public virtual void test_formula()
{
CoxRossRubinsteinLatticeSpecification test = new CoxRossRubinsteinLatticeSpecification();
DoubleArray computed = test.getParametersTrinomial(VOL, RATE, DT);
double u = Math.Exp(VOL * Math.Sqrt(2.0 * DT));
double d = Math.Exp(-VOL * Math.Sqrt(2.0 * DT));
double up = Math.Pow((Math.Exp(0.5 * RATE * DT) - Math.Exp(-VOL * Math.Sqrt(0.5 * DT))) / (Math.Exp(VOL * Math.Sqrt(0.5 * DT)) - Math.Exp(-VOL * Math.Sqrt(0.5 * DT))), 2);
double dp = Math.Pow((Math.Exp(VOL * Math.Sqrt(0.5 * DT)) - Math.Exp(0.5 * RATE * DT)) / (Math.Exp(VOL * Math.Sqrt(0.5 * DT)) - Math.Exp(-VOL * Math.Sqrt(0.5 * DT))), 2);
DoubleArray expected = DoubleArray.of(u, 1d, d, up, 1d - up - dp, dp);
assertTrue(DoubleArrayMath.fuzzyEquals(computed.toArray(), expected.toArray(), 1.0e-14));
}
/// <summary>
/// Test consistency between price methods, and Greek via finite difference.
/// </summary>
public virtual void test_trinomialTree()
{
int nSteps = 135;
double dt = TIME / nSteps;
LatticeSpecification lattice = new CoxRossRubinsteinLatticeSpecification();
double fdEps = 1.0e-4;
foreach (bool isCall in new bool[] { true, false })
{
foreach (double strike in STRIKES)
{
foreach (double interest in INTERESTS)
{
foreach (double vol in VOLS)
{
foreach (double dividend in DIVIDENDS)
{
OptionFunction function = EuropeanVanillaOptionFunction.of(strike, TIME, PutCall.ofPut(!isCall), nSteps);
double[] @params = lattice.getParametersTrinomial(vol, interest - dividend, dt).toArray();
DoubleArray time = DoubleArray.of(nSteps + 1, i => dt * i);
DoubleArray df = DoubleArray.of(nSteps, i => Math.Exp(-interest * dt));
double[][] stateValue = new double[nSteps + 1][];
stateValue[0] = new double[] { SPOT };
IList <DoubleMatrix> prob = new List <DoubleMatrix>();
double[] probs = new double[] { @params[5], @params[4], @params[3] };
for (int i = 0; i < nSteps; ++i)
{
int index = i;
stateValue[i + 1] = DoubleArray.of(2 * i + 3, j => SPOT * Math.Pow(@params[2], index + 1 - j) * Math.Pow(@params[1], j)).toArray();
double[][] probMatrix = new double[2 * i + 1][];
Arrays.fill(probMatrix, probs);
prob.Add(DoubleMatrix.ofUnsafe(probMatrix));
}
RecombiningTrinomialTreeData treeData = RecombiningTrinomialTreeData.of(DoubleMatrix.ofUnsafe(stateValue), prob, df, time);
double priceData = TRINOMIAL_TREE.optionPrice(function, treeData);
double priceParams = TRINOMIAL_TREE.optionPrice(function, lattice, SPOT, vol, interest, dividend);
assertEquals(priceData, priceParams);
ValueDerivatives priceDeriv = TRINOMIAL_TREE.optionPriceAdjoint(function, treeData);
assertEquals(priceDeriv.Value, priceData);
double priceUp = TRINOMIAL_TREE.optionPrice(function, lattice, SPOT + fdEps, vol, interest, dividend);
double priceDw = TRINOMIAL_TREE.optionPrice(function, lattice, SPOT - fdEps, vol, interest, dividend);
double fdDelta = 0.5 * (priceUp - priceDw) / fdEps;
assertEquals(priceDeriv.getDerivative(0), fdDelta, 3.0e-2);
}
}
}
}
}
}