public static void SmallTreeBetaGraph()
{
int numberOfSteps = 10;
var tree = new CapmBinTree(numberOfSteps);
tree.InitialStockPrice = 100;
tree.Volatility = 0.2;
tree.StrikePrice = 105;
tree.TotalTimeYears = 0.5;
tree.RiskFree = 0.03;
tree.MarketRiskPremium = 0.06;
tree.StockBeta = 1;
// B&S = call: 4.17 (con strike =105)
double callPriceBS = BlackScholes.CallPrice((double)tree.InitialStockPrice,
(double)tree.StrikePrice,
(double)tree.TotalTimeYears,
(double)tree.RiskFree,
(double)tree.Volatility);
Console.WriteLine("call B&S: " + callPriceBS.ToString("##0.######"));
tree.CalculateStockPrices();
tree.CalculateOptionPrices();
Console.WriteLine();
OutputTree(tree, delegate(BinTree.Node node) {
return((-node.ReplPortBond / (node.StockPrice * node.ReplPortDelta + node.ReplPortBond)).ToString("##0.##"));
});
}
private static void SingleConvergeTest()
{
int numberOfSteps = 2000;
var tree = new CapmBinTree(numberOfSteps);
tree.InitialStockPrice = 100;
tree.Volatility = 0.2;
tree.StrikePrice = 105;
tree.TotalTimeYears = 0.5;
tree.RiskFree = 0.03;
tree.MarketRiskPremium = 0.06;
tree.StockBeta = 1;
// B&S = call: 4.17 (con strike =105)
double callPriceBS = BlackScholes.CallPrice((double)tree.InitialStockPrice,
(double)tree.StrikePrice,
(double)tree.TotalTimeYears,
(double)tree.RiskFree,
(double)tree.Volatility);
Console.WriteLine("call B&S: " + callPriceBS.ToString("##0.######"));
tree.CalculateStockPrices();
tree.CalculateOptionPrices();
Console.WriteLine();
//OutputTree(tree, delegate(BinTree.Node node) { return node.StockPrice.ToString("##0.##"); });
Console.WriteLine("call: " + tree.GetRootNode().OptionPrice.ToString("##0.######"));
}
public void IterateNodes()
{
var tree = new CapmBinTree(4);
var nodes = new System.Collections.Generic.List <BinTree.Node>(tree.IterateNodesOfStep(4));
Assert.AreEqual(4, nodes.Count);
Assert.AreEqual(7, nodes[0].NodeIndex);
Assert.AreEqual(8, nodes[1].NodeIndex);
Assert.AreEqual(9, nodes[2].NodeIndex);
Assert.AreEqual(10, nodes[3].NodeIndex);
}
private static void IterateByAmountOfSteps()
{
double InitialStockPrice = 100;
double Volatility = 0.2;
double StrikePrice = 105;
double TotalTimeYears = 0.5;
double RiskFree = 0.03;
double MarketRiskPremium = 0.06;
double StockBeta = 1;
double callPriceBS = BlackScholes.CallPrice((double)InitialStockPrice,
(double)StrikePrice,
(double)TotalTimeYears,
(double)RiskFree,
(double)Volatility);
int minNumberOfSteps = 7000;
int maxNumberOfSteps = 9000;
bool createHeaders = !File.Exists("output.csv");
using (var writer = new StreamWriter("output.csv", true))
{
if (createHeaders)
{
writer.WriteLine("Steps,CallValueBS,CallValueCAPM");
}
var tree = new CapmBinTree(maxNumberOfSteps);
tree.InitialStockPrice = InitialStockPrice;
tree.Volatility = Volatility;
tree.StrikePrice = StrikePrice;
tree.TotalTimeYears = TotalTimeYears;
tree.RiskFree = RiskFree;
tree.MarketRiskPremium = MarketRiskPremium;
tree.StockBeta = StockBeta;
for (int steps = minNumberOfSteps; steps < maxNumberOfSteps; steps += (int)Math.Pow(Math.Log10(steps), 3))
{
tree.NumberOfSteps = steps;
tree.ResetTreeParameterCalcs();
tree.CalculateStockPrices();
tree.CalculateOptionPrices();
writer.WriteLine(steps + "," + callPriceBS.ToString("##0.#############################") +
", " + tree.GetRootNode().OptionPrice.ToString("##0.#############################"));
writer.Flush();
Console.WriteLine("Step Number: " + steps);
}
}
}
public void RecombineNodesInTree()
{
var tree = new CapmBinTree(4);
var node2 = tree.GetUpDependantNode(tree.GetRootNode());
var node3 = tree.GetDownDependantNode(tree.GetRootNode());
Assert.AreEqual(2, node2.NodeIndex);
Assert.AreEqual(3, node3.NodeIndex);
var node5A = tree.GetDownDependantNode(node2);
var node5B = tree.GetUpDependantNode(node3);
Assert.AreSame(node5A, node5B);
}
/// <summary>
/// Grafico en 3D de la beta en cada nodo. Grafica todo el arbol. 3D TREE!
