/// <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));
}
/// <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));
}
/// <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)));
}