public static double BSImpVolBisec(string cpflg, double S,
double x, double T, double r, double b, double cm, double epsilon)
{
double vLow, vHigh, vi;
double cLow, cHigh;
double counter;
vLow = 0.005;
vHigh = 4;
cLow = BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vLow);
cHigh = BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vHigh);
counter = 0;
vi = vLow + (cm - cLow) * (vHigh - vLow) / (cHigh - cLow);
while (Math.Abs(cm - BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vi)) > epsilon)
{
counter = counter + 1;
if (counter == 100)
{
return(double.NaN);
}
if (BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vi) < cm)
{
vLow = vi;
}
else
{
vHigh = vi;
}
cLow = BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vLow);
cHigh = BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vHigh);
vi = vLow + (cm - cLow) * (vHigh - vLow) / (cHigh - cLow);
}
return(vi);
}
public static double BSImpVolNR(string cpflg, double S, double x,
double T, double r, double b, double cm, double epsilon)
{
double vi, ci;
double vegai;
double minDiff;
//Manaster and Koehler seed value (vi)
vi = Math.Sqrt(Math.Abs(Math.Log(S / x) + r * T) * 2 / T);
ci = BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vi);
vegai = BlackScholesMethod.Vega(S, x, T, r, b, vi);
minDiff = Math.Abs(cm - ci);
while (Math.Abs(cm - ci) >= epsilon && Math.Abs(cm - ci) <= minDiff)
{
vi = vi - (ci - cm) / vegai;
ci = BlackScholesMethod.BlackScholes(cpflg, S, x, T, r, b, vi);
vegai = BlackScholesMethod.Vega(S, x, T, r, b, vi);
minDiff = Math.Abs(cm - ci);
}
if (Math.Abs(cm - ci) < epsilon)
{
return(vi);
}
else
{
return(double.NaN);
}
}
public static double BSAmericanCallApprox2002(double S, double X, double T, double r, double b, double v)
{
double option_price = double.NaN;
double t1 = 0.5 * (Math.Sqrt(5) - 1) * T;
if (b >= r)//Never optimal to exercise before maturity
{
option_price = BlackScholesMethod.BlackScholes("c", S, X, T, r, b, v);
}
else
{
double beta = (0.5 - b / (v * v)) + Math.Sqrt(Math.Pow((b / (v * v) - 0.5), 2) + 2 * r / (v * v));
double binfinity = beta / (beta - 1) * X;
double b0 = Math.Max(X, r / (r - b) * X);
double ht1 = -(b * t1 + 2 * v * Math.Sqrt(t1)) * X * X / ((binfinity - b0) * b0);
double ht2 = -(b * T + 2 * v * Math.Sqrt(T)) * X * X / ((binfinity - b0) * b0);
double I1 = b0 + (binfinity - b0) * (1 - Math.Exp(ht1));
double I2 = b0 + (binfinity - b0) * (1 - Math.Exp(ht2));
double alfa1 = (I1 - X) * Math.Pow(I1, -beta);
double alfa2 = (I2 - X) * Math.Pow(I2, -beta);
if (S >= I2)
{
option_price = S - X;
}
else
{
option_price = alfa2 * Math.Pow(S, beta) - alfa2 * phi(S, t1, beta, I2, I2, r, b, v)
+ phi(S, t1, 1, I2, I2, r, b, v) - phi(S, t1, 1, I1, I2, r, b, v)
- X * phi(S, t1, 0, I2, I2, r, b, v) + X * phi(S, t1, 0, I1, I2, r, b, v)
