Я начал с решения 0x69 , но со временем некоторые новые сценарии привели к сбою метода Ньютона.Я создал «умную» версию, которая использует метод деления пополам (медленнее) при сбое Ньютона.
Обратите внимание на встроенные ссылки на несколько источников, которые я использовал для этого решения.
Наконец, вы нечтобы иметь возможность воспроизвести некоторые из этих сценариев в Excel, для самого Excel используется метод Ньютона.Обратитесь к XIRR, а? для интересного обсуждения этого вопроса.
using System;
using System.Collections.Generic;
using System.Linq;</p>
<p>// See the following articles:
// <a href="http://blogs.msdn.com/b/lucabol/archive/2007/12/17/bisection-based-xirr-implementation-in-c.aspx" rel="nofollow noreferrer">http://blogs.msdn.com/b/lucabol/archive/2007/12/17/bisection-based-xirr-implementation-in-c.aspx</a>
// <a href="http://www.codeproject.com/Articles/79541/Three-Methods-for-Root-finding-in-C" rel="nofollow noreferrer">http://www.codeproject.com/Articles/79541/Three-Methods-for-Root-finding-in-C</a>
// <a href="http://www.financialwebring.org/forum/viewtopic.php?t=105243&highlight=xirr" rel="nofollow noreferrer">http://www.financialwebring.org/forum/viewtopic.php?t=105243&highlight=xirr</a>
// Default values based on Excel doc
// <a href="http://office.microsoft.com/en-us/excel-help/xirr-function-HP010062387.aspx" rel="nofollow noreferrer">http://office.microsoft.com/en-us/excel-help/xirr-function-HP010062387.aspx</a></p>
<p>namespace Xirr
{
public class Program
{
private const Double DaysPerYear = 365.0;
private const int MaxIterations = 100;
private const double DefaultTolerance = 1E-6;
private const double DefaultGuess = 0.1;</p>
<code> private static readonly Func<IEnumerable<CashItem>, Double> NewthonsMethod =
cf => NewtonsMethodImplementation(cf, Xnpv, XnpvPrime);
private static readonly Func<IEnumerable<CashItem>, Double> BisectionMethod =
cf => BisectionMethodImplementation(cf, Xnpv);
public static void Main(string[] args)
{
RunScenario(new[]
{
// this scenario fails with Newton's but succeeds with slower Bisection
new CashItem(new DateTime(2012, 6, 1), 0.01),
new CashItem(new DateTime(2012, 7, 23), 3042626.18),
new CashItem(new DateTime(2012, 11, 7), -491356.62),
new CashItem(new DateTime(2012, 11, 30), 631579.92),
new CashItem(new DateTime(2012, 12, 1), 19769.5),
new CashItem(new DateTime(2013, 1, 16), 1551771.47),
new CashItem(new DateTime(2013, 2, 8), -304595),
new CashItem(new DateTime(2013, 3, 26), 3880609.64),
new CashItem(new DateTime(2013, 3, 31), -4331949.61)
});
RunScenario(new[]
{
new CashItem(new DateTime(2001, 5, 1), 10000),
new CashItem(new DateTime(2002, 3, 1), 2000),
new CashItem(new DateTime(2002, 5, 1), -5500),
new CashItem(new DateTime(2002, 9, 1), 3000),
new CashItem(new DateTime(2003, 2, 1), 3500),
new CashItem(new DateTime(2003, 5, 1), -15000)
});
}
private static void RunScenario(IEnumerable<CashItem> cashFlow)
{
try
{
try
{
var result = CalcXirr(cashFlow, NewthonsMethod);
Console.WriteLine("XIRR [Newton's] value is {0}", result);
}
catch (InvalidOperationException)
{
// Failed: try another algorithm
var result = CalcXirr(cashFlow, BisectionMethod);
Console.WriteLine("XIRR [Bisection] (Newton's failed) value is {0}", result);
}
}
catch (ArgumentException e)
{
Console.WriteLine(e.Message);
}
catch (InvalidOperationException exception)
{
Console.WriteLine(exception.Message);
}
}
private static double CalcXirr(IEnumerable<CashItem> cashFlow, Func<IEnumerable<CashItem>, double> method)
{
if (cashFlow.Count(cf => cf.Amount > 0) == 0)
throw new ArgumentException("Add at least one positive item");
if (cashFlow.Count(c => c.Amount < 0) == 0)
throw new ArgumentException("Add at least one negative item");
