public void InitializeBackBones(double[] a, double[] sigma)
{
Debug.Assert(a.Length == _times.Length && sigma.Length == _times.Length);
/// 0, 1, ..., N 時点 分割数はN : N分割するとき、back boneはN個用いる
_TreeBackBones[0] = new TreeBackBone();
_TreeBackBones[0].t = _times[0];
_TreeBackBones[0].a = a[0];
_TreeBackBones[0].sigma = sigma[0];
_TreeBackBones[0].dt = _times[1] - _times[0];
_TreeBackBones[0].dx = 0;
_TreeBackBones[0].V = ComputeV(a[0], sigma[0], _TreeBackBones[0].dt);
/// i = 1, ..., N - 1
for (int i = 1; i < GetTimeSeparationNumber(); ++i)
{
_TreeBackBones[i] = new TreeBackBone();
_TreeBackBones[i].t = _times[i];
_TreeBackBones[i].a = a[i];
_TreeBackBones[i].sigma = sigma[i];
_TreeBackBones[i].dt = _times[i + 1] - _times[i];
_TreeBackBones[i].dx = _TreeBackBones[i - 1].V * Math.Sqrt(3);
_TreeBackBones[i].V = ComputeV(a[i], sigma[i], _TreeBackBones[i].dt);
}
int ii = GetTimeSeparationNumber();
_TreeBackBones[ii] = new TreeBackBone();
_TreeBackBones[ii].t = _times[ii];
_TreeBackBones[ii].a = a[ii];
_TreeBackBones[ii].sigma = sigma[ii];
_TreeBackBones[ii].dt = 0;
_TreeBackBones[ii].dx = _TreeBackBones[ii - 1].V * Math.Sqrt(3);
_TreeBackBones[ii].V = ComputeV(a[ii], sigma[ii], _TreeBackBones[ii].dt);
}
/// <summary>
/// 入力されたbondPriceに合わせるalpha[]を求め、rを設定する.
/// </summary>
/// <param name="bondPrices">ツリーの分割時点に対する割引債価格</param>
public void FitToInputBondPrice(double[] bondPrices)
{
Debug.Assert(bondPrices.Length == _TreeBackBones.Length);
/// alphaの算出
double initialAlpha = 0D;
for (int i = 0; i < _TreeBackBones.Length - 1; ++i)
{
FitToInputBondPrice(i, bondPrices[i + 1], initialAlpha);
if (_TreeBackBones[i].alpha == Double.NegativeInfinity)
{
initialAlpha = 0D;
}
initialAlpha = _TreeBackBones[i].alpha;
}
/// rの設定
for (int i = 0; i < bondPrices.Length - 1; ++i)
{
TreeBackBone bone = _TreeBackBones[i];
int jSize = bone.jMax - bone.jMin + 1;
for (int j = 0; j < jSize; ++j)
{
_TreeNodes[i][j].r = ConvertToShortRate(bone.alpha, _TreeNodes[i][j].j * bone.dx);
}
}
}
/// <summary>
/// 時点iのalphaを時点i+1に対するpriceに合わせる
/// </summary>
/// <param name="i"></param>
/// <param name="price"></param>
/// <returns>収束誤差</returns>
public double FitToInputBondPrice(int i, double price, double initialAlpha = 0D)
{
TreeBackBone bone = _TreeBackBones[i];
if (i == 0)
{
bone.alpha = Math.Log(-Math.Log(price, Math.E) / bone.dt, Math.E);
double dummy;
ComputeBondPrice(0, out dummy);
ComputeBondPrice(1, out dummy);
return(0D);
}
/// Newtow法
/// 誤差
double error = 1e-15;
/// alphaの初期値
bone.alpha = initialAlpha;
/// treeにより算出する価格
double priceByTree;
do
{
/// priceByTree - priceに対するalphaの微分係数
double derivative;
/// 時点i+1の価格を計算して時点iのalphaを決定する
priceByTree = ComputeBondPrice(i + 1, out derivative);
bone.alpha = bone.alpha - (priceByTree - price) / derivative;
} while (Math.Abs(priceByTree - price) > error);
return(Math.Abs(priceByTree - price));
}
public void OutputCsvTreeBackBones(string filepath)
{
using (var sw = new System.IO.StreamWriter(filepath, false))
{
sw.WriteLine(TreeBackBone.ToStringValuesHeader());
for (int i = 0; i < _TreeBackBones.Length; ++i)
{
sw.WriteLine(_TreeBackBones[i].ToStringValues());
}
}
}
/// <summary>
/// 計算済みの時点i-1ノードのQ値を用いてツリーによる割引債価格P(0,i)を算出&設定する.
/// 引き続いて時点iに対する全ノードのQ値を計算する.
