public BinomialLattice(int periods)
{
Dimension = periods;
Nodes = new BinomialLatticeNode[periods + 1][];
for (int i = 0; i < periods + 1; i++)
{
Nodes[i] = new BinomialLatticeNode[i + 1];
}
InterestRates = 0d.Repeat(periods + 1);
}
public static void ComputeOption(Option option, double interestRate, int periods)
{
var n = periods;
var maturity = option.TimeToMaturity;
var dt = maturity / n;
var style = option.Style;
var strike = option.Strike;
var q = option.Underlying.YieldRate;
var r = interestRate;
var sig = option.Underlying.Volatility;
var lattice = new BinomialLattice(n);
var node = new BinomialLatticeNode
{
Stage = 0,
Index = 0,
UnderlyingValue = option.Underlying.MarketPrice
};
lattice.Root = node;
lattice.InterestRates[0] = r;
// from node to leaves; excludes root node
for (int stage = 0; stage <= n; stage++)
{
var tempIndex = stage == n ? stage - 1 : stage;
var u = Math.Exp(sig * Math.Sqrt(dt));
var d = 1 / u;
var p = (Math.Exp((r - q) * dt) - d) / (u - d);
var lowerNodeFactor = d / u;
// compute current stage
for (int i = 0; i <= stage; i++)
{
lattice[stage][i].Stage = stage;
lattice[stage][i].Index = i;
lattice[stage][i].UpRatio = u;
lattice[stage][i].DownRatio = d;
lattice[stage][i].UpRiskNeutralProbability = p;
lattice[stage][i].DownRiskNeutralProbability = 1 - p;
lattice.InterestRates[stage] = r;
}
if (stage == n)
{
continue;
}
// compute next stage
lattice[stage + 1][0] = new BinomialLatticeNode
{
UnderlyingValue = lattice[stage][0].UnderlyingValue * lattice[stage][0].UpRatio
};
for (int i = 1; i <= stage + 1; i++)
{
lattice[stage + 1][i] = new BinomialLatticeNode
{
UnderlyingValue = lattice[stage + 1][i - 1].UnderlyingValue * lowerNodeFactor
};
}
}
// process the leaves
for (int i = 0; i <= lattice.Dimension; i++)
{
node = lattice.Get(lattice.Dimension, i);
var exerciseValue = option.Type == OptionType.Call
? node.UnderlyingValue - strike
: strike - node.UnderlyingValue;
node.DerivedValue = Math.Max(exerciseValue, 0);
}
// from last 2nd level leaves to nodes; includes root node
for (int stage = n - 1; stage >= 0; stage--)
{
var disc = Math.Exp(-lattice.InterestRates[stage] * dt);
var pUp = node.UpRiskNeutralProbability;
var pDown = node.DownRiskNeutralProbability;
for (int i = 0; i < lattice[stage].Length; i++)
{
node = lattice[stage][i];
var childUp = lattice[stage + 1][i]; // up child
var childDown = lattice[stage + 1][i + 1]; // down child
node.DerivedValue = disc * (pUp * childUp.DerivedValue + pDown * childDown.DerivedValue);
if (style == OptionStyleType.American)
{
var exerciseValue = option.Type == OptionType.Call
? node.UnderlyingValue - strike
: strike - node.UnderlyingValue;
node.DerivedValue = Math.Max(exerciseValue, node.DerivedValue);
}
}
}
option.FairPrice = lattice.Root.DerivedValue;
}
