/// <summary>
/// Compute option price and delta under the specified trinomial tree gird.
/// <para>
/// The delta is the first derivative of the price with respect to spot, and approximated by the data embedded in
/// the trinomial tree.
///
/// </para>
/// </summary>
/// <param name="function"> the option </param>
/// <param name="data"> the trinomial tree data </param>
/// <returns> the option price and spot delta </returns>
public virtual ValueDerivatives optionPriceAdjoint(OptionFunction function, RecombiningTrinomialTreeData data)
{
int nSteps = data.NumberOfSteps;
ArgChecker.isTrue(nSteps == function.NumberOfSteps, "mismatch in number of steps");
DoubleArray values = function.getPayoffAtExpiryTrinomial(data.getStateValueAtLayer(nSteps));
double delta = 0d;
for (int i = nSteps - 1; i > -1; --i)
{
values = function.getNextOptionValues(data.getDiscountFactorAtLayer(i), data.getProbabilityAtLayer(i), data.getStateValueAtLayer(i), values, i);
if (i == 1)
{
DoubleArray stateValue = data.getStateValueAtLayer(1);
double d1 = (values.get(2) - values.get(1)) / (stateValue.get(2) - stateValue.get(1));
double d2 = (values.get(1) - values.get(0)) / (stateValue.get(1) - stateValue.get(0));
delta = 0.5 * (d1 + d2);
}
}
return(ValueDerivatives.of(values.get(0), DoubleArray.of(delta)));
}
/// <summary>
/// Price an option under the specified trinomial tree gird.
/// </summary>
/// <param name="function"> the option </param>
/// <param name="data"> the trinomial tree data </param>
/// <returns> the option price </returns>
public virtual double optionPrice(OptionFunction function, RecombiningTrinomialTreeData data)
{
int nSteps = data.NumberOfSteps;
ArgChecker.isTrue(nSteps == function.NumberOfSteps, "mismatch in number of steps");
DoubleArray values = function.getPayoffAtExpiryTrinomial(data.getStateValueAtLayer(nSteps));
for (int i = nSteps - 1; i > -1; --i)
{
values = function.getNextOptionValues(data.getDiscountFactorAtLayer(i), data.getProbabilityAtLayer(i), data.getStateValueAtLayer(i), values, i);
}
return(values.get(0));
}