/// </summary>
/// <param name="i"></param>
/// <param name="priceDerivativeAlpha">ツリーによる割引債価格のalphaによる微分係数</param>
/// <returns>ツリーにより算出された割引債価格</returns>
/// <remarks>i=0から順に呼び出すこと</remarks>
public double ComputeBondPrice(int i, out double priceDerivativeAlpha)
{
priceDerivativeAlpha = 0;
if (i == 0)
{
_TreeBackBones[0].bondPrice = 1D;
_TreeNodes[0][0].Q = 1D;
/// priceDerivativeAlphaは使わないのでダミー0を返す
return(1D);
}
/// i-1時点データ
TreeBackBone pBone = _TreeBackBones[i - 1];
TreeNode[] pNodes = _TreeNodes[i - 1];
int pNodeCount = pBone.jMax - pBone.jMin + 1;
/// BondPrice BK tree
double bondPrice = 0;
for (int j = 0; j < pNodeCount; ++j)
{
double commonTerm = ConvertToShortRate(pBone.alpha, pNodes[j].j * pBone.dx) * pBone.dt;
double priceTerm = pNodes[j].Q * Math.Exp(-commonTerm);
bondPrice += priceTerm;
priceDerivativeAlpha += priceTerm * commonTerm;
}
/// BondPrice BK tree
/// 価格の微分係数そのものにしておくため, マイナスをつける
priceDerivativeAlpha = -priceDerivativeAlpha;
/// i時点のQ値の計算
/// i-1時点ノードを走査して, i時点の各ノードに対するQ値を一度に計算する
TreeBackBone bone = _TreeBackBones[i];
TreeNode[] nodes = _TreeNodes[i];
int nodeCount = bone.jMax - bone.jMin + 1;
/// i時点の各ノードに対するQ値の初期化
for (int j = 0; j < nodeCount; ++j)
{
nodes[j].Q = 0;
}
/// Q値の計算
for (int j = 0; j < pNodeCount; ++j)
{
/// down, mid, up nodeの順に集計
int kIndex = pNodes[j].k - bone.jMin;
/// BK tree
double temp = pNodes[j].Q * Math.Exp(-ConvertToShortRate(pBone.alpha, pNodes[j].j * pBone.dx) * pBone.dt);
nodes[kIndex - 1].Q += pNodes[j].pd * temp;
nodes[kIndex].Q += pNodes[j].pm * temp;
nodes[kIndex + 1].Q += pNodes[j].pu * temp;
}
bone.bondPrice = bondPrice;
return(bondPrice);
}
/// <summary>
/// ツリーノードの構築
/// </summary>
/// <remarks>InitializeBackBonesを実行済みであること</remarks>
public void SetUpTreeNodes()
{
/// Root Node
_TreeNodes[0] = new TreeNode[1];
_TreeNodes[0][0] = new TreeNode();
_TreeNodes[0][0].Initialize(0, 0, Math.Exp(-_TreeBackBones[0].a * _TreeBackBones[0].dt)
, _TreeBackBones[1].dx, _TreeBackBones[0].V, _TreeBackBones[0].V * _TreeBackBones[0].V);
_TreeBackBones[0].jMin = 0;
_TreeBackBones[0].jMax = 0;
/// i = 1, 2, ..., N (Leaf Nodeに該当)
int preNodeCount = 1;
for (short i = 1; i < _times.Length; ++i)
{
/// i時点のTreeBackBone
TreeBackBone ithBone = _TreeBackBones[i];
/// jMin, jMaxの取得
ithBone.jMax = (short)(_TreeNodes[i - 1][preNodeCount - 1].k + 1);
ithBone.jMin = (short)(_TreeNodes[i - 1][0].k - 1);
/// i時点のノード数
int nodeCount = ithBone.jMax - ithBone.jMin + 1;
/// i時点のノードのnew
_TreeNodes[i] = new TreeNode[nodeCount];
for (short j = 0; j < nodeCount; ++j)
{
_TreeNodes[i][j] = new TreeNode();
}
/// 最終時点より前と最終時点で分ける
if (i < GetTimeSeparationNumber())
{
/// j = jMin, ..., jMax に対するnodeを順に初期化する
/// j = jMin, ..., jMax に対応する配列index 0,1,...,nodeCount-1
TreeBackBone nextBone = _TreeBackBones[i + 1];
double expMinusADeltaT = Math.Exp(-ithBone.a * ithBone.dt);
double V2 = ithBone.V * ithBone.V;
for (short j = 0; j < nodeCount; ++j)
{
_TreeNodes[i][j].Initialize((short)(j + ithBone.jMin), ithBone.dx, expMinusADeltaT, nextBone.dx, ithBone.V, V2);
}
}
else
{
for (short j = 0; j < nodeCount; ++j)
{
_TreeNodes[i][j].InitializeLeafNode((short)(j + ithBone.jMin), ithBone.dx);
}
}
/// preNodeCount
preNodeCount = nodeCount;
}
}
public void OutputCsvTreeNodes(string filepath)
{
using (var sw = new System.IO.StreamWriter(filepath, false))
{
sw.WriteLine("i,{0}", TreeNode.ToStringValuesHeader());
for (int i = 0; i < _TreeBackBones.Length; ++i)
{
TreeBackBone bone = _TreeBackBones[i];
for (short j = 0; j < bone.jMax - bone.jMin + 1; ++j)
{
sw.Write("{0},", i);
sw.WriteLine(_TreeNodes[i][j].ToStringValues());
}
}
}
}