public static double Delta(double S, double t0, BSOption opt)
{
double T = opt.gettimeexp();
double K = opt.getstrike();
double vol = opt.getvolatility();
double q = opt.getyield();
double r = opt.getriskfreerate();
string opttype = opt.getoption();
double dvalue;
double d1 = (Math.Log(S / K) + (r - q + 0.5 * Math.Pow(vol, 2)) * (T - t0)) / (vol * Math.Sqrt(T - t0));
double d2 = d1 - vol * Math.Sqrt(T - t0);
if (S <= 0 || K <= 0 || vol <= 0 || T - t0 <= 0)
{
dvalue = 0;
}
if (opttype == "call")
{
dvalue = Math.Round(Math.Exp(-q * (T - t0)) * (RandLib.NormalCDF((Math.Log(S / K) + (r - q + 0.5 * Math.Pow(vol, 2)) * (T - t0)) / (vol * Math.Sqrt(T - t0)))), 4);
}
else
{
dvalue = Math.Round(Math.Exp(-q * (T - t0)) * (RandLib.NormalCDF((Math.Log(S / K) + (r - q + 0.5 * Math.Pow(vol, 2)) * (T - t0)) / (vol * Math.Sqrt(T - t0)))) - 1, 4);
}
return(dvalue);
}
public static double Theta(double S, double t0, BSOption opt)
{
double T = opt.gettimeexp();
double K = opt.getstrike();
double vol = opt.getvolatility();
double q = opt.getyield();
double r = opt.getriskfreerate();
string opttype = opt.getoption();
double thetavalue;
double d1 = (Math.Log(S / K) + (r - q + 0.5 * Math.Pow(vol, 2)) * (T - t0)) / (vol * Math.Sqrt(T - t0));
double d2 = d1 - vol * Math.Sqrt(T - t0);
if (S <= 0 || K <= 0 || vol <= 0 || T - t0 <= 0)
{
thetavalue = 0;
}
if (opttype == "call")
{
thetavalue = Math.Round(((-S * Math.Exp(-q * (T - t0)) * RandLib.NormalPDF(d1) * 0.5 * vol / (Math.Sqrt(T - t0))) + q * S * Math.Exp(-q * (T - t0)) * RandLib.NormalCDF(d1) - r * K * Math.Exp(-r * (T - t0)) * RandLib.NormalCDF(d2)) / 365, 4);
}
else
{
thetavalue = Math.Round((-S * Math.Exp(-q * (T - t0)) * RandLib.NormalPDF(d1) * 0.5 * vol / (Math.Sqrt(T - t0)) + r * K * Math.Exp(-r * (T - t0)) * RandLib.NormalCDF(-d2) - q * S * Math.Exp(-q * (T - t0)) * RandLib.NormalCDF(-d1)) / 365, 4);
}
return(thetavalue);
}
static void Main()
{
double K;
double S;
double r;
double q;
double vol;
double t;
double t0;
string optype;
double target;
double impvol = 0.01;
Console.WriteLine("please enter an option strike price = ");
K = double.Parse(Console.ReadLine());
Console.WriteLine("please enter a current Stock price = ");
S = double.Parse(Console.ReadLine());
Console.WriteLine("please enter a risk free rate(%) = ");
r = double.Parse(Console.ReadLine());
Console.WriteLine("please enter a dividend yield(%) = ");
q = double.Parse(Console.ReadLine());
Console.WriteLine("please enter a stock volatility(%) = ");
vol = double.Parse(Console.ReadLine());
Console.WriteLine("please enter T, expiration time = ");
t = double.Parse(Console.ReadLine());
Console.WriteLine("please enter t0, start time = ");
t0 = double.Parse(Console.ReadLine());
Console.WriteLine("please enter the option: call or put");
optype = Console.ReadLine();
RandLib rd = new RandLib();
BSOption option = new BSOption(K, r, q, vol, t, optype);
double fairvalue = BSFairValue(S, t0, option);
double delta = Delta(S, t0, option);
double gamma = Gamma(S, t0, option);
double vega = Vega(S, t0, option);
double rho = Rho(S, t0, option);
double theta = Theta(S, t0, option);
Console.WriteLine($"The fair value of the option is {fairvalue}");
Console.WriteLine($"The delta of the option is {delta}");
Console.WriteLine($"The gamma of the option is {gamma}");
Console.WriteLine($"The vega of the option is {vega}");
Console.WriteLine($"The rho of the option is {rho}");
Console.WriteLine($"The theta of the option is {theta}");
Console.WriteLine("please enter the target option value to calculate implied volatility");
target = double.Parse(Console.ReadLine());
BSImpvol(S, t0, target, 5, 0.001, 0.001, ref impvol, option);
Console.WriteLine($"The implied volatility of the option is {impvol}");
}
public static double Vega(double S, double t0, BSOption opt)
{
double T = opt.gettimeexp();
double K = opt.getstrike();
double vol = opt.getvolatility();
double q = opt.getyield();
double r = opt.getriskfreerate();
string opttype = opt.getoption();
double vvalue;
double d1 = (Math.Log(S / K) + (r - q + 0.5 * Math.Pow(vol, 2)) * (T - t0)) / (vol * Math.Sqrt(T - t0));
double d2 = d1 - vol * Math.Sqrt(T - t0);
if (S <= 0 || K <= 0 || vol <= 0 || T - t0 <= 0)
{
vvalue = 0;
}
vvalue = Math.Round(.01 * S * Math.Exp(-q * (T - t0)) * Math.Sqrt(T - t0) * RandLib.NormalPDF(d1), 4);
return(vvalue);
}
public static bool BSImpvol(double S, double t0, double target, int max_iter, double Opt_tol, double vol_tol, ref double impvol, BSOption opt)
{
bool bool_value = true;
double T = opt.gettimeexp();
double K = opt.getstrike();
double vol = opt.getvolatility();
double q = opt.getyield();
double r = opt.getriskfreerate();
double vol_in = 0.4;
double vol_f = 0;
string opttype = opt.getoption();
double V;
double vega;
double d1 = (Math.Log(S / K) + (r - q + 0.5 * Math.Pow(vol, 2)) * (T - t0)) / (vol * Math.Sqrt(T - t0));
double d2 = d1 - vol * Math.Sqrt(T - t0);
for (int i = 0; i <= max_iter; i++)
{
if (opttype == "call")
{
V = S * Math.Exp(-q * (T - t0)) * RandLib.NormalCDF(d1) - K * Math.Exp(-r * (T - t0)) * RandLib.NormalCDF(d2);
}
else
{
V = K * Math.Exp(-r * (T - t0)) * RandLib.NormalCDF(-d2) - S * Math.Exp(-q * (T - t0)) * RandLib.NormalCDF(-d1);
}
vega = S * Math.Exp(-q * (T - t0)) * RandLib.NormalPDF(d1) * Math.Sqrt(T - t0);
if (i == 0)
{
vol_f = vol_in - (V - target) / vega;
}
else
{
if (Math.Abs(V - target) <= Opt_tol && Math.Abs((vol_f - vol_in)) <= vol_tol)
{
vol_f = vol_in;
vol_f = vol_in - (V - target) / vega;
}
}
}
impvol = vol_f;
return(bool_value);
}