/// <summary>
/// Gets the theta.
/// </summary>
/// <returns></returns>
public double GetTheta()
{
double spot = Tree.Underlying(0, 0);
double _tau = Tree.Time;
int n1 = _divdays.Length;
int n2 = _ratedays.Length;
BinomialTreePricer lhs1 = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', _tau, _vol, Tree.Columns, _flatFlag, Style, Smoothing, _ratedays, _rateamts, _divdays, _divamts, _treeType);
int[] _divdays1 = new int[n1];
for (int idx = 0; idx < n1; idx++)
{
_divdays1[idx] = Math.Max(_divdays[idx] - 1, 0);
}
int[] _ratedays1 = new int[n2];
for (int idx = 0; idx < n2; idx++)
{
_ratedays1[idx] = Math.Max(_ratedays[idx] - 1, 0);
}
BinomialTreePricer lhs2 = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', _tau - 1.0 / 365.0, _vol, Tree.Columns, _flatFlag, Style, Smoothing, _ratedays1, _rateamts, _divdays1, _divamts, _treeType);
double p1 = lhs1.GetPrice();
double p2 = lhs2.GetPrice();
double theta = lhs2.GetPrice() - lhs1.GetPrice();
return(theta);
}
//Smoothing as describe in Orc quant guide.
private void Smooth(string str, ITree spotTree)
{
if (str != null)
{
double dt = spotTree.Tau / spotTree.Gridsteps;
if ((str.ToLower() == "y") | (str.ToLower() == "yes"))
{
int centre = 0;
int k, j;
int idx = Gridsteps - 1;
for (k = 1; spotTree.GetSpotMatrix(idx, k - 1) <= Strike &&
spotTree.GetSpotMatrix(idx, k) <= Strike &&
k <= Gridsteps - 1; k++)
{
}
if (k == 1)
{
centre = 2;
}
else if (k >= Gridsteps - 1)
{
centre = Gridsteps - 2;
}
else if (k <= Gridsteps - 2 && (k > 1))
{
if (Math.Abs(spotTree.GetSpotMatrix(idx, k - 2) / Strike - 1) >
Math.Abs(spotTree.GetSpotMatrix(idx, k + 1) / Strike - 1))
{
centre = k;
}
else
{
centre = k - 1;
}
}
for (j = centre - 1; j <= centre + 1; j++)
{
double temp;
if (Payoff.ToLower() == "c" || (Payoff.ToLower() == "call"))
{
//temp = BSprice(SpotTree.Get_SpotMatrix(idx, j)
//, dt, Strike, get_r(idx), SpotTree.sig, "C");
double fwd = spotTree.GetSpotMatrix(idx, j) - spotTree.GetDiv(idx);
fwd *= Math.Exp(spotTree.GetR(idx) * dt);
temp = BSprice(fwd, dt, Strike, spotTree.GetR(idx), spotTree.Sig, "C");
SetPriceMatrix(idx, j, temp);
}
else if ((Payoff.ToLower() == "p") || (Payoff.ToLower() == "put"))
{
//temp = BSprice(SpotTree.Get_SpotMatrix(idx, j)
//, dt, Strike, get_r(idx), SpotTree.sig, "P");
double fwd = spotTree.GetSpotMatrix(idx, j) - spotTree.GetDiv(idx);
fwd *= Math.Exp(spotTree.GetR(idx) * dt);
temp = BSprice(fwd, dt, Strike, spotTree.GetR(idx), spotTree.Sig, "P");
SetPriceMatrix(idx, j, temp);
}
}
}
}
}
//Make grid passing in a tree object.
public void MakeGrid(ITree spotTree)
{
Gridsteps = spotTree.Gridsteps;
EmptyArrays();
MakeArrays();
FillRates(spotTree);
TermValue(spotTree);
FillP(spotTree);
PreTermValue(spotTree);
Smooth(Smoothing, spotTree);
//Iterate backward through tree to price American or Euro calls or puts.
