static public double CalcDeltaValue(
InitialTerm.InitialParameter param,
double forward,
double strike,
double volatility,
InitialTerm.CallPutType type,
InitialTerm.DeltaType deltaType)
{
var d1 = DFuncCalculator.CalcDValue(param, volatility, param.tau, forward, strike);
var d2 = d1 - volatility * Math.Sqrt(param.tau);
switch (deltaType)
{
case InitialTerm.DeltaType.PipsSpotDelta:
return((int)type
* Math.Exp(-param.rateOfForeign * param.tau) * CDF((int)type * d1));
case InitialTerm.DeltaType.PercentageSpotDelta:
return((int)type
* Math.Exp(-param.rateOfDomestic * param.tau) * strike
/ param.spotRate * CDF((int)type * d2));
default:
return(0.0);
}
}
static public double CalcStrike(
InitialTerm.InitialParameter param,
double forward,
double volatility,
InitialTerm.DeltaType deltaType,
InitialTerm.VolatilityType volatilityType)
{
switch (volatilityType)
{
case InitialTerm.VolatilityType.ATM:
return(CalcAtmStrike(param, forward, volatility, deltaType));
case InitialTerm.VolatilityType.MS25Call:
return(CalcInvCdf(
param, volatility, forward, 0.25, Type, deltaType));
case InitialTerm.VolatilityType.MS25Put:
return(CalcInvCdf(
param, volatility, forward, -0.25, Type, deltaType));
case InitialTerm.VolatilityType.MS10Call:
return(CalcInvCdf(
param, volatility, forward, 0.1, Type, deltaType));
case InitialTerm.VolatilityType.MS10Put:
return(CalcInvCdf(
param, volatility, forward, -0.1, Type, deltaType));
default:
return(0);
}
}
static public double CalcDValue(
InitialTerm.InitialParameter param,
double vol,
double tau,
double forward,
double strike)
{
return((Math.Log(forward / strike)
* 0.5 * Math.Pow(vol, 2.0) * tau)
/ (vol * Math.Sqrt(tau)));
}
static public double CalcOptionPrice(
InitialTerm.InitialParameter param,
double forward,
double strike,
double d1,
double d2,
InitialTerm.CallPutType type)
{
return((int)type * forward * Math.Exp(-param.rateOfForeign * param.tau)
* Normal.CDF(0, 1, (int)type * d1)
- strike * Normal.CDF(0, 1, (int)type * d2));
}
public static List <double> PriceSetting(InitialTerm.InitialParameter param)
{
var priceList = new List <double>();
var forward = ForwardCalculator.CalcForwardRate(param);
foreach (InitialTerm.VolatilityType volatilityType
in Enum.GetValues(typeof(InitialTerm.VolatilityType)))
{
var type = JudgeMaterial.JudgeOfCallPut.CallOrPut(volatilityType);
var volatility = JudgeMaterial.JudgeOfVolatility.Volatility(param, volatilityType);
var strike = StrikrCalcultor.CalcStrike(param, forward, volatility, param.deltaType, volatilityType);
var d1 = DFuncCalculator.CalcDValue(param, volatility, param.tau, forward, strike);
var d2 = d1 - volatility * Math.Sqrt(param.tau);
priceList.Add(FlyAdjustment.PriceCalculator.CalcOptionPrice(param, forward, strike, d1, d2, type));
}
return(priceList);
}
public static List <double> StrikeSetting(InitialTerm.InitialParameter param)
{
var strikeList = new List <double>();
var forward = ForwardCalculator.CalcForwardRate(param);
foreach (InitialTerm.VolatilityType volatilityType
in Enum.GetValues(typeof(InitialTerm.VolatilityType)))
{
var volatility = JudgeMaterial.JudgeOfVolatility.Volatility(param, volatilityType);
strikeList.Add(StrikrCalcultor.CalcStrike(
param,
forward,
volatility,
param.deltaType,
volatilityType));
}
return(strikeList);
}
private static double CalcAtmStrike(
