalibrationEngine to use</param>
/// <param name="exerciseTime">Option Expiry index</param>
/// <param name="assetCode">Swap Tenor index</param>
/// <param name="strike">The strike to calculate Volatility for</param>
/// <returns></returns>
public decimal SABRInterpolateVolatility(string engineHandle, string exerciseTime, string assetCode, decimal strike)
{
decimal result = 0;
string errmsg = "";
// Only process if the engine object holder holds the engine for this exercise/asset key
if (_sabrEngines.ContainsKey(engineHandle))
{
// Extract the information we need from this engine holder
var engine = _sabrEngines[engineHandle];
var key = new SABRKey(SABRHelper.GenerateTenorLabel(exerciseTime), SABRHelper.GenerateTenorLabel(assetCode));
// Check that the engine for this exercise/asset key exists
if (engine.ContainsKey(key))
{
SABRCalibrationEngine calibrationEngine = engine[key];
if (!calibrationEngine.IsSABRModelCalibrated)
{
throw new ArgumentException(string.Format(CultureInfo.CurrentCulture, "SABR Engine with key: {0}:{1} is not calibrated", new object[] { key.Expiry, key.Tenor }));
}
// Create SABRImpliedVolatility parameters
decimal assetPrice = _engineRatesGrid.ContainsKey(engineHandle) ? _engineRatesGrid[engineHandle].GetAssetPrice(exerciseTime, assetCode) : calibrationEngine.AssetPrice;
decimal strikeValue = strike;
var expiry = (decimal)SABRHelper.GenerateDayValue(exerciseTime, 365.0d);
//decimal strikeValue = strike / 100.0m;
// build an ImpliedVolatility object
SABRParameters parameters = calibrationEngine.GetSABRParameters;
var vol = new SABRImpliedVolatility(parameters, true);
// value the strike (interpolate as necessary)
if (!vol.SABRInterpolatedVolatility(assetPrice, expiry, strikeValue, ref errmsg, ref result, true))
{
throw new ArgumentException(errmsg);
}
}
else
{
throw new ArgumentException("The Calibration Engine with Key(" + exerciseTime + "," + assetCode + ") not found.");
}
}
else
{
throw new ArgumentException("Calibration Engine " + engineHandle + " not found.");
}
return(result);
}
public void TestSabrInterpolatedVolatilityComputeXDouble()
{
const double Alpha = 0.219540520585315;
const double Beta = 1;
const double Nu = 0.0000000000021506467396720648;
const double Rho = 0.999999999999999;
SABRParameters sabrParameters = new SABRParameters(Alpha, Beta, Nu, Rho);
const double AssetPrice = 0.07226393165;
const double ExerciseTime = 1d / 12;
const double Strike = 0.0722905443874852823;
const bool CheckImpliedVolParameters = false;
double answer = 0;
string error = "";
SABRImpliedVolatility impliedVolObject = new SABRImpliedVolatility(sabrParameters, CheckImpliedVolParameters);
bool result = impliedVolObject.SABRInterpolatedVolatility(AssetPrice, ExerciseTime, Strike,
ref error, ref answer, CheckImpliedVolParameters);
Assert.IsTrue(result);
Assert.AreEqual("", error);
Assert.AreEqual(6.72317387E-15, answer, 1E-23);
}
public void TestSABRInterpolatedVolatility()
{
#region Tests: SABR Implied Volatility for beta = 0.0
// Test computation of the SABR implied volatility for
// the case beta = 0.0.
_alpha = 0.60897d / 100d;
_beta = 0.0d;
_nu = 32.0d / 100d;
_rho = 17.0d / 100d;
_checkSABRParameters = false;
SABRParameters sabrParameters1 =
new SABRParameters(_alpha, _beta, _nu, _rho);
SABRImpliedVolatility impliedVolObj1 =
new SABRImpliedVolatility(sabrParameters1,
_checkSABRParameters);
// Strike = ATM - 200bp.
_strike = _assetPrice - 200.0d / 10000d;
_expected = 23.96039d / 100d;
const double tolerance1 = 1.0E-5d;
_isSuccessful =
impliedVolObj1.SABRInterpolatedVolatility(
_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkImpliedVolParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance1);
// Strike = ATM.
_strike = _assetPrice;
_expected = 15.99991d / 100d;
_isSuccessful =
impliedVolObj1.SABRInterpolatedVolatility(
_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkImpliedVolParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance1);
// Strike = ATM + 200bp.
_strike = _assetPrice + 200.0d / 10000d;
_expected = 15.62789d / 100d;
_isSuccessful =
impliedVolObj1.SABRInterpolatedVolatility(
_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkImpliedVolParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance1);
#endregion Tests: SABR Implied Volatility for beta = 0.0
#region Tests: SABR Implied Volatility for beta = 0.5
// Test computation of the SABR implied volatility for
// the case beta = 0.5.
_alpha = 3.05473d / 100d;
_beta = 0.5d;
_nu = 34.0d / 100d;
_rho = -11.0d / 100d;
_checkSABRParameters = false;
SABRParameters sabrParameters2 =
new SABRParameters(_alpha, _beta, _nu, _rho);
SABRImpliedVolatility impliedVolObj2 =
new SABRImpliedVolatility(sabrParameters2,
_checkSABRParameters);
// Strike = ATM - 200bp.
_strike = _assetPrice - 200.0d / 10000d;
_expected = 23.73848d / 100d;
const double tolerance2 = 1.0E-5d;
_isSuccessful =
impliedVolObj2.SABRInterpolatedVolatility(_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkSABRParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance2);
// Strike = ATM
_strike = _assetPrice;
_expected = 16.00001d / 100d;
_isSuccessful =
impliedVolObj2.SABRInterpolatedVolatility(_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkSABRParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance2);
// Strike = ATM + 200bp
_strike = _assetPrice + 200.0d / 10000d;
_expected = 15.75552d / 100d;
_isSuccessful =
impliedVolObj2.SABRInterpolatedVolatility(_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkSABRParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance2);
#endregion Tests: SABR Implied Volatility for beta = 0.5
#region Tests: SABR Implied Volatility for beta = 1.0
// Test computation of the SABR implied volatility for
// the case beta = 1.0.
_alpha = 15.53173d / 100d;
_beta = 1.0d;
_nu = 40.0d / 100d;
_rho = -33.0d / 100d;
_checkSABRParameters = false;
SABRParameters sabrParameters3 =
new SABRParameters(_alpha, _beta, _nu, _rho);
SABRImpliedVolatility impliedVolObj3 =
new SABRImpliedVolatility(sabrParameters3,
_checkSABRParameters);
// Strike = ATM - 200bp.
_strike = _assetPrice - 200.0d / 10000d;
_expected = 23.79395d / 100d;
const double tolerance3 = 1.0E-5d;
_isSuccessful =
impliedVolObj3.SABRInterpolatedVolatility
(_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkImpliedVolParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance3);
// Strike = ATM
_strike = _assetPrice;
_expected = 16.00000d / 100d;
_isSuccessful =
impliedVolObj3.SABRInterpolatedVolatility
(_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkImpliedVolParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance3);
// Strike = ATM + 200bp
_strike = _assetPrice + 200.0d / 10000d;
_expected = 16.05579d / 100d;
_isSuccessful =
impliedVolObj3.SABRInterpolatedVolatility
(_assetPrice,
_exerciseTime,
_strike,
ref _errorMessage,
ref _result,
_checkImpliedVolParameters);
Assert.IsTrue(_isSuccessful);
Assert.AreEqual(_expected,
_result,
tolerance3);
#endregion Tests: SABR Implied Volatility for beta = 1.0
}