double temp;
double dt = spotTree.Tau / spotTree.Gridsteps;
if ((Style.ToLower() == "a") | (Style.ToLower() == "american"))
{
for (int i = Gridsteps - 2; i >= 0; i--)
{
for (int j = 0; j <= i; j++)
{
if ((Payoff.ToLower() == "c") | (Payoff.ToLower() == "call"))
{
temp = Math.Max(Math.Exp(-spotTree.GetR(i) * dt) * (GetP(i) *
GetPriceMatrix(i + 1, j + 1) + (1 - GetP(i)) *
GetPriceMatrix(i + 1, j)), spotTree.GetSpotMatrix(i, j)
- Strike);
SetPriceMatrix(i, j, temp);
}
else if ((Payoff.ToLower() == "p") | (Payoff.ToLower() == "put"))
{
temp = Math.Max(Math.Exp(-spotTree.GetR(i) * dt) * (GetP(i) *
GetPriceMatrix(i + 1, j + 1) + (1 - GetP(i)) *
GetPriceMatrix(i + 1, j)), Strike - spotTree.GetSpotMatrix(i, j));
SetPriceMatrix(i, j, temp);
}
}
}
}
else if ((Style.ToLower() == "e") | (Style.ToLower() == "european"))
{
for (int i = Gridsteps - 2; i >= 0; i--)
{
for (int j = 0; j <= i; j++)
{
temp = Math.Exp(-spotTree.GetR(i) * dt) * (GetP(i) *
GetPriceMatrix(i + 1, j + 1) + (1 - GetP(i)) *
GetPriceMatrix(i + 1, j));
SetPriceMatrix(i, j, temp);
}
}
}
}
/// <summary>
/// Makes the grid.
/// </summary>
private void MakeGrid()
{
EmptyArrays();
MakeArrays();
TermValue();
PreTermValue();
Smooth(Smoothing);
//Iterate backward through tree to price American or Euro calls or puts.
int n = Tree.Columns;
double _tau = Tree.Time;
double temp = 0;
double dt = _tau / Tree.Columns;
if ((Style.ToLower() == "a") | (Style.ToLower() == "american"))
{
for (int i = n - 2; i >= 0; i--)
{
for (int j = 0; j <= i; j++)
{
if ((Payoff.ToLower() == "c") | (Payoff.ToLower() == "call"))
{
temp = Math.Max(Math.Exp(-Tree.Rate(i) * dt) * (GetP(i) *
GetPriceMatrix(i + 1, j + 1) + (1 - GetP(i)) *
GetPriceMatrix(i + 1, j)), Tree.Underlying(i, j)
- Strike);
SetPriceMatrix(i, j, temp);
}
else if ((Payoff.ToLower() == "p") | (Payoff.ToLower() == "put"))
{
temp = Math.Max(Math.Exp(-Tree.Rate(i) * dt) * (GetP(i) *
GetPriceMatrix(i + 1, j + 1) + (1 - GetP(i)) *
GetPriceMatrix(i + 1, j)), Strike - Tree.Underlying(i, j));
SetPriceMatrix(i, j, temp);
}
}
}
}
else if ((Style.ToLower() == "e") | (Style.ToLower() == "european"))
{
for (int i = n - 2; i >= 0; i--)
{
for (int j = 0; j <= i; j++)
{
temp = Math.Exp(-Tree.Rate(i) * dt) * (GetP(i) *
GetPriceMatrix(i + 1, j + 1) + (1 - GetP(i)) *
GetPriceMatrix(i + 1, j));
SetPriceMatrix(i, j, temp);
}
}
}
}
/// <summary>
/// Gets the vega.