/// </summary>
private static void BetaGraph3()
{
const string graphPrefix = "beta_graph_3";
int numberOfSteps = 200; //7000
double InitialStockPrice = 100;
double Volatility = 0.2;
double StrikePrice = 105;
double TotalTimeYears = 0.5;
double RiskFree = 0.03;
double MarketRiskPremium = 0.06;
double StockBeta = 1;
const int showOneEveryNSteps = 2; //50 (QUE SEA PAR!)
const int showOneEveryNNodes = 1; //4 (QUE SEA PAR!)
var tree = new CapmBinTree(numberOfSteps);
tree.InitialStockPrice = InitialStockPrice;
tree.Volatility = Volatility;
tree.StrikePrice = StrikePrice;
tree.TotalTimeYears = TotalTimeYears;
tree.RiskFree = RiskFree;
tree.MarketRiskPremium = MarketRiskPremium;
tree.StockBeta = StockBeta;
Console.WriteLine("Calculating stock prices...");
tree.CalculateStockPrices();
Console.WriteLine("Calculating option prices...");
tree.CalculateOptionPrices();
Console.WriteLine("Outputing the betas...");
//OutputTree(tree, delegate(BinTree.Node node) { return node.StockPrice.ToString("##0.##"); }); return;
Console.WriteLine("The format of the output file will be (col and row headers excl):");
Console.WriteLine(" P=120 P=119 ... P=100 ... P=80");
Console.WriteLine("t=1 B B B B ");
Console.WriteLine("t=2 B B B B ");
Console.WriteLine("t=... B B B B ");
Console.WriteLine("(where B is the beta of that node)");
List <double> pricesSaved = new List <double>(500);
List <int> stepNumbers = new List <int>(500);
using (var writer = new StreamWriter(graphPrefix + ".matrix", false))
{
int lastStepNumber;
// Find the last step, and the steps to print
for (int s = 1; s < numberOfSteps; s += showOneEveryNSteps)
{
stepNumbers.Add(s);
}
lastStepNumber = stepNumbers[stepNumbers.Count - 1];
// Find the prices that will be outputed
int idx = 0;
foreach (var node in tree.IterateNodesOfStep(lastStepNumber))
{
if ((idx++ % showOneEveryNNodes) != 0)
{
continue;
}
pricesSaved.Add(node.StockPrice);
}
PrintMatrixFileHeaders(writer, "betas", stepNumbers.Count, pricesSaved.Count);
// only output half of the nodes, para que los nodos coincidan (por ser recombinante)!
