public double CalculateIVByOptionPrice(double stockPrice, int dayLefts)
{
var blackNScholesCaculator = new BlackNScholesCaculator()
{
DayLefts = dayLefts,
RiskFreeInterestRate = RiskFreeInterestRate,
StockPrice = stockPrice,
Strike = StrikePrice
};
double iv = 0;
try
{
iv = OptionType == EOptionType.Call
? blackNScholesCaculator.GetCallIVBisections(BaseOptionPrice)
: blackNScholesCaculator.GetPutIVBisections(BaseOptionPrice);
}
catch (Exception ex)
{
Logger.Error(ex.Message + ": wrong calculation, ImpliedVolatilitiesBase = 0 !!!!", ex);
}
ImpliedVolatilitiesBase = iv;
return(iv);
}
public void Calculate()
{
var blackNScholesCaculator = new BlackNScholesCaculator
{
DayLefts = DayLefts,
ImpliedVolatilities = ImpliedVolatilities,
RiskFreeInterestRate = RiskFreeInterestRate,
StockPrice = StockPrice,
Strike = StrikePrice,
Multiplier = Multiplier
};
blackNScholesCaculator.CalculateAll();
if (OptionType == EOptionType.Call)
{
ResultDataValues.OptionPrice = Double.IsNaN(blackNScholesCaculator.CallValue) ? 0 : blackNScholesCaculator.CallValue;
ResultDataValues.Delta = blackNScholesCaculator.DeltaCall;
ResultDataValues.Gamma = blackNScholesCaculator.GamaCall;
ResultDataValues.Theta = blackNScholesCaculator.ThetaCall;
ResultDataValues.Vega = blackNScholesCaculator.VegaCall;
}
else
{
ResultDataValues.OptionPrice = Double.IsNaN(blackNScholesCaculator.PutValue) ? 0 : blackNScholesCaculator.PutValue;
//ResultDataValues.OptionPrice = blackNScholesCaculator.PutValue;
ResultDataValues.Delta = blackNScholesCaculator.DeltaPut;
ResultDataValues.Gamma = blackNScholesCaculator.GamaPut;
ResultDataValues.Theta = blackNScholesCaculator.ThetaPut;
ResultDataValues.Vega = blackNScholesCaculator.VegaPut;
}
}
public static bool TestPutCalculation()
{
var o = new BlackNScholesCaculator
{
DayLefts = 90,
ImpliedVolatilities = 0.2,
OptionType = EOptionType.Call,
RiskFreeInterestRate = 0.1,
StockPrice = 50,
Strike = 40
};
var putValue = o.CalculatePutValue();
return(!(Abs(putValue - 0.078) > 0.001));
}
//public double CalculateImpliedVolatilityBNSNewton(double callOptionPrice)
//{
// double impliedVolatility = OptionPriceImpliedVolatilityCallBlackScholesNewton(StockPrice, Strike,
// RiskFreeInterestRate, ExpiryTime, callOptionPrice);
// return impliedVolatility;
//}
/// <summary>
/// Calculates implied volatility for the Black Scholes formula using
/// the Newton-Raphson formula
///
/// Converted to C# from "Financial Numerical Recipes in C" by:
/// Bernt Arne Odegaard
/// http://finance.bi.no/~bernt/gcc_prog/index.html
///
/// (NOTE: In the original code a large negative number was used as an
/// exception handling mechanism. This has been replace with a generic
/// 'Exception' that is thrown. The original code is in place and commented
/// if you want to use the pure version of this code)
/// </summary>
/// <param name="spot">spot (underlying) price</param>
/// <param name="strike">strike (exercise) price</param>
/// <param name="interestRate">interest rate</param>
/// <param name="time">time to maturity</param>
/// <param name="optionPrice">The price of the option</param>
/// <returns>Sigma (implied volatility)</returns>
public double OptionPriceImpliedVolatilityCallBlackScholesNewton(double spot, double strike, double interestRate,
double time, double optionPrice)
{
// check for arbitrage violations. Option price is too low if this happens
if (optionPrice < 0.99 * (spot - strike * Exp(-time * interestRate)))
{
return(0.0);
}
const int MAX_ITERATIONS = 100;
const double ACCURACY = 1.0e-5;
double tSqrt = Sqrt(time);
var blackNScholesCaculator = new BlackNScholesCaculator
{
ExpiryTime = time,
RiskFreeInterestRate = interestRate,
StockPrice = spot,
Strike = strike,
//ImpliedVolatilities = sigmaHigh
};
double sigma = (optionPrice / spot) / (0.398 * tSqrt); // find initial value
for (int i = 0; i < MAX_ITERATIONS; i++)
{