/// </summary>
/// <returns></returns>
public double GetVega()
{
double spot = Tree.Underlying(0, 0);
double _tau = Tree.Time;
BinomialTreePricer lhs1 = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', _tau, 0.99 * _vol, Tree.Columns, _flatFlag, Style, Smoothing, _ratedays, _rateamts, _divdays, _divamts, _treeType);
BinomialTreePricer lhs2 = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', _tau, 1.01 * _vol, Tree.Columns, _flatFlag, Style, Smoothing, _ratedays, _rateamts, _divdays, _divamts, _treeType);
double P1 = lhs1.GetPrice();
double P2 = lhs2.GetPrice();
double vega = 0.0;
if (_vol != 0)
{
vega = 0.01 * (P2 - P1) / (2 * 0.01 * _vol);
}
return(vega);
}
/// <summary>
/// Gets the vega.
/// </summary>
/// <returns></returns>
public double GetVega()
{
double spot = Tree.Underlying(0, 0);
double tau = Tree.Time;
BinomialTreePricer lhs1 = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', tau, 0.99 * _volatility, Tree.Columns, _flatFlag, Style, Smoothing, _rateDays, _rateAmounts, _dividendDays, _dividendAmounts, _treeType);
BinomialTreePricer lhs2 = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', tau, 1.01 * _volatility, Tree.Columns, _flatFlag, Style, Smoothing, _rateDays, _rateAmounts, _dividendDays, _dividendAmounts, _treeType);
double p1 = lhs1.GetPrice();
double p2 = lhs2.GetPrice();
double vega = 0.0;
if (_volatility != 0)
{
vega = 0.01 * (p2 - p1) / (2 * 0.01 * _volatility);
}
return(vega);
}
/// <summary>
/// Gets the gamma.
/// </summary>
/// <returns></returns>
public double GetGamma()
{
double spot = Tree.Underlying(0, 0);
int steps = Tree.Columns + 2;
double tau = Tree.Time * (1 + 2 / steps);
BinomialTreePricer clone = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', tau, _vol, steps, _flatFlag, Style, Smoothing, _ratedays, _rateamts, _divdays, _divamts, _treeType);
double[] S = new double[3];
double[] C = new double[3];
for (int i = 0; i <= 2; ++i)
{
S[i] = clone.Tree.Underlying(2, i);
C[i] = clone.GetPriceMatrix(2, i);
}
double gamma = 2 * (S[0] * (C[1] - C[2]) + S[1] * (C[2] - C[0]) + S[2] * (C[0] - C[1]))
/ (S[1] - S[0]) / (S[2] - S[0]) / (S[2] - S[1]);
return(gamma);
}
/// <summary>
/// Gets the gamma.
/// </summary>
/// <returns></returns>
public double GetGamma()
{
double spot = Tree.Underlying(0, 0);
int steps = Tree.Columns + 2;
double tau = Tree.Time * (1 + 2 / steps);
BinomialTreePricer clone = new BinomialTreePricer(spot, Strike, Payoff.ToLower()[0] == 'p', tau, _volatility, steps, _flatFlag, Style, Smoothing, _rateDays, _rateAmounts, _dividendDays, _dividendAmounts, _treeType);
double[] s = new double[3];
double[] c = new double[3];
for (int i = 0; i <= 2; ++i)
{
s[i] = clone.Tree.Underlying(2, i);
c[i] = clone.GetPriceMatrix(2, i);
}
double gamma = 2 * (s[0] * (c[1] - c[2]) + s[1] * (c[2] - c[0]) + s[2] * (c[0] - c[1]))
/ (s[1] - s[0]) / (s[2] - s[0]) / (s[2] - s[1]);
return(gamma);
}
//Assign terminal payoff condition.