int totalPrices = pricesSaved.Count;
double beta;
foreach (int step in stepNumbers)
{
var nodes = new List <BinTree.Node>(tree.IterateNodesOfStep(step));
var nodesMatched = nodes.FindAll(n => pricesSaved.FindIndex(p => AreDoublesEqual(p, n.StockPrice)) >= 0);
int nodesRemainingEachSide = (totalPrices - nodesMatched.Count) / 2;
// Print left missing nodes
for (var n = 0; n < nodesRemainingEachSide; n++)
{
writer.Write(" 999999");
}
// Print existent nodes
foreach (var node in nodesMatched)
{
beta = node.OptionBeta;
if (beta <= 0 || beta > 999999)
{
beta = 999999;
}
writer.Write(" " + beta.ToString("0.##"));
}
// Print right missing nodes
for (var n = 0; n < nodesRemainingEachSide; n++)
{
writer.Write(" 999999");
}
writer.WriteLine();
}
writer.Flush();
}
Console.WriteLine("Output saved. See: " + graphPrefix + ".matrix");
Console.WriteLine("Now saving price list and step list.");
using (var writer = new StreamWriter(graphPrefix + "-prices.matrix", false))
{
PrintMatrixFileHeaders(writer, "prices", pricesSaved.Count, 1);
foreach (var p in pricesSaved)
{
writer.WriteLine(" " + p.ToString("0.##"));
}
}
using (var writer = new StreamWriter(graphPrefix + "-steps.matrix", false))
{
PrintMatrixFileHeaders(writer, "steps", stepNumbers.Count, 1);
foreach (var p in stepNumbers)
{
writer.WriteLine(" " + p);
}
}
Console.WriteLine("Now done! See: <" + graphPrefix + "-prices.matrix> and <" + graphPrefix + "-steps.matrix>");
}
/// <summary>
/// Datos de las betas segun el percentil del valor del arbol (beta en 10% sup, 20% sup, ...)
/// </summary>
private static void BetaGraph1()
{
int numberOfSteps = 2000;
double InitialStockPrice = 100;
double Volatility = 0.2;
double StrikePrice = 105;
double TotalTimeYears = 0.5;
double RiskFree = 0.03;
double MarketRiskPremium = 0.06;
double StockBeta = 1;
var tree = new CapmBinTree(numberOfSteps);
tree.InitialStockPrice = InitialStockPrice;
tree.Volatility = Volatility;
tree.StrikePrice = StrikePrice;
tree.TotalTimeYears = TotalTimeYears;
tree.RiskFree = RiskFree;
tree.MarketRiskPremium = MarketRiskPremium;
tree.StockBeta = StockBeta;
Console.WriteLine("Calculating stock prices...");
tree.CalculateStockPrices();
Console.WriteLine("Calculating option prices...");
tree.CalculateOptionPrices();
Console.WriteLine("Outputing the betas...");
int divisions = 70;
using (var writer = new StreamWriter("beta_graph_1.csv", false))
{
writer.Write("Step");
for (int i = 1; i <= divisions; i++)
{
writer.Write(",n" + i);
}
writer.WriteLine();
var indexes = new List <int>(divisions);
for (int step = 1; step < numberOfSteps; step++)
{
int nodeCount = BinTree.GetIndexLastNodeInStep(step) - BinTree.GetIndexFirstNodeInStep(step);
indexes.Clear();
for (int stp = 0; stp < divisions; stp++)
{
indexes.Add(nodeCount * stp / divisions);
}
writer.Write(step + ",");
int i = 0;
foreach (var node in tree.IterateNodesOfStep(step))
{
if (indexes.Contains(i))
{
if (node.OptionBeta <= 0)
{
break;
}
writer.Write(node.OptionBeta + ",");
}
i++;
}
writer.WriteLine();
}
}
Console.WriteLine("Done. See: beta_graph_1.csv");
}
/// <summary>
/// Grafico en 3D de la beta en cada nodo, de forma que salga un cuadrado
/// correspondiente al centro del arbol
/// </summary>
private static void BetaGraph2()
{
int numberOfSteps = 100; //7000
double InitialStockPrice = 100;
double Volatility = 0.2;
double StrikePrice = 105;
double TotalTimeYears = 0.5;
double RiskFree = 0.03;
double MarketRiskPremium = 0.06;
double StockBeta = 1;
const int minPrice = 60;
const int maxPrice = 140;