+ alfa1 * phi(S, t1, beta, I1, I2, r, b, v) - alfa1 * ksi(S, T, beta, I1, I2, I1, t1, r, b, v)
+ ksi(S, T, 1, I1, I2, I1, t1, r, b, v) - ksi(S, T, 1, X, I2, I1, t1, r, b, v)
- X * ksi(S, T, 0, I1, I2, I1, t1, r, b, v) + X * ksi(S, T, 0, X, I2, I1, t1, r, b, v);
}
}
return(option_price);
}
public static double ForwardStart(string cpflg, double S0, double t, double T, double r, double b, double vol, double a)
{
double return_value = double.NaN;
return_value = DoubleExponentialTransformation.Integrate((y) => { return(Normal.PDF(0, 1, y)
* BlackScholesMethod.BlackScholes(cpflg, S0 * Math.Exp((b - 0.5 * vol * vol) * t + y * vol
* Math.Sqrt(t)), Math.Max(S0 * Math.Exp((b - 0.5 * vol * vol) * t + y * vol * Math.Sqrt(t)) + a, 0),
T - t, r, b, vol)); }, -200, 200, 1e-4);
return(return_value);
}
public static double DiscreteAsianHHM(string cpflg, double S, double SA, double X,
double t1, double T, double n, double m, double r, double b, double v)
{
double d1, d2, h, EA, EA2, vA, OptionValue, SA1, X1, price;
SA1 = SA;
X1 = X;
h = (T - t1) / (n - 1);
if (b == 0)
{
EA = S;
}
else
{
EA = S / n * Exp(b * t1) * (1 - Exp(b * h * n)) / (1 - Exp(b * h));
}
if (m > 0)
{
if (SA > n / m * X)
{
if (cpflg == "p")
{
price = 0;
return(price);
}
else if (cpflg == "c")
{
SA = SA * m / n + EA * (n - m) / n;
price = (SA - X) * Exp(-r * T);
return(price);
}
SA = SA1;
}
}
if (m == n - 1)
{
X = n * X - (n - 1) * SA;
price = BlackScholesMethod.BlackScholes(cpflg, S, X, T, r, b, v) * 1 / n;
X = X1;
SA = SA1;
return(price);
}
if (b == 0)
{
EA2 = S * S * Exp(v * v * t1) / (n * n)
* ((1 - Exp(v * v * h * n)) / (1 - Exp(v * v * h))
+ 2 / (1 - Exp(v * v * h)) * (n - (1 - Exp(v * v * h * n))));
}
else
{
EA2 = S * S * Exp((2 * b + v * v) * t1) / (n * n)
* ((1 - Exp((2 * b + v * v) * h * n)) / (1 - Exp((2 * b + v * v) * h))
+ 2 / (1 - Exp((b + v * v) * h)) * ((1 - Exp(b * h * n)) / (1 - Exp(b * h))
- (1 - Exp((2 * b + v * v) * h * n)) /
(1 - Exp((2 * b + v * v) * h))));
}
vA = Sqr((Log(EA2) - 2 * Log(EA)) / T);
OptionValue = 0;
if (m > 0)
{
X = n / (n - m) * X - m / (n - m) * SA;
}
d1 = (Log(EA / X) + vA * vA / 2 * T) / (vA * Sqr(T));
d2 = d1 - vA * Sqr(T);
if (cpflg == "c")
{
OptionValue = Exp(-r * T) * (EA * CND(d1) - X * CND(d2));
}
else if (cpflg == "p")
{
OptionValue = Exp(-r * T) * (X * CND(-d2) - EA * CND(-d1));
}
price = OptionValue * (n - m) / n;
return(price);
}
public static double SoftBarrierOption(string tpflag, double S,
double X, double L, double U, double T,
double r, double b, double vol)
{
int eta;
double price = double.NaN;
string OutInFlag;
string CallPutFlag;
OutInFlag = tpflag.Substring(1, 2);
CallPutFlag = tpflag.Substring(0, 1);
if (OutInFlag == "di" | OutInFlag == "ui")
{
if (CallPutFlag == "c")
{
eta = 1;
}
else
{
eta = -1;
}