private void TermValue(ITree spotTree)
{
if (spotTree != null)
{
for (int j = 0; j <= Gridsteps; j++)
{
double temp;
Payoff = Payoff.ToLower();
if ((Payoff == "c") | (Payoff == "call"))
{
temp = Math.Max(spotTree.GetSpotMatrix(Gridsteps, j) - Strike, 0);
SetPriceMatrix(Gridsteps, j, temp);
}
else if ((Payoff.ToLower() == "p") | (Payoff.ToLower() == "put"))
{
temp = Math.Max(Strike - spotTree.GetSpotMatrix(Gridsteps, j), 0);
SetPriceMatrix(Gridsteps, j, temp);
}
}
}
}
private double Bisection(double prem, double fwdPrice)
{
double right = 0.75;
double left = 0.35;
double mid;
var cp = Payoff.ToLower() == "c" ? 1 : -1;
int days = Expiry.Subtract(Today).Days;
double t = days / 365.0;
var priceClone = (AmOptionAnalytics)Clone();
if (fwdPrice <= 0 || Strike <= 0 || t <= 0 || prem <= 0)
{
return(0);
}
double df = Convert.ToDouble(RateCurve.GetDf(days));
if (prem < Math.Max(cp * df * (fwdPrice - priceClone.Strike), 0))
{
throw new System.Exception("No solution for volatility");
}
do
{
mid = (right + left) / 2;
priceClone.Sig = left;
double fleft = priceClone.Price() - prem;
priceClone.Sig = right;
double fright = priceClone.Price() - prem;
priceClone.Sig = mid;
double fmid = priceClone.Price() - prem;
if (fleft * fmid < 0)
{
right = mid;
}
else if (fright * fmid < 0)
{
left = mid;
}
} while (Math.Abs(right - left) > 2 * Eps);
return(mid);
}
//Assign values at Gridsteps-1 node.
private void PreTermValue(Tree SpotTree)
{
if (SpotTree != null)
{
double temp = 0;
double dt = SpotTree.Tau / SpotTree.Gridsteps;
int idx = Gridsteps - 1;
for (int j = 0; j <= Gridsteps - 1; j++)
{
if ((Style.ToLower() == "a") | (Style.ToLower() == "american"))
{
if ((Payoff.ToLower() == "c") | (Payoff.ToLower() == "call"))
{
temp = Math.Max(Math.Exp(-SpotTree.GetR(idx) * dt) * (Get_P(idx) *
Get_PriceMatrix(idx + 1, j + 1) + (1 - Get_P(idx)) *
Get_PriceMatrix(idx + 1, j)), SpotTree.GetSpotMatrix(idx, j)
- Strike);
Set_PriceMatrix(idx, j, temp);
}
else if ((Payoff.ToLower() == "p") | (Payoff.ToLower() == "put"))
{
temp = Math.Max(Math.Exp(-SpotTree.GetR(idx) * dt) * (Get_P(idx) *
Get_PriceMatrix(idx + 1, j + 1) + (1 - Get_P(idx)) *
Get_PriceMatrix(idx + 1, j)), -SpotTree.GetSpotMatrix(idx, j)
+ Strike);
Set_PriceMatrix(idx, j, temp);
}
}
else if ((Style.ToLower() == "e") | (Style.ToLower() == "european"))
{
temp = Math.Exp(-SpotTree.GetR(idx) * dt) * (Get_P(idx) *
Get_PriceMatrix(idx + 1, j + 1) + (1 - Get_P(idx)) *
Get_PriceMatrix(idx + 1, j));
Set_PriceMatrix(idx, j, temp);
}
}
}
}
private double Newton(double prem, double fwdPrice)
{
double dvol;
var cp = Payoff.ToLower() == "c" ? 1 : -1;
int days = Expiry.Subtract(Today).Days;
double t = days / 365.0;
var priceClone = (AmOptionAnalytics)Clone();
if (fwdPrice <= 0 || Strike <= 0 || t <= 0 || prem <= 0)
{
return(0);
}
//double df = Convert.ToDouble(_rateCurve.getDf(days));
if (prem < Math.Max(cp * (fwdPrice - priceClone.Strike), 0))
{
throw new System.Exception("No solution for volatility");
}
int idx = 0;
do
{
var price = priceClone.Price();
priceClone.MakeVega();
var vega = priceClone.Vega;
if (vega == 0 || idx > Maxits)
{
throw new System.Exception("No volatility solution");
}
dvol = (price - prem) / (100 * vega);
priceClone.Sig -= dvol;
if (priceClone.Sig < 0)
{
priceClone.Sig = 0;
}
idx++;
} while (Math.Abs(dvol) > Eps);
return(priceClone.Sig);
}
/// <summary>
/// Assign terminal payoff condition.
