Binomial Model

  1using System;
  2using FinMath.Derivatives;
  3
  4namespace FinMath.Samples
  5{
  6    class BinomialSample
  7    {
  8        static void Main()
  9        {
 10            Double stockPrice = 350;
 11            Double strikePrice = 370;
 12            Double riskFreeRate = 0.009;
 13            Double annualDividendYield = 0.05;
 14            Double timeToMaturity = 1.06;
 15            Int32 numberOfSteps = 200;
 16            Double volatility = 0.22;
 17
 18            // Use of static methods for option value computation.
 19            Double optionValue = Binomial.OptionValue(stockPrice, strikePrice, riskFreeRate, annualDividendYield,
 20                timeToMaturity, OptionType.Put, OptionStyle.American, numberOfSteps, volatility);
 21
 22            Console.WriteLine($"Option value = {optionValue:0.000}");
 23
 24            // Use of static methods for implied volatility computation.
 25            Double impliedVolatility = Binomial.ImpliedVolatility(stockPrice, strikePrice, riskFreeRate,
 26                annualDividendYield, timeToMaturity, OptionType.Put, OptionStyle.American, numberOfSteps, optionValue);
 27
 28            Console.WriteLine($"Implied volatility = {impliedVolatility:0.000}");
 29            Console.WriteLine();
 30
 31            // Create new Binomial instance.
 32            Binomial binomial = new Binomial();
 33
 34            // Discrete dividends usage sample.
 35            Dividend[] dividens = new Dividend[4];
 36            dividens[0].timeToPayment = 0.355;
 37            dividens[0].dividendsAmount = 3.45;
 38
 39            dividens[1].timeToPayment = 1.055;
 40            dividens[1].dividendsAmount = 4.45;
 41
 42            // Order of elements in list is inessential.
 43            dividens[2].timeToPayment = 0.755;
 44            dividens[2].dividendsAmount = 5.45;
 45
 46            // Dividends paid in the past or after option expiration are ignored.
 47            dividens[3].timeToPayment = -0.045;
 48            dividens[3].dividendsAmount = 3.45;
 49
 50            // Set option parameters.
 51            binomial.InitByVolatility(stockPrice, strikePrice, riskFreeRate, dividens,
 52                timeToMaturity, OptionType.Put, OptionStyle.American, numberOfSteps, volatility);
 53
 54            Console.WriteLine($"Option value = {binomial.Value:0.000}");
 55            Console.WriteLine($"Delta = {binomial.Delta:0.000}");
 56
 57            Double stockPrice2 = 352;
 58            Double timeToMaturity2 = 1.05;
 59
 60            // Update asset stock price and time to maturity.
 61            binomial.Update(stockPrice2, timeToMaturity2);
 62
 63            Console.WriteLine($"Option value = {binomial.Value:0.000}");
 64            Console.WriteLine($"Delta = {binomial.Delta:0.000}");
 65
 66            // Initialize Binomial by option value.
 67            Binomial binomialByValue = new Binomial();
 68            binomialByValue.InitByOptionPrice(stockPrice2, strikePrice, riskFreeRate, dividens,
 69                timeToMaturity2, OptionType.Put, OptionStyle.American, numberOfSteps, binomial.Value);
 70
 71            Console.WriteLine($"Implied volatility = {binomialByValue.Volatility:0.000}");
 72            Console.WriteLine($"Delta = {binomialByValue.Delta:0.000}");
 73            Console.WriteLine();
 74
 75            // Use of accelerated computation.
 76            binomial = new Binomial(OptionValuation.ModelOutputs.OptionValue | OptionValuation.ModelOutputs.Delta, 100000);
 77
 78            // Change acceleration granularity.
 79            binomial.SetAccelerationGranularity(0.001, 0.001, 0.001, 0.001, 0.001);
 80
 81            // Initialize.
 82            binomial.InitByVolatility(stockPrice, strikePrice, riskFreeRate, annualDividendYield,
 83                timeToMaturity, OptionType.Put, OptionStyle.American, numberOfSteps, volatility);
 84
 85            // Use of accelerated version of option valuation.
 86            Console.WriteLine($"Option value = {binomial.Value:0.000}");
 87            Console.WriteLine($"Delta = {binomial.Delta:0.000}");
 88
 89            // Enable implied volatility and delta computation acceleration.
 90            binomialByValue = new Binomial(OptionValuation.ModelOutputs.Volatility | OptionValuation.ModelOutputs.Delta, 100000);
 91
 92            // Change acceleration granularity.
 93            binomialByValue.SetAccelerationGranularity(0.001, 0.001, 0.001, 0.001, 0.001);
 94
 95            // Initialize.
 96            binomialByValue.InitByOptionPrice(stockPrice, strikePrice, riskFreeRate, annualDividendYield,
 97                timeToMaturity, OptionType.Put, OptionStyle.American, numberOfSteps, optionValue);
 98
 99            // Use of accelerated version of implied volatility and delta valuation.
100            Console.WriteLine($"Implied volatility = {binomialByValue.Volatility:0.000}");
101            Console.WriteLine($"Delta = {binomialByValue.Delta:0.000}");
102            Console.WriteLine();
103
104            // Use of advanced acceleration.
105            binomial = new Binomial(
106                OptionValuation.ModelInputs.StockPrice | OptionValuation.ModelInputs.StrikePrice | OptionValuation.ModelInputs.Volatility,
107                OptionValuation.ModelOutputs.OptionValue | OptionValuation.ModelOutputs.Delta, 100000);
108
109            binomial.SetAccelerationGranularity(0.1, 0.1, 0.001, 0.1, 0.1);
110            binomial.InitByVolatility(stockPrice, strikePrice, riskFreeRate, annualDividendYield,
111                timeToMaturity, OptionType.Put, OptionStyle.American, numberOfSteps, volatility);
112            Console.WriteLine($"Option value = {binomial.Value:0.000}");
113            Console.WriteLine($"Delta = {binomial.Delta:0.000}");
114
115            binomialByValue = new Binomial(
116                OptionValuation.ModelInputs.StockPrice | OptionValuation.ModelInputs.StrikePrice | OptionValuation.ModelInputs.OptionPrice,
117                OptionValuation.ModelOutputs.Volatility | OptionValuation.ModelOutputs.Delta, 100000);
118            binomial.SetAccelerationGranularity(0.1, 0.1, 0.001, 0.1, 0.1);
119            binomialByValue.InitByOptionPrice(stockPrice, strikePrice, riskFreeRate, annualDividendYield,
120                timeToMaturity, OptionType.Put, OptionStyle.American, numberOfSteps, optionValue);
121            Console.WriteLine($"Implied volatility = {binomialByValue.Volatility:0.000}");
122            Console.WriteLine($"Delta = {binomialByValue.Delta:0.000}");
123            Console.WriteLine();
124        }
125    }
126}