double mu = (b + vol * vol / 2) / vol / vol;
double lambda1 = Exp(-0.5 * vol * vol * T * (mu + 0.5) * (mu - 0.5));
double lambda2 = Exp(-0.5 * vol * vol * T * (mu - 0.5) * (mu - 1.5));
double d1 = Log(U * U / S / X) / vol / Sqr(T) + mu * vol * Sqr(T);
double d2 = d1 - (mu + 0.5) * vol * Sqr(T);
double d3 = Log(U * U / S / X) / vol / Sqr(T) + (mu - 1) * vol * Sqr(T);
double d4 = d1 - (mu - 0.5) * vol * Sqr(T);
double e1 = Log(L * L / S / X) / vol / Sqr(T) + mu * vol * Sqr(T);
double e2 = e1 - (mu + 0.5) * vol * Sqr(T);
double e3 = Log(L * L / S / X) / vol / Sqr(T) + (mu - 1) * vol * Sqr(T);
double e4 = e3 - (mu - 0.5) * vol * Sqr(T);
price = (eta * S * Exp((b - r) * T) * Math.Pow(S, -2 * mu) * Math.Pow(S * X, 0.5 + mu) / (2 * mu + 1) * (Math.Pow(U * U / S / X, mu + 0.5
) * CND(eta * d1) - lambda1 * CND(eta * d2) - Math.Pow(L * L / S / X, mu + 0.5) * CND(eta * e1) + lambda1 * CND(eta * e2))
- eta * X * Exp(-r * T) * Math.Pow(S, -2 * mu + 2) * Math.Pow(S * X, -0.5 + mu) / (2 * mu - 1) * (Math.Pow(U * U / S / X, mu - 0.5
) * CND(eta * d3) - lambda2 * CND(eta * d4) - Math.Pow(L * L / S / X, mu - 0.5) * CND(eta * e3) + lambda2 * CND(eta * e4))) / (U - L);
return(price);
}
else if (OutInFlag == "do" | OutInFlag == "uo")
{
if (CallPutFlag == "c")
{
eta = 1;
}
else
{
eta = -1;
}
double mu = (b + vol * vol / 2) / vol / vol;
double lambda1 = Exp(-0.5 * vol * vol * T * (mu + 0.5) * (mu - 0.5));
double lambda2 = Exp(-0.5 * vol * vol * T * (mu - 0.5) * (mu - 1.5));
double d1 = Log(U * U / S / X) / vol / Sqr(T) + mu * vol * Sqr(T);
double d2 = d1 - (mu + 0.5) * vol * Sqr(T);
double d3 = Log(U * U / S / X) / vol / Sqr(T) + (mu - 1) * vol * Sqr(T);
double d4 = d1 - (mu - 0.5) * vol * Sqr(T);
double e1 = Log(L * L / S / X) / vol / Sqr(T) + mu * vol * Sqr(T);
double e2 = e1 - (mu + 0.5) * vol * Sqr(T);
double e3 = Log(L * L / S / X) / vol / Sqr(T) + (mu - 1) * vol * Sqr(T);
double e4 = e3 - (mu - 0.5) * vol * Sqr(T);
price = BlackScholesMethod.BlackScholes(CallPutFlag, S, X, T, r, b, vol) - (eta * S * Exp((b - r) * T) * Math.Pow(S, -2 * mu) * Math.Pow(S * X, 0.5 + mu) / (2 * mu + 1) * (Math.Pow(U * U / S / X, mu + 0.5
) * CND(eta * d1) - lambda1 * CND(eta * d2) - Math.Pow(L * L / S / X, mu + 0.5) * CND(eta * e1) + lambda1 * CND(eta * e2))
- eta * X * Exp(-r * T) * Math.Pow(S, -2 * mu + 2) * Math.Pow(S * X, -0.5 + mu) / (2 * mu - 1) * (Math.Pow(U * U / S / X, mu - 0.5
) * CND(eta * d3) - lambda2 * CND(eta * d4) - Math.Pow(L * L / S / X, mu - 0.5) * CND(eta * e3) + lambda2 * CND(eta * e4))) / (U - L);
return(price);
}
return(price);
}
public static double DoubleBarrier(string TypeFlag, double S, double X, double l, double U, double T,
double r, double b, double v, double delta1, double delta2)
{
double E, F, Sum1, Sum2, d1, d2, d3, d4, mu1, mu2, mu3, OutValue, price;