/// </summary>
private void TermValue()
{
int n = Tree.Columns;
if (Tree != null)
{
for (int j = 0; j <= n; j++)
{
double temp = 0.0;
Payoff = Payoff.ToLower();
if ((Payoff == "c") | (Payoff == "call"))
{
temp = Math.Max(Tree.Underlying(n, j) - Strike, 0);
SetPriceMatrix(n, j, temp);
}
else if ((Payoff.ToLower() == "p") | (Payoff.ToLower() == "put"))
{
temp = Math.Max(Strike - Tree.Underlying(n, j), 0);
SetPriceMatrix(n, j, temp);
}
}
}
}
/// <summary>
/// Assign values at Gridsteps-1 node.
/// </summary>
private void PreTermValue()
{
if (Tree != null)
{
int n = Tree.Columns;
double temp = 0;
double dt = Tree.Time / n;
int idx = n - 1;
for (int j = 0; j <= n - 1; j++)
{
if ((Style.ToLower() == "a") | (Style.ToLower() == "american"))
{
if ((Payoff.ToLower() == "c") | (Payoff.ToLower() == "call"))
{
temp = Math.Max(Math.Exp(-Tree.Rate(idx) * dt) * (GetP(idx) *
GetPriceMatrix(idx + 1, j + 1) + (1 - GetP(idx)) *
GetPriceMatrix(idx + 1, j)), Tree.Underlying(idx, j) - Strike);
SetPriceMatrix(idx, j, temp);
}
else if ((Payoff.ToLower() == "p") | (Payoff.ToLower() == "put"))
{
temp = Math.Max(Math.Exp(-Tree.Rate(idx) * dt) * (GetP(idx) *
GetPriceMatrix(idx + 1, j + 1) + (1 - GetP(idx)) *
GetPriceMatrix(idx + 1, j)), -Tree.Underlying(idx, j) + Strike);
SetPriceMatrix(idx, j, temp);
}
}
else if ((Style.ToLower() == "e") | (Style.ToLower() == "european"))
{
temp = Math.Exp(-Tree.Rate(idx) * dt) * (GetP(idx) *
GetPriceMatrix(idx + 1, j + 1) + (1 - GetP(idx)) *
GetPriceMatrix(idx + 1, j));
SetPriceMatrix(idx, j, temp);
}
}
}
}
/// <summary>
///Here we Smooth the 3 -closest nodes to the strike at the second last timestep. This involves
///replacing the tree calculated price with the BS price. This has minimal effect on the price
///but significant effect on smoothness of spatial derivatives especially second order like gamma
/// </summary>
/// <param name="str">The STR.</param>
private void Smooth(string str)
{
double _tau = Tree.Time;
int n = Tree.Columns;
if (str != null)
{
double dt = _tau / Tree.Columns;
if ((str.ToLower() == "y") | (str.ToLower() == "yes"))
{
int Centre = 0;
int k, j;
int idx = Tree.Columns - 1;
k = 1;
for (k = 1; ((Tree.Underlying(idx, k - 1) <= Strike) &&
((Tree.Underlying(idx, k) <= Strike)) &&
((k <= n - 1))); k++)
{
}
if (k == 1)
{
Centre = 2;
}
else if (k >= n - 1)
{
Centre = n - 2;
}
else if ((k <= n - 2) && (k > 1))
{
if (Math.Abs(Tree.Underlying(idx, k - 2) / Strike - 1) >