const int showOneEveryNSteps = 2; //50
const int showOneEveryNNodes = 1; //4
var tree = new CapmBinTree(numberOfSteps);
tree.InitialStockPrice = InitialStockPrice;
tree.Volatility = Volatility;
tree.StrikePrice = StrikePrice;
tree.TotalTimeYears = TotalTimeYears;
tree.RiskFree = RiskFree;
tree.MarketRiskPremium = MarketRiskPremium;
tree.StockBeta = StockBeta;
Console.WriteLine("Calculating stock prices...");
tree.CalculateStockPrices();
Console.WriteLine("Calculating option prices...");
tree.CalculateOptionPrices();
Console.WriteLine("Outputing the betas...");
//OutputTree(tree, delegate(BinTree.Node node) { return node.StockPrice.ToString("##0.##"); }); return;
Console.WriteLine("The format of the output file will be (col and row headers excl):");
Console.WriteLine(" P=120 P=119 ... P=100 ... P=80");
Console.WriteLine("t=1 B B B B ");
Console.WriteLine("t=2 B B B B ");
Console.WriteLine("t=... B B B B ");
Console.WriteLine("(where B is the beta of that node)");
List <double> pricesSaved = new List <double>(500);
List <int> stepNumbers = new List <int>(500);
using (var writer = new StreamWriter("beta_graph_2.matrix", false))
{
bool headersPrinted = false;
bool pricesAlreadyStoredInList = false;
// only output half of the nodes, para que los nodos coincidan (por ser recombinante)!
for (int step = 1; step < numberOfSteps; step += showOneEveryNSteps)
{
int idx = 0;
if (!headersPrinted)
{
// Skip first steps where are only a few nodes.
if (tree.GetFirstNodeInStep(step).StockPrice <= maxPrice)
{
continue;
}
if (tree.GetLastNodeInStep(step).StockPrice >= minPrice)
{
continue;
}
// I cannot do the last node index less the first index because it
// might happen that the upper node is OK while the bottom node
// is still not down enough
int inboundNodes = 0;
foreach (var node in tree.IterateNodesOfStep(step))
{
// skip higher order and less order nodes
if (node.StockPrice > maxPrice)
{
continue;
}
if (node.StockPrice < minPrice)
{
continue;
}
if ((idx++ % showOneEveryNNodes) != 0)
{
continue;
}
inboundNodes++;
}
int rows = (int)Math.Ceiling((double)(numberOfSteps - step + 1) / showOneEveryNSteps);
PrintMatrixFileHeaders(writer, "betas", rows, inboundNodes);
headersPrinted = true;
}
bool firstNode = true;
idx = 0;
foreach (var node in tree.IterateNodesOfStep(step))
{
if (firstNode)
{
stepNumbers.Add(step);
}
firstNode = false;
// skip higher order and less order nodes
if (node.StockPrice > maxPrice)
{
continue;
}
if (node.StockPrice < minPrice)
{
continue;
}
if ((idx++ % showOneEveryNNodes) != 0)
{
continue;
}
if (!pricesAlreadyStoredInList)
{
pricesSaved.Add(node.StockPrice);
}
if (node.OptionBeta <= 0 || node.OptionBeta > 999999)
{
node.OptionBeta = 999999;
}
writer.Write(" " + node.OptionBeta.ToString("0.##"));
}
if (!firstNode)
{
writer.WriteLine();
}
if (pricesSaved.Count > 0)
{
pricesAlreadyStoredInList = true;
}
}
writer.Flush();
}
Console.WriteLine("Output saved. See: beta_graph_2.matrix");
Console.WriteLine("Now saving price list and step list.");
using (var writer = new StreamWriter("beta_graph_2-prices.matrix", false))
{
PrintMatrixFileHeaders(writer, "prices", pricesSaved.Count, 1);
foreach (var p in pricesSaved)
{
writer.WriteLine(" " + p.ToString("0.##"));
}
}
using (var writer = new StreamWriter("beta_graph_2-steps.matrix", false))
{
PrintMatrixFileHeaders(writer, "steps", stepNumbers.Count, 1);
foreach (var p in stepNumbers)
{
writer.WriteLine(" " + p);
}
}
Console.WriteLine("Now done! See: <beta_graph_2-prices.matrix> and <beta_graph_2-steps.matrix>");
}