var result = method(cashFlow);
if (Double.IsInfinity(result))
throw new InvalidOperationException("Could not calculate: Infinity");
if (Double.IsNaN(result))
throw new InvalidOperationException("Could not calculate: Not a number");
return result;
}
private static Double NewtonsMethodImplementation(IEnumerable<CashItem> cashFlow,
Func<IEnumerable<CashItem>, Double, Double> f,
Func<IEnumerable<CashItem>, Double, Double> df,
Double guess = DefaultGuess,
Double tolerance = DefaultTolerance,
int maxIterations = MaxIterations)
{
var x0 = guess;
var i = 0;
Double error;
do
{
var dfx0 = df(cashFlow, x0);
if (Math.Abs(dfx0 - 0) < Double.Epsilon)
throw new InvalidOperationException("Could not calculate: No solution found. df(x) = 0");
var fx0 = f(cashFlow, x0);
var x1 = x0 - fx0/dfx0;
error = Math.Abs(x1 - x0);
x0 = x1;
} while (error > tolerance && ++i < maxIterations);
if (i == maxIterations)
throw new InvalidOperationException("Could not calculate: No solution found. Max iterations reached.");
return x0;
}
internal static Double BisectionMethodImplementation(IEnumerable<CashItem> cashFlow,
Func<IEnumerable<CashItem>, Double, Double> f,
Double tolerance = DefaultTolerance,
int maxIterations = MaxIterations)
{
// From "Applied Numerical Analysis" by Gerald
var brackets = Brackets.Find(Xnpv, cashFlow);
if (Math.Abs(brackets.First - brackets.Second) < Double.Epsilon)
throw new ArgumentException("Could not calculate: bracket failed");
Double f3;
Double result;
var x1 = brackets.First;
var x2 = brackets.Second;
var i = 0;
do
{
var f1 = f(cashFlow, x1);
var f2 = f(cashFlow, x2);
if (Math.Abs(f1) < Double.Epsilon && Math.Abs(f2) < Double.Epsilon)
throw new InvalidOperationException("Could not calculate: No solution found");
if (f1*f2 > 0)
throw new ArgumentException("Could not calculate: bracket failed for x1, x2");
result = (x1 + x2)/2;
f3 = f(cashFlow, result);
if (f3*f1 < 0)
x2 = result;
else
x1 = result;
} while (Math.Abs(x1 - x2)/2 > tolerance && Math.Abs(f3) > Double.Epsilon && ++i < maxIterations);
if (i == maxIterations)
throw new InvalidOperationException("Could not calculate: No solution found");
return result;
}
private static Double Xnpv(IEnumerable<CashItem> cashFlow, Double rate)
{
if (rate <= -1)
rate = -1 + 1E-10; // Very funky ... Better check what an IRR <= -100% means
var startDate = cashFlow.OrderBy(i => i.Date).First().Date;
return
(from item in cashFlow
let days = -(item.Date - startDate).Days
select item.Amount*Math.Pow(1 + rate, days/DaysPerYear)).Sum();
}
private static Double XnpvPrime(IEnumerable<CashItem> cashFlow, Double rate)
{
var startDate = cashFlow.OrderBy(i => i.Date).First().Date;
return (from item in cashFlow
let daysRatio = -(item.Date - startDate).Days/DaysPerYear
select item.Amount*daysRatio*Math.Pow(1.0 + rate, daysRatio - 1)).Sum();
}
public struct Brackets
{
public readonly Double First;
public readonly Double Second;
public Brackets(Double first, Double second)
{
First = first;
Second = second;
}
internal static Brackets Find(Func<IEnumerable<CashItem>, Double, Double> f,
IEnumerable<CashItem> cashFlow,
Double guess = DefaultGuess,
int maxIterations = MaxIterations)
{
const Double bracketStep = 0.5;
var leftBracket = guess - bracketStep;
var rightBracket = guess + bracketStep;
var i = 0;
while (f(cashFlow, leftBracket)*f(cashFlow, rightBracket) > 0 && i++ < maxIterations)
{
leftBracket -= bracketStep;
rightBracket += bracketStep;
}
return i >= maxIterations
? new Brackets(0, 0)
: new Brackets(leftBracket, rightBracket);
}
}
public struct CashItem
{
public DateTime Date;
public Double Amount;
public CashItem(DateTime date, Double amount)
{
Date = date;
Amount = amount;
}
}
}
</code> }