blackNScholesCaculator.ImpliedVolatilities = sigma;
blackNScholesCaculator.CalculateAll();
double price = blackNScholesCaculator.CallValue;
// price = OptionPriceCallBlackScholes(spot, strike, interestRate, sigma, time);
double diff = optionPrice - price;
if (Abs(diff) < ACCURACY)
{
return(sigma);
}
double d1 = (Log(spot / strike) + interestRate * time) / (sigma * tSqrt) + 0.5 * sigma * tSqrt;
double vega = spot * tSqrt * CumulativeNormDist(d1);
sigma = sigma + diff / vega;
}
//return -99e10; // something screwy happened, should throw exception // <--- original code
throw new Exception("An error occurred"); // Comment this line if you uncomment the line above
}
public static bool TestCallCalculation()
{
var o = new BlackNScholesCaculator
{
//ExpiryTime = 0.25,
DayLefts = 90,
ImpliedVolatilities = 0.2,
OptionType = EOptionType.Call,
RiskFreeInterestRate = 0.1,
StockPrice = 50,
Strike = 40
};
double callValue = o.CalculateCallValue();
if (Abs(callValue - 11.01) > 0.1)
{
return(false);
}
return(true);
}
/// <summary>
/// Calculates implied volatility for the Black Scholes formula using
/// binomial search algorithm
///
/// Converted to C# from "Financial Numerical Recipes in C" by:
/// Bernt Arne Odegaard
/// http://finance.bi.no/~bernt/gcc_prog/index.html
///
/// (NOTE: In the original code a large negative number was used as an
/// exception handling mechanism. This has been replace with a generic
/// 'Exception' that is thrown. The original code is in place and commented
/// if you want to use the pure version of this code)
/// </summary>
/// <param name="spot">spot (underlying) price</param>
/// <param name="strike">strike (exercise) price</param>
/// <param name="interestRate">interest rate</param>
/// <param name="time">time to maturity</param>
/// <param name="optionPrice">The price of the option</param>
/// <returns>Sigma (implied volatility)</returns>
public double PutOptionPriceIVBisections(double spot, double strike, double interestRate,
double time, double optionPrice)
{
// check for arbitrage violations.
if (optionPrice < 0.99 * (spot - strike * Exp(-time * interestRate)))
{
return(0.0); // Option price is too low if this happens
}
// simple binomial search for the implied volatility.
// relies on the value of the option increasing in volatility
const double ACCURACY = 1.0e-5; // make this smaller for higher accuracy
const int MAX_ITERATIONS = 100;
const double HIGH_VALUE = 1e10;
//const double ERROR = -1e40; // <--- original code
// want to bracket sigma. first find a maximum sigma by finding a sigma
// with a estimated price higher than the actual price.
double sigmaLow = 1e-5;
double sigmaHigh = 0.3;
var blackNScholesCaculator = new BlackNScholesCaculator
{
ExpiryTime = time,
RiskFreeInterestRate = interestRate,
StockPrice = spot,
Strike = strike,
ImpliedVolatilities = sigmaHigh
};
blackNScholesCaculator.CalculateAll();
double price = blackNScholesCaculator.PutValue;
while (price < optionPrice)
{
sigmaHigh = 2.0 * sigmaHigh; // keep doubling.
blackNScholesCaculator.ImpliedVolatilities = sigmaHigh;
blackNScholesCaculator.CalculateAll();
price = blackNScholesCaculator.PutValue;
if (sigmaHigh > HIGH_VALUE)
{
//return ERROR; // panic, something wrong. // <--- original code
throw new Exception("panic, something wrong."); // Comment this line if you uncomment the line above
}
}
for (int i = 0; i < MAX_ITERATIONS; i++)
{
double sigma = (sigmaLow + sigmaHigh) * 0.5;
blackNScholesCaculator.ImpliedVolatilities = sigma;
blackNScholesCaculator.CalculateAll();
price = blackNScholesCaculator.PutValue;
double test = (price - optionPrice);
if (Abs(test) < ACCURACY)
{
IterationCounter = i;
return(sigma);
}
if (test < 0.0)
{
sigmaLow = sigma;
}
else
{
sigmaHigh = sigma;
}
}
//return ERROR; // <--- original code
throw new Exception("An error occurred"); // Comment this line if you uncomment the line above
}