InitialTerm.InitialParameter param,
double forward,
double volatility,
InitialTerm.DeltaType deltaType)
{
double strike = 0.0;
if (deltaType == InitialTerm.DeltaType.PipsSpotDelta ||
deltaType == InitialTerm.DeltaType.PercentageForwardDelta)
{
strike = forward * Math.Exp(volatility * volatility * param.tau / 2.0);
}
else
{
strike = forward * Math.Exp(-volatility * volatility * param.tau / 2.0);
}
return(strike);
}
public static double CalcInvCdf(
InitialTerm.InitialParameter param,
double volatility,
double forward,
double delta,
InitialTerm.CallPutType type,
InitialTerm.DeltaType deltaType)
{
Volatility = volatility;
Forward = forward;
DeltaType = deltaType;
Number = delta;
var strikeCalculator = new StrikrCalcultor(param);
return(UseBisection.Calc(
strikeCalculator.DeltaFunctionOfStrike,
0.5 * param.spotRate,
2.0 * param.spotRate));
}
static void CalcUSDJPY()
{
var spot = 106.925;
var rateOfDomestic = -0.00085034363976;
var rateOfForeign = 0.02216698493974;
var tau = 1.0;
var volAtm = 0.071;
var vol25MS = 0.002;
var vol10MS = 0.0105;
var vol25RR = -0.021;
var vol10RR = -0.042;
var deltaType = InitialTerm.DeltaType.PercentageSpotDelta;
var param = new InitialTerm.InitialParameter(
spot,
rateOfDomestic,
rateOfForeign,
tau,
volAtm,
vol25MS,
vol10MS,
vol25RR,
vol10RR,
deltaType
);
var forward = ForwardCalculator.CalcForwardRate(param);
var strikeList = InitialSetting.StrikeSetting(param);
//var interpolationName = "PolynomialInDelta";
var interpolationName = "SABR";
var vTarget = 4.5;
var Ans = Calibration.Solve(
interpolationName,
param,
forward,
vTarget,
strikeList);
Console.WriteLine(Ans);
}
static public double CalcForwardRate(InitialTerm.InitialParameter param)
{
return(param.spotRate * Math.Exp((param.rateOfDomestic - param.rateOfForeign) * param.tau));
}
public static Vector <double> Solve(
string interpolationName,
InitialTerm.InitialParameter param,
double forward,
double vtarget,
List <double> strikeList)
{
InterpolationName = interpolationName;
Param = param;
StrikeList = strikeList;
K25Call = strikeList[3];
KATM = strikeList[2];
K25Put = strikeList[1];
VolSS25 = param.volMS25;
var tol = 1.0E-5;
var error = 1.0;
var LowerVector = Vector <double> .Build.DenseOfArray(new double[] { 0.00001, 0.00001, -0.99999 });
var UpperVector = Vector <double> .Build.DenseOfArray(new double[] { 100, 100, 0.99999 });
VolParameter = Vector <double> .Build.DenseOfArray(new double[] { 0.1, 0.1, -0.1 });
while (Math.Abs(error) > tol)
{
if (InterpolationName == "SABR")
{
VolParameter = FindMinimum.OfFunctionConstrained(
FuncOfVolCondtion,
LowerVector,
UpperVector,
VolParameter);
//VolParameter = FindMinimum.OfFunction(FuncOfVolCondtion, VolParameter);
}
else
{
VolParameter = FindMinimum.OfFunction(FuncOfVolCondtion, VolParameter);
}
CalcStrikeList(VolParameter);
var vTrial = CalcValueTrial(VolParameter);
error = vTrial - vtarget;
if (error > 0)
{
VolSS25 -= tol / 100;
}
else
{
VolSS25 += tol / 100;
}
}
var volRR25 = VolCalculator(K25Call, VolParameter) - VolCalculator(K25Put, VolParameter);
var Ans = Vector <double> .Build.DenseOfArray(new double[]
{
VolParameter[0],
VolParameter[1],
VolParameter[2],
K25Call,
K25Put,
VolSS25,
volRR25
});
return(Ans);
}
public StrikrCalcultor(InitialTerm.InitialParameter param)
{
this.Param = param;
}