Math.Abs(Tree.Underlying(idx, k + 1) / Strike - 1))
{
Centre = k;
}
else
{
Centre = k - 1;
}
}
for (j = Centre - 1; j <= Centre + 1; j++)
{
double temp = 0;
if ((Payoff.ToLower() == "c") || (Payoff.ToLower() == "call"))
{
//temp = BSprice(tree.Get_SpotMatrix(idx, j)
//, dt, Strike, get_r(idx), tree.sig, "C");
double fwd = Tree.Underlying(idx, j) - Tree.Dividend(idx);
fwd *= Math.Exp(Tree.Rate(idx) * dt);
temp = BSprice(fwd, dt, Strike, Tree.Rate(idx), Tree.Volatility, "C");
SetPriceMatrix(idx, j, temp);
}
else if ((Payoff.ToLower() == "p") || (Payoff.ToLower() == "put"))
{
//temp = BSprice(tree.Get_SpotMatrix(idx, j)
//, dt, Strike, get_r(idx), tree.sig, "P");
double fwd = Tree.Underlying(idx, j) - Tree.Dividend(idx);
fwd *= Math.Exp(Tree.Rate(idx) * dt);
temp = BSprice(fwd, dt, Strike, Tree.Rate(idx), Tree.Volatility, "P");
SetPriceMatrix(idx, j, temp);
}
}
}
}
}
//Smoothing as describe in Orc quant guide.
private void Smooth(string str, Tree SpotTree)
{
if (str != null)
{
double dt = SpotTree.Tau / SpotTree.Gridsteps;
if ((str.ToLower() == "y") | (str.ToLower() == "yes"))
{
int Centre = 0;
int k, j;
int idx = Gridsteps - 1;
k = 1;
for (k = 1; ((SpotTree.GetSpotMatrix(idx, k - 1) <= Strike) &&
((SpotTree.GetSpotMatrix(idx, k) <= Strike)) &&
((k <= Gridsteps - 1))); k++)
{
}
if (k == 1)
{
Centre = 2;
}
else if (k >= Gridsteps - 1)
{
Centre = Gridsteps - 2;
}
else if ((k <= Gridsteps - 2) && (k > 1))
{
if (Math.Abs(SpotTree.GetSpotMatrix(idx, k - 2) / Strike - 1) >
Math.Abs(SpotTree.GetSpotMatrix(idx, k + 1) / Strike - 1))
{
Centre = k;
}
else
{
Centre = k - 1;
}
}
for (j = Centre - 1; j <= Centre + 1; j++)
{
double temp = 0;
if ((Payoff.ToLower() == "c") || (Payoff.ToLower() == "call"))
{
//temp = BSprice(SpotTree.Get_SpotMatrix(idx, j)
//, dt, Strike, get_r(idx), SpotTree.sig, "C");
double fwd = SpotTree.GetSpotMatrix(idx, j) - SpotTree.get_div(idx);
fwd *= Math.Exp(SpotTree.GetR(idx) * dt);
temp = BSprice(fwd, dt, Strike, SpotTree.GetR(idx), SpotTree.Sig, "C");
Set_PriceMatrix(idx, j, temp);
}
else if ((Payoff.ToLower() == "p") || (Payoff.ToLower() == "put"))
{
//temp = BSprice(SpotTree.Get_SpotMatrix(idx, j)
//, dt, Strike, get_r(idx), SpotTree.sig, "P");
double fwd = SpotTree.GetSpotMatrix(idx, j) - SpotTree.get_div(idx);
fwd *= Math.Exp(SpotTree.GetR(idx) * dt);
temp = BSprice(fwd, dt, Strike, SpotTree.GetR(idx), SpotTree.Sig, "P");
Set_PriceMatrix(idx, j, temp);
}
}
}
}
}