OutValue = 0;
price = double.NaN;
F = U * Exp(delta1 * T);
E = l * Exp(delta2 * T);
Sum1 = 0;
Sum2 = 0;
if (TypeFlag == "co" | TypeFlag == "ci")
{
for (int n = -5; n < 5; n++)
{
d1 = (Log(S * Math.Pow(U, 2 * n) / (X * Math.Pow(l, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
d2 = (Log(S * Math.Pow(U, 2 * n) / (F * Math.Pow(l, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
d3 = (Log(Math.Pow(l, 2 * n + 2) / (X * S * Math.Pow(U, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
d4 = (Log(Math.Pow(l, 2 * n + 2) / (F * S * Math.Pow(U, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
mu1 = 2 * (b - delta2 - n * (delta1 - delta2)) / (v * v) + 1;
mu2 = 2 * n * (delta1 - delta2) / (v * v);
mu3 = 2 * (b - delta2 + n * (delta1 - delta2)) / (v * v) + 1;
Sum1 = Sum1 + Math.Pow((Math.Pow(U, n) / Math.Pow(l, n)), mu1) * Math.Pow(l / S, mu2) * (CND(d1) - CND(d2)) - (Math.Pow(Math.Pow(l, n + 1) / (Math.Pow(U, n) * S), mu3)) * (CND(d3) - CND(d4));
Sum2 = Sum2 + Math.Pow((Math.Pow(U, n) / Math.Pow(l, n)), (mu1 - 2)) * Math.Pow(l / S, mu2) * (CND(d1 - v * Sqr(T)) - CND(d2 - v * Sqr(T))) - (Math.Pow(Math.Pow(l, n + 1) / (Math.Pow(U, n) * S), mu3 - 2) * (CND(d3 - v * Sqr(T)) - CND(d4 - v * Sqr(T))));
}
OutValue = S * Exp((b - r) * T) * Sum1 - X * Exp(-r * T) * Sum2;
}
else if (TypeFlag == "po" | TypeFlag == "pi")
{
for (int n = -5; n < 5; n++)
{
d1 = (Log(S * Math.Pow(U, 2 * n) / (E * Math.Pow(l, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
d2 = (Log(S * Math.Pow(U, 2 * n) / (X * Math.Pow(l, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
d3 = (Log(Math.Pow(l, 2 * n + 2) / (E * S * Math.Pow(U, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
d4 = (Log(Math.Pow(l, 2 * n + 2) / (X * S * Math.Pow(U, 2 * n))) + (b + v * v / 2) * T) / (v * Sqr(T));
mu1 = 2 * (b - delta2 - n * (delta1 - delta2)) / (v * v) + 1;
mu2 = 2 * n * (delta1 - delta2) / (v * v);
mu3 = 2 * (b - delta2 + n * (delta1 - delta2)) / (v * v) + 1;
Sum1 = Sum1 + Math.Pow((Math.Pow(U, n) / Math.Pow(l, n)), mu1) * Math.Pow(l / S, mu2) * (CND(d1) - CND(d2)) - (Math.Pow(Math.Pow(l, n + 1) / (Math.Pow(U, n) * S), mu3)) * (CND(d3) - CND(d4));
Sum2 = Sum2 + Math.Pow((Math.Pow(U, n) / Math.Pow(l, n)), (mu1 - 2)) * Math.Pow(l / S, mu2) * (CND(d1 - v * Sqr(T)) - CND(d2 - v * Sqr(T))) - (Math.Pow(Math.Pow(l, n + 1) / (Math.Pow(U, n) * S), mu3 - 2) * (CND(d3 - v * Sqr(T)) - CND(d4 - v * Sqr(T))));
}
OutValue = X * Exp(-r * T) * Sum2 - S * Exp((b - r) * T) * Sum1;
}
if (TypeFlag == "co" | TypeFlag == "po")
{
price = OutValue;
}
else if (TypeFlag == "ci")
{
price = BlackScholesMethod.BlackScholes("c", S, X, T, r, b, v) - OutValue;
}
else if (TypeFlag == "pi")
{
price = BlackScholesMethod.BlackScholes("p", S, X, T, r, b, v) - OutValue;
}
return(price);
}