public static object DupireSsviVolatility([ExcelArgument(Description = "the current risky asset price")] double underlyingPrice,
[ExcelArgument(Description = "constant continuously compounded rate of return")] double riskFreeRate,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double alpha,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double beta,
[ExcelArgument(Description = "SSVI parameter")] double gamma,
[ExcelArgument(Description = "SSVI parameter")] double eta,
[ExcelArgument(Description = "SSVI parameter")] double rho,
[ExcelArgument(Description = "option maturity (time to expiry)")] double maturity,
[ExcelArgument(Description = "option strike")] double strike)
{
// This is useful for methods that take a while to run.
if (ExcelDnaUtil.IsInFunctionWizard())
{
return(null);
}
try
{
double k = Math.Log(strike * Math.Exp(-riskFreeRate * maturity) / underlyingPrice);
Ssvi SsviSurface = new Ssvi(alpha, beta, gamma, eta, rho);
return(Math.Sqrt(SsviSurface.OmegaSsvi(maturity, k) / maturity));
}
catch (Exception e)
{
XLInterfaceBase.AddErrorMessage("DupireSsviVolatility error: " + e.Message);
}
return(FunctionError);
}
public static object DupireSsviEuropeanVanillaOptionPrice([ExcelArgument(Description = "the current risky asset price")] double S0,
[ExcelArgument(Description = "constant continuously compounded rate of return")] double riskFreeRate,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double alpha,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double beta,
[ExcelArgument(Description = "SSVI parameter")] double gamma,
[ExcelArgument(Description = "SSVI parameter")] double eta,
[ExcelArgument(Description = "SSVI parameter")] double rho,
[ExcelArgument(Description = "option maturity (time to expiry)")] double maturity,
[ExcelArgument(Description = "option strike")] double strike,
[ExcelArgument(Description = "option type, 'C' for call 'P' for put")] string type)
{
try
{
Ssvi SsviSurface = new Ssvi(alpha, beta, gamma, eta, rho);
double k = Math.Log(strike * Math.Exp(-riskFreeRate * maturity) / S0);
double sigmaBs = Math.Sqrt(SsviSurface.OmegaSsvi(maturity, k) / maturity);
if (type == "Call" || type == "call" || type == "C" || type == "c")
{
return(BlackScholesFormula.CalculateCallOptionPrice(sigmaBs, S0, k, riskFreeRate, maturity));
}
else if (type == "Put" || type == "put" || type == "P" || type == "p")
{
return(BlackScholesFormula.CalculatePutOptionPrice(sigmaBs, S0, k, riskFreeRate, maturity));
}
else
{
throw new ArgumentException("Input must be either Call, call, C, c, Put, put, P or p.");
}
}
catch (Exception e)
{
XLInterfaceBase.AddErrorMessage("DupireSsviEuropeanVanillaOptionPrice error: " + e.Message);
}
return(FunctionError);
}
public static object DupireSsviCalculateSigmaDup([ExcelArgument(Description = "the current risky asset price")] double S0,
[ExcelArgument(Description = "constant continuously compounded rate of return")] double riskFreeRate,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double alpha,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double beta,
[ExcelArgument(Description = "SSVI parameter")] double gamma,
[ExcelArgument(Description = "SSVI parameter")] double eta,
[ExcelArgument(Description = "SSVI parameter")] double rho,
[ExcelArgument(Description = "The value of S for which we want the Dupire Local Vol")] double S,
[ExcelArgument(Description = "The value of t for which we want the Dupire Local Vol")] double t)
{
try
{
Ssvi SsviSurface = new Ssvi(alpha, beta, gamma, eta, rho);
double k = Math.Log(S * Math.Exp(-riskFreeRate * t) / S0);
return(SsviSurface.VolatilityDup(t, k));
}
catch (Exception e)
{
XLInterfaceBase.AddErrorMessage("DupireSsviCalculateSigmaDup error: " + e.Message);
}
return(FunctionError);
}
public static object[,] CalibrateDupireSsviParametersNonATM(
[ExcelArgument(Description = "A 3x2 XL Range with guess values for gamma, eta, rho")] object guessModelParameters,
[ExcelArgument(Description = "constant continuously compounded rate of return")] double riskFreeRate,
