public virtual void test_trinomialTree()
{
int nSteps = 135;
LatticeSpecification[] lattices = new LatticeSpecification[]
{
new CoxRossRubinsteinLatticeSpecification(),
new TrigeorgisLatticeSpecification()
};
double tol = 5.0e-3;
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 exact = BlackScholesFormulaRepository.price(SPOT, strike, TIME, vol, interest, interest - dividend, isCall);
foreach (LatticeSpecification lattice in lattices)
{
double computed = TRINOMIAL_TREE.optionPrice(function, lattice, SPOT, vol, interest, dividend);
assertEquals(computed, exact, Math.Max(exact, 1d) * tol);
}
}
}
}
}
}
}
/// <summary>
/// Price an option under the specified trinomial lattice.
/// <para>
/// It is assumed that the volatility, interest rate and continuous dividend rate are constant
/// over the lifetime of the option.
///
/// </para>
/// </summary>
/// <param name="function"> the option </param>
/// <param name="lattice"> the lattice specification </param>
/// <param name="spot"> the spot </param>
/// <param name="volatility"> the volatility </param>
/// <param name="interestRate"> the interest rate </param>
/// <param name="dividendRate"> the dividend rate </param>
/// <returns> the option price </returns>
public virtual double optionPrice(OptionFunction function, LatticeSpecification lattice, double spot, double volatility, double interestRate, double dividendRate)
{
int nSteps = function.NumberOfSteps;
double timeToExpiry = function.TimeToExpiry;
double dt = timeToExpiry / (double)nSteps;
double discount = Math.Exp(-interestRate * dt);
DoubleArray @params = lattice.getParametersTrinomial(volatility, interestRate - dividendRate, dt);
double middleFactor = @params.get(1);
double downFactor = @params.get(2);
double upProbability = @params.get(3);
double midProbability = @params.get(4);
double downProbability = @params.get(5);
ArgChecker.isTrue(upProbability > 0d, "upProbability should be greater than 0");
ArgChecker.isTrue(upProbability < 1d, "upProbability should be smaller than 1");
ArgChecker.isTrue(midProbability > 0d, "midProbability should be greater than 0");
ArgChecker.isTrue(midProbability < 1d, "midProbability should be smaller than 1");
ArgChecker.isTrue(downProbability > 0d, "downProbability should be greater than 0");
DoubleArray values = function.getPayoffAtExpiryTrinomial(spot, downFactor, middleFactor);
for (int i = nSteps - 1; i > -1; --i)
{
values = function.getNextOptionValues(discount, upProbability, midProbability, downProbability, values, spot, downFactor, middleFactor, i);
}
return(values.get(0));
}
