【C#】 25. 根据Option组成的投资组合的payoff，识别组成成分

今天终于做了一个很久之前就想完成的option应用！

假设现在有一个全部由Option构成的投资组合，这些option的underlying都是同一个股票，有相同的maturity。

在Excel中写个函数，它可以根据portfolio在不同underlying price时的Payoff来识别投资组合中各个option组成。

上图左边的表格就是Input，Payoff图在其下方（strangle）；而右边的表格就是计算得到的结果，我写的这个函数名字为 OpTypeStrikeContractNum。

using System;using System.Collections.Generic;using System.Linq;using System.Text;using ExcelDna.Integration;using FinMktReverseEngineering;using Excel = Microsoft.Office.Interop.Excel;using System.Runtime.InteropServices;using Microsoft.SolverFoundation.Services;using Microsoft.SolverFoundation.Solvers;namespace OptionFunctions{    //Solver Class for calculate the contract number for options    public class CSolver    {        private double[] interpolatedStockPrice;        private double[] interpolatedTargetPayoffs;        private Option[] options;        private int optionNum;        //Constructor        public CSolver(Option[] Options,double[] InterpolatedTargetPayoffs, double[] InterpolatedStockPrice)        {            this.options = Options;            this.interpolatedTargetPayoffs = InterpolatedTargetPayoffs;            this.interpolatedStockPrice = InterpolatedStockPrice;            this.optionNum = options.Length;        }        //Target Function        public double TargetFunction(double[] ContractNum)        {            double sum2OfDiff=0.0;            double sum2OfContractNum=0.0;            double totalPayoff;            for (int i = 0; i < interpolatedStockPrice.Length; i++)            {                totalPayoff = 0.0;                for (int j = 0;  j < options.Length;  j++)                {                    totalPayoff+= options[j].Payoff(interpolatedStockPrice[i]) * ContractNum[j];                    sum2OfContractNum += Math.Pow(ContractNum[j]-Math.Round(ContractNum[j],0), 2);  //Very important! To avoid trivial answers!!!                }                sum2OfDiff += Math.Pow(interpolatedTargetPayoffs[i] - totalPayoff, 2);   //Residuals^2            }            return sum2OfDiff+sum2OfContractNum;        }        //Solver        internal double[] IndidualSolve()        {            var hls = new HybridLocalSearchSolver();            int[] contractNumID = new int[optionNum];            double[] results=new double[optionNum];            //Add variable in the solver            for (int i = 0; i < contractNumID.Length; i++)            {                hls.AddVariable(out contractNumID[i],                    Microsoft.SolverFoundation.Common.Rational.NegativeInfinity,                    Microsoft.SolverFoundation.Common.Rational.PositiveInfinity,                     false);              }            //Solving            hls.AddGoal(hls.CreateNaryFunction(TargetFunction, contractNumID));//目标函数最小化            var hlsr = hls.Solve(new HybridLocalSearchParameters());            //Set results            for (int i = 0; i < results.Length; i++)            {                results[i] = hlsr.GetValue(contractNumID[i]);            }            return results;       }    }        public class OptionFunctions        {            //Function OptionPrice            [ExcelFunction(Description = "Exact solution for European option", Category = "Option Functions")]            public static double OptionPrice([ExcelArgument(Description = @"Call (""C"") or a put (""P"")")]string optionType,                [ExcelArgument(Description = @"Stock")]double underlying, [ExcelArgument(Description = @"Risk-free rate")]double interestRate,                 [ExcelArgument(Description = @"Volatility")]double volatility, [ExcelArgument(Description = @"Strike price")]double strikePrice,                  [ExcelArgument(Description = @"Time to maturity(in years)")]double timeToMaturity, [ExcelArgument(Description = @"Cost of carry")]double costOfCarry)            {                // Basic validation -                if (underlying <= 0.0 || volatility <= 0.0 || timeToMaturity <= 0.0 || strikePrice <= 0.0)                {                    // Exception will be returned to Excel as #VALUE.                    throw new ArgumentException();                }                Option o = new Option();                o.otyp = optionType;                o.r = interestRate;                o.sigma = volatility;                o.K = strikePrice;                o.T = timeToMaturity;                o.b = costOfCarry;                return o.Price(underlying);            }            //Function OptionPriceGreeks            [ExcelFunction(Description = "Compute exact solution for a European option, and returns price and greeks as a two-column, "                + "six-row array with names and values", Category = "Option Functions")]            public static object[,] OptionPriceGreeks([ExcelArgument(Description = @"Call (""C"") or a put (""P"")")]string optionType,                [ExcelArgument(Description = @"Value of the underlying stock")]double underlying, [ExcelArgument(Description = @"Risk-free rate")]double interestRate,                 [ExcelArgument(Description = @"Volatility")]double volatility, [ExcelArgument(Description = @"Strike price")]double strikePrice,                  [ExcelArgument(Description = @"Time to maturity(years)")]double timeToMaturity, [ExcelArgument(Description = @"Cost of carry")]double costOfCarry)            {                // Basic validation                if (underlying <= 0.0 || volatility <= 0.0 || timeToMaturity <= 0.0 || strikePrice <= 0.0)                {                    // Exception will be returned to Excel as #VALUE.                    