[ExcelArgument(Description = "the current risky asset price")] double underlyingPrice,
[ExcelArgument(Description = "the SSVI alpha from ATM calibration")] double alpha,
[ExcelArgument(Description = "the SSVI beta from ATM calibration")] double beta,
[ExcelArgument(Description = "An Nx1 XL Range of option strikes")] object strikes,
[ExcelArgument(Description = "An Nx1 XL Range of option maturities")] object maturities,
[ExcelArgument(Description = "An Nx1 XL Range of option either C or P for Calls and Puts")] object type,
[ExcelArgument(Description = "An Nx1 XL Range of option prices")] object observedPrices,
[ExcelArgument(Description = "Accuracy parameter for calibration")] double accuracy,
[ExcelArgument(Description = "Number of iterations parameter for calibration")] int maxIterations)
{
try
{
if (ExcelDnaUtil.IsInFunctionWizard())
{
return(null);
}
double[] strikesArray = XLInterfaceBase.ConvertToVector <double>(strikes);
double[] maturitesArray = XLInterfaceBase.ConvertToVector <double>(maturities);
string[] typeArray = XLInterfaceBase.ConvertToVector <string>(type);
double[] observedPricesArray = XLInterfaceBase.ConvertToVector <double>(observedPrices);
if (strikesArray.Length != maturitesArray.Length ||
maturitesArray.Length != typeArray.Length ||
typeArray.Length != observedPricesArray.Length)
{
XLInterfaceBase.AddErrorMessage("CalibrateSsviParameters: strikes, maturites, types and observedPrices must be of same length.");
return(null);
}
KeyValuePair <string, double>[] paramPairs = XLInterfaceBase.ConvertToKeyValuePairs(guessModelParameters);
if (paramPairs.Length != 3)
{
XLInterfaceBase.AddErrorMessage("CalibrateSsviParameters: guessModelParameters must be three key - value pairs.");
return(null);
}
double eta = 0; double gamma = 0; double rho = 0;
for (int paramIdx = 0; paramIdx < paramPairs.Length; ++paramIdx)
{
KeyValuePair <string, double> pair = paramPairs[paramIdx];
string key = pair.Key;
double value = pair.Value;
if (key.Equals("eta", StringComparison.CurrentCultureIgnoreCase))
{
eta = value;
}
else if (key.Equals("gamma", StringComparison.CurrentCultureIgnoreCase))
{
gamma = value;
}
else if (key.Equals("rho", StringComparison.CurrentCultureIgnoreCase))
{
rho = value;
}
else
{
XLInterfaceBase.AddErrorMessage("CalibrateSsviParameters: guessModelParameters: unknown key: " + key);
return(null);
}
}
SsviCalibrator ssviCalibrator = new SsviCalibrator(riskFreeRate, underlyingPrice, accuracy, maxIterations);
ssviCalibrator.SetGuessParameters(alpha, beta, gamma, eta, rho);
int numObservedOptions = strikesArray.Length;
for (int optionIdx = 0; optionIdx < numObservedOptions; ++optionIdx)
{
ssviCalibrator.AddObservedOption(maturitesArray[optionIdx], strikesArray[optionIdx], observedPricesArray[optionIdx], typeArray[optionIdx]);
}
ssviCalibrator.CalibrateEtaGammaRhoNonATM();
CalibrationOutcome outcome = CalibrationOutcome.NotStarted;
double calibrationError = 0;
ssviCalibrator.GetCalibrationStatus(ref outcome, ref calibrationError);
Ssvi calibratedModel = ssviCalibrator.GetCalibratedModel();
// for output
const int numCols = 2;
const int numRows = 5;
object[,] output = new object[numRows, numCols];
output[0, 0] = "Gamma"; output[0, 1] = calibratedModel.GetGamma();
output[1, 0] = "Eta"; output[1, 1] = calibratedModel.GetEta();
output[2, 0] = "Rho"; output[2, 1] = calibratedModel.GetRho();
output[3, 0] = "Minimizer Status";
if (outcome == CalibrationOutcome.FinishedOK)
{
output[3, 1] = "OK";
}
else if (outcome == CalibrationOutcome.FailedMaxItReached)
{
output[3, 1] = "Reached max. num. iterations.";
}
else if (outcome == CalibrationOutcome.FailedOtherReason)
{
output[3, 1] = "Failed.";
}
else
{
output[3, 1] = "Unknown outcome.";
}
output[4, 0] = "Pricing error"; output[4, 1] = Math.Sqrt(calibrationError);
return(output);
}
catch (Exception e)
{
XLInterfaceBase.AddErrorMessage("CalibrateParameters: unknown error: " + e.Message);
}
return(null);
}
