public static object AmericanFutureOptionImpliedVol(
[ExcelArgument(Description = "Time-to-expiry")] double T,
[ExcelArgument(Description = "Strike")] double K,
[ExcelArgument(Description = "Forward")] double F,
[ExcelArgument(Description = "Discounting rate")] double R,
[ExcelArgument(Description = "Option Premium")] double PV,
[ExcelArgument(Description = "Call or Put")] string CP,
[ExcelArgument(Description = "Pricing method (Defult Trinomial)")] string Method)
{
return(ExcelHelper.Execute(_logger, () =>
{
if (!Enum.TryParse(CP, out OptionType optType))
{
return $"Could not parse call or put flag - {CP}";
}
if (!Enum.TryParse(Method, out AmericanPricingType method))
{
return $"Could not parse pricing type - {Method}";
}
if (method == AmericanPricingType.Binomial)
{
return BinomialTree.AmericanFuturesOptionImpliedVol(F, K, R, T, PV, optType);
}
else
{
return TrinomialTree.AmericanFuturesOptionImpliedVol(F, K, R, T, PV, optType);
}
}));
}
public override Lattice tree( TimeGrid grid)
{
TermStructureFittingParameter phi= new TermStructureFittingParameter(termStructure());
ShortRateDynamics numericDynamics=
new Dynamics(phi, a(), sigma());
TrinomialTree trinomial=
new TrinomialTree(numericDynamics.process(), grid);
ShortRateTree numericTree =
new ShortRateTree(trinomial, numericDynamics, grid);
TermStructureFittingParameter.NumericalImpl impl =
(TermStructureFittingParameter.NumericalImpl)phi.implementation();
impl.reset();
double value = 1.0;
double vMin = -50.0;
double vMax = 50.0;
for (int i=0; i<(grid.size() - 1); i++) {
double discountBond = termStructure().link.discount(grid[i+1]);
double xMin = trinomial.underlying(i, 0);
double dx = trinomial.dx(i);
Helper finder = new Helper(i, xMin, dx, discountBond, numericTree);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
impl.setvalue(grid[i], value);
// vMin = value - 10.0;
// vMax = value + 10.0;
}
return numericTree;
}
public override Lattice tree(TimeGrid grid) {
TermStructureFittingParameter phi = new TermStructureFittingParameter(termStructure());
ShortRateDynamics numericDynamics = new Dynamics(phi, a(), sigma());
TrinomialTree trinomial = new TrinomialTree(numericDynamics.process(), grid);
ShortRateTree numericTree = new ShortRateTree(trinomial, numericDynamics, grid);
TermStructureFittingParameter.NumericalImpl impl =
(TermStructureFittingParameter.NumericalImpl)phi.implementation();
impl.reset();
for (int i=0; i<(grid.size() - 1); i++) {
double discountBond = termStructure().link.discount(grid[i+1]);
Vector statePrices = numericTree.statePrices(i);
int size = numericTree.size(i);
double dt = numericTree.timeGrid().dt(i);
double dx = trinomial.dx(i);
double x = trinomial.underlying(i,0);
double value = 0.0;
for (int j=0; j<size; j++) {
value += statePrices[j]*Math.Exp(-x*dt);
x += dx;
}
value = Math.Log(value/discountBond)/dt;
impl.setvalue(grid[i], value);
}
return numericTree;
}
public static void Main()
{
// Declare and initialise the parameters
TrinomialParameters myData;
// Clewlow p. 55 C = 8.42534 for N = 3
myData.sigma = 0.2;
myData.T = 1.0; // One year
myData.r = 0.06;
myData.K = 100;
myData.div = 0.03;
myData.type = 'C';
myData.exercise = false;
myData.NumberOfSteps = 3;
Console.WriteLine("How many timesteps: ");
myData.NumberOfSteps = Convert.ToInt32(Console.ReadLine());
// Now define option-related calculations and price
TrinomialTree myTree = new TrinomialTree(myData);
Console.WriteLine("Price {0}", myTree.Price(100));
// Clewlow p. 14 check against binomial method C = 10.1457
myData.sigma = 0.2;
myData.T = 1.0; // One year
myData.r = 0.06;
myData.K = 100;
myData.div = 0.0;
myData.type = 'C';
myData.exercise = false;
//myData.NumberOfSteps = 3;
TrinomialTree myTree2 = new TrinomialTree(myData);
Console.WriteLine("Price {0}", myTree2.Price(100));
// Clewlow p. 63 American Put
myData.sigma = 0.2;
myData.T = 1.0; // One year
myData.r = 0.06;
myData.K = 100;
myData.div = 0.0;
myData.type = 'P'; // Put
myData.exercise = true;
//myData.NumberOfSteps = 3;
TrinomialTree myTree3 = new TrinomialTree(myData);
Console.WriteLine("Price {0}", myTree3.Price(100));
}
public void PVFacts()
{
var t = 1.0;
var k = 0;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
var df = System.Math.Exp(-rf * t);
//zero strike put is worthless
var PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
//zero strike call is worth fwd with no discounting
cp = OptionType.C;
PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(f, PV, 10);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(f, PV, 10);
//and has delta = 1.0
var greeks = TrinomialTree.AmericanFutureOption(f, k, rf, t, vol, cp);
Assert.Equal(1.0, (double)greeks[1, 0], 10);
greeks = BinomialTree.AmericanFutureOption(f, k, rf, t, vol, cp);
Assert.Equal(1.0, (double)greeks[1, 0], 10);
//OTM option with zero vol is worthless
vol = 0.0;
k = f + 1;
PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
//option worth >= black in all cases for same inputs
vol = 0.32;
k = f + 20;
var PVBlack = BlackFunctions.BlackPV(f, k, rf, t, vol, cp);
PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.True(PV >= PVBlack);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.True(PV >= PVBlack);
}
public void PVFacts()
{
var t = 1.0;
var k = 0.0;
var f = 100.0;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
//zero strike put is worthless
var PV = TrinomialTree.AmericanAssetOptionPV(f, k, rf, f, t, vol, cp);
Assert.Equal(0, PV, 10);
PV = BinomialTree.AmericanPV(t, f, k, rf, vol, cp, rf, 100);
Assert.Equal(0, PV, 10);
var flatInterp = new DummyPointInterpolator(new[] { 1.0 }, new[] { rf });
var flatFwdInterp = new DummyPointInterpolator(new[] { 1.0 }, new[] { f });
PV = TrinomialTree.VanillaPV(t, f, k, flatInterp, vol, cp, flatFwdInterp, 100, true);
Assert.Equal(0, PV, 10);
//zero strike call is worth fwd with no discounting
cp = OptionType.C;
PV = TrinomialTree.AmericanAssetOptionPV(f, k, rf, f, t, vol, cp);
Assert.Equal(f, PV, 10);
PV = BinomialTree.AmericanPV(t, f, k, rf, vol, cp, rf, 100);
Assert.Equal(f, PV, 10);
//OTM option with zero vol is worthless
vol = 0.0;
k = f + 1.0;
PV = BinomialTree.AmericanPV(t, f, k, rf, vol, cp, rf, 100);
Assert.Equal(0, PV, 10);
PV = TrinomialTree.AmericanAssetOptionPV(f, k, rf, f, t, vol, cp);
Assert.Equal(0, PV, 10);
//option worth >= black in all cases for same inputs
vol = 0.32;
k = f + 20;
var PVBlack = BlackFunctions.BlackPV(f, k, rf, t, vol, cp);
PV = BinomialTree.AmericanPV(t, f, k, rf, vol, cp, rf, 100);
Assert.True(PV >= PVBlack);
PV = TrinomialTree.AmericanAssetOptionPV(f, k, rf, f, t, vol, cp);
Assert.True(PV >= PVBlack);
}
public void ImpliedVolFacts()
{
var t = 1.0;
var k = 120;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
var PVbi = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
var PVtri = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
var impliedVolBi = BinomialTree.AmericanFuturesOptionImpliedVol(f, k, rf, t, PVbi, cp);
var impliedVolTri = TrinomialTree.AmericanFuturesOptionImpliedVol(f, k, rf, t, PVtri, cp);
Assert.Equal(vol, impliedVolBi, 10);
Assert.Equal(vol, impliedVolTri, 10);
}
public void EuropeanOnGridFacts()
{
var t = 1.0;
var k = 120;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
var PVBlack = BlackFunctions.BlackPV(f, k, rf, t, vol, cp);
var PVbi = BinomialTree.EuropeanPV(t, f, k, rf, vol, cp, rf, 100);
var PVtri = TrinomialTree.EuropeanPV(t, f, k, rf, vol, cp, rf, 100);
Assert.Equal(PVBlack, PVbi, 1);
Assert.Equal(PVBlack, PVtri, 1);
PVbi = BinomialTree.EuropeanFuturePV(t, f, k, rf, vol, cp, 100);
PVtri = TrinomialTree.EuropeanFuturePV(t, f, k, rf, vol, cp, 100);
Assert.Equal(PVBlack, PVbi, 1);
Assert.Equal(PVBlack, PVtri, 1);
}
/// <summary>
/// Build a trinomial tree for given yield curve and time grids.
/// For better pricing, one tree shall be rebuilt for each trade because of different coupon time and call/put dates.
/// </summary>
/// <param name="times">The times.</param>
/// <param name="r0">The r0.</param>
/// <param name="yieldCurve">The yield curve.</param>
/// <returns></returns>
public override NumericTree Tree(double[] times, double r0, IYieldCurve yieldCurve = null)
{
var tree = new TrinomialTree(new OrnsteinUhlenbeckProcess(_a, _sigma), times, 0);
return(new NumericTree(this, tree, yieldCurve));
}
private TrinomialTree(TrinomialTree tritree)
{// Copy-constructor
// No body
}
public override Lattice tree(TimeGrid grid){
TrinomialTree trinomial = new TrinomialTree(dynamics().process(), grid, true);
return new ShortRateTree(trinomial, dynamics(), grid);
}