﻿using System; using Excel = Microsoft.Office.Interop.Excel; namespace Binomial { class SOEURecursiveUtility { static void Main() { double alpha = 40; //CRUA, utility will be computed for a range of values double beta = 0.03; //rate of impatience double gamma = 40; //CRRA double delta = 1/1.5; //inverse EIS double c0 = 100; //time-zero consumption double muHigh = 0.05; //high drift scenario double muLow = 0.00; //low drift scenario double sigma = 0.03; //known consumption volatility int nPeriods = 120; //number of periods double h = 10 / (double)nPeriods; //period time-length = time horizon / nPeriods double qHigh = (1 + (muHigh / sigma) * Math.Sqrt(h)) / 2; //optimistic up prob double qLow = (1 + (muLow / sigma) * Math.Sqrt(h)) / 2; //pessimistic up prob double upcgrowth = Math.Exp(sigma * Math.Sqrt(h)); //up consumption growth double downcgrowth = 1 / upcgrowth; //down consumption growth double discount = Math.Exp(-beta*h); //build the consumption tree BinomialTree c = c0.ConstVolTree(nPeriods, upcgrowth, downcgrowth); Console.WriteLine("There are {0} periods and {1} nodes.", c.Periods, c.Nodes); double cmin = c0 * Math.Pow(downcgrowth, nPeriods); Console.WriteLine("Worst-case terminal consumption is {0}.", cmin); //construct the CE and time aggregator var hi = new SIEU(qHigh, gamma); //optimistic SI EU var lo = new SIEU(qLow, gamma); //pessimistic SI EU var so = new SIEU(0.5, alpha); //second-order SI EU Aggregator CE = (x, y) => so.CE(hi.CE(x, y), lo.CE(x, y)); //overall CE var tagg = new SIEU(discount, delta); //the time aggregator is tagg.CE BinomialTree U = c.BackwardRecursiveTree(tagg.CE, CE); Console.WriteLine("For CRUA = {0}, the time-zero utility is {1}.", so.CRRA, U[0, 0]); //uncomment following line to output consumption and utility trees to spreadsheet //TreeBuilder.ToSpreadsheet(c, U); Console.ReadKey(); } } public class SIEU //Scale-Invariant Expected Utility { double p; public SIEU(double upProbability, double CRRA) { this.upProbability = upProbability; this.CRRA = CRRA; } public double upProbability { get { return p; } set { if ((value < 0) || (value > 1)) throw new ArgumentException("probability must be in (0,1). ", "upProbability"); p = value; } } public double CRRA {get; set;} public double CE(double x, double y) { if (CRRA == 1) return Math.Exp(p * Math.Log(x) + (1 - p) * Math.Log(y)); else { var power = 1 - CRRA; return Math.Pow(p * Math.Pow(x, power) + (1 - p) * Math.Pow(y, power), 1 / power); } } } public delegate double Aggregator(double up, double down); public class BinomialTree { readonly int T; // the number of periods, time runs through 0,1,...,T readonly int N; // the number of nodes double[] values; // lexicographically by (time, ups): (0,0), (1,0), (1,1), ... static int node(int t, int ups) { //map (t,ups) to node index of the values array return (t * (t + 1) / 2) + ups; } public BinomialTree(int nPeriods) { T = nPeriods; N = 1 + node(T, T); values = new double[N]; } public int Periods { get { return T; } } public int Nodes { get { return N; } } public double this[int t, int u] { set { if (u > t) throw new ArgumentException ("the number of time t nodes cannot exceed t", "ups"); values[node(t, u)] = value; } get { if (u > t) throw new ArgumentException ("the number of time t nodes cannot exceed t", "ups"); return values[node(t, u)]; } } } public static class TreeBuilder { public static BinomialTree ConstVolTree(this double initial, int nPeriods, double upReturn, double downReturn) { var C = new BinomialTree(nPeriods); C[0, 0] = initial; for (int t = 1; t <= nPeriods; t++) { C[t, 0] = C[t - 1, 0] * downReturn; for (int ups = 1; ups <= t; ups++) C[t, ups] = C[t - 1, ups - 1] * upReturn; } return C; } public static BinomialTree BackwardRecursiveTree(this BinomialTree cons, Aggregator tAgg, Aggregator CE) { int N = cons.Periods; var U = new BinomialTree(N); for (int ups = 0; ups <= N; ups++) U[N, ups] = cons[N, ups]; for (int t = N - 1; t >= 0; t--) { for (int ups = 0; ups <= t; ups++) U[t, ups] = tAgg(CE(U[t + 1, ups + 1], U[t + 1, ups]), cons[t, ups]); } return U; } public static void ToSpreadsheet(BinomialTree c, BinomialTree U) { int N = U.Periods; var excel = new Excel.Application(); excel.Visible = true; var workBook = excel.Workbooks.Add(); for (int t = 0; t <= N; t++) for (int ups = 0; ups <= t; ups++) { int downs = t - ups; excel.Cells[1 + downs, 1 + t].Value = U[t, ups]; excel.Cells[N + 3 + downs, 1 + t].Value = c[t, ups]; } // workBook.SaveAs(@"C:\Users\...\RecursiveUtility.xlsx"); } } }