throw new ArgumentException();                }                Option o = new Option();                o.otyp = optionType;                o.r = interestRate;                o.sigma = volatility;                o.K = strikePrice;                o.T = timeToMaturity;                o.b = costOfCarry;                return new object[7, 2]{            {"Price", o.Price(underlying)},            {"Delta", o.Delta(underlying)},            {"Gamma", o.Gamma(underlying)},            {"Vega", o.Vega(underlying)},            {"Theta", o.Theta(underlying)},            {"Rho", o.Rho(underlying)},            {"Coc", o.Coc(underlying)}            };            }            //Function Payoff            [ExcelFunction(Description = "Payoff for European option", Category = "Option Functions")]            public static object[,] Payoff(                [ExcelArgument(Description = @"Call (""C"") or a put (""P"")")]object[] optionType,                [ExcelArgument(Description = @"Strike price")]object[] strikes)            {                int len=optionType.Length;                //Option and Stock Price at T array<span style="white-space:pre"></span>        Option[] options;                double[] st;                 double[] payoffs;                  options= new Option[len];                st = new double[len + 2];                payoffs=new double[len+2];                //Initiate the first element st=0.0                st[0] = 0.0;                st[len + 1] = (double)strikes[len-1]+10.0;    //The last ST is last strike +10.0                for (int i = 0; i < len; i++)<span style="white-space:pre"></span>    {<span style="white-space:pre"></span>        options[i]=new Option();                    options[i].otyp=(string)optionType[i];                    options[i].K=(double)strikes[i];                    st[i + 1] = (double)strikes[i]; //Set st as strike price                }                //Payoffs at different strockPrice                payoffs = COptionPayoff.OptionPayoff(st, options);                //Return result: St and corresponding Payoff                    object[,] result;                result = new object[len+2,2];                for (int i = 0; i < len+2; i++)<span style="white-space:pre"></span>    {<span style="white-space:pre"></span>        result[i,0]=(double)st[i];                    result[i,1]=(double)payoffs[i];<span style="white-space:pre"></span>    }                return result;            }            //Return corresponding option contract number by minimizing square of sum of the payoff difference             //ST:       0,  100,    110,    120,    140,    150            //Payoff:  0,   10,     20,     20,     10,     10               [ExcelFunction(Description = "Return corresponding option contract number by minimizing square of sum of the payoff difference ", Category = "Option Functions")]            public static object[,] OpTypeStrikeContractNum(                [ExcelArgument(Description = @"Stock price at maturity")]object[] StockPrices,                [ExcelArgument(Description = @"Target payoffs")]object[] TargetPayoffs)            {                int obsNum = StockPrices.Length;    //input number of stock price and target payoffs                int optionNumNeeded = 2*(obsNum - 2);   //option number needed                int numAfterInterpolation = obsNum * 2 - 2;                double[] ContractNum;     //1st col: Type; 2nd col: Strike; 3rd col: ContractNum                double[] interpolatedStockPrice;                    double[] interpolatedTargetPayoffs;                Option[] options;                                //Initiate the needed options                options = new Option[optionNumNeeded];                ContractNum = new double[optionNumNeeded];                interpolatedStockPrice = new double[numAfterInterpolation]; //10                interpolatedTargetPayoffs = new double[numAfterInterpolation];  //10                                //Set options strike prices                for (int i = 0; i < obsNum-2; i++) //0,1,2,3                {                    //Set the Option Instances                    options[i] = new Option();                    options[i].otyp = "C";                    options[i].K = (double)StockPrices[i + 1];                    options[i + optionNumNeeded / 2] = new Option();                    options[i + optionNumNeeded / 2].otyp = "P";                    options[i + optionNumNeeded / 2].K = (double)StockPrices[i + 1];                    //Set certain interpolated stock prices                    interpolatedStockPrice[i*2]=(double)StockPrices[i]; //0,2,4,6                    interpolatedTargetPayoffs[i*2]=(double)TargetPayoffs[i];                }                //Set the last two elements in the interpolation                interpolatedStockPrice[numAfterInterpolation - 2] = (double)StockPrices[obsNum - 2];                interpolatedStockPrice[numAfterInterpolation - 1] = (double)StockPrices[obsNum - 1];                interpolatedTargetPayoffs[numAfterInterpolation - 2] = (double)TargetPayoffs[obsNum - 2];                interpolatedTargetPayoffs[numAfterInterpolation - 1] = (double)TargetPayoffs[obsNum - 1];                //Interpolation                for (int i = 1; i < optionNumNeeded; i += 2)                {                    interpolatedStockPrice[i] = 0.5 * (interpolatedStockPrice[i - 1] + interpolatedStockPrice[i + 1]);                    interpolatedTargetPayoffs[i] = 0.5 * (interpolatedTargetPayoffs[i - 1] + interpolatedTargetPayoffs[i + 1]);                }                //Solver                CSolver solver = new CSolver(options, interpolatedTargetPayoffs, interpolatedStockPrice);                ContractNum = solver.IndidualSolve();                //result => 1st column is option type; 2nd column is strike; 3rd column is contract number                object[,] result = new object[optionNumNeeded,3];                for (int i = 0; i < optionNumNeeded; i++)                {                    result[i, 0] = (string)options[i].otyp;                    result[i, 1] = (double)options[i].K;                    result[i,2] =(double) ContractNum[i];                }                return result;            }        }    }

之前一直困惑我的问题是，当用许多option（不同的K）去求解时，会出现很多小数contract number的问题，最后终于想到了一个办法，那就是把它作为目标函数的一部分写进去！结果成功！！！好爽！！！

例如，一个Strangle+Put：