/// <summary>
/// 计算器初始化，计算中间变量
/// </summary>
/// <param name="info"></param>
public AmericanOptionCalc(AmericanOptionInfo info)
{
try
{
#region 期权信息检查
if (info.OptionType != 1 && info.OptionType != -1)
{
throw new Exception("期权类型非法");
}
if (info.N < 2)
{
throw new Exception("期数(执行步数)非法");
}
if (info.AssetPrice < 0)
{
throw new Exception("标的当前价格非法");
}
if (info.ExercisePrice < 0)
{
throw new Exception("执行价格非法");
}
if (info.EndDate <= info.StartDate)
{
throw new Exception("起始到期日期非法");
}
if (info.r < 0)
{
throw new Exception("无风险利率r非法");
}
if (info.q < 0)
{
throw new Exception("股息率q非法");
}
if (info.sigma == 0)
{
throw new Exception("波动率非法");
}
#endregion
ExpiryDays = (info.EndDate - info.StartDate).Days;
AnnualTimePerStep = (double)ExpiryDays / 365 / info.N;
b = info.r - info.q;
a = Math.Exp(b * AnnualTimePerStep);
DiscountRate = Math.Exp(-info.r * AnnualTimePerStep);
OptionType = info.OptionType;
Info = info;
Calc(info, out u, out d, out p, out pNegative, out TreeAssetPrice, out TreeOptionPrice);
}
catch (Exception ex)
{
throw ex;
}
}
private void Calc(AmericanOptionInfo info, out double tu, out double td, out double tp, out double tpNegative, out double[] tTreeAssetPrice, out double[] tTreeOptionPrice)
{
tu = Math.Exp(info.sigma * Math.Sqrt(AnnualTimePerStep));
td = Math.Exp(-info.sigma * Math.Sqrt(AnnualTimePerStep));
tp = (a - td) / (tu - td);
tpNegative = 1 - tp;
#region 生成二叉树
int numberOfNodes = (info.N + 2) * (info.N + 1) / 2;
//计算标的价格
tTreeAssetPrice = new double[numberOfNodes];
//根节点
tTreeAssetPrice[0] = info.AssetPrice;
for (int i = 1; i <= info.N; i++) //i为层数，第i层有i+1个点，根节点在0层
{
int index = (i * (i + 1) / 2); //第i层第1个点的索引
int father = index - i; //第i层第1个点父节点的索引
tTreeAssetPrice[index] = tTreeAssetPrice[father] * tu; //第i层第1个点由父节点上涨一次所得，乘上涨幅度u
for (int j = 2; j <= i + 1; j++) //j为点数，首个点编号为1
{
index = (i * (i + 1) / 2) + j - 1; //第i层第j个点的索引
father = index - i - 1; //父节点的索引
tTreeAssetPrice[index] = tTreeAssetPrice[father] * td; //由父节点下跌一次所得，乘下跌幅度d
}
}
//计算期权价格
tTreeOptionPrice = new double[numberOfNodes];
//首先计算最底层N，共N+1个点
for (int i = numberOfNodes - info.N - 1; i < numberOfNodes; i++)
{
tTreeOptionPrice[i] = Math.Max((tTreeAssetPrice[i] - info.ExercisePrice) * OptionType, 0);
}
//倒推
int level = info.N - 1; //当前层数，初始在N-1层
int cnt = 0;
for (int i = numberOfNodes - info.N - 2; i >= 0; i--) //i为索引
{
cnt++; //当前为本层倒数第cnt个点
double tmp1 = tp * tTreeOptionPrice[i + level + 1] + tpNegative * tTreeOptionPrice[i + level + 2];
double tmp2 = Math.Exp(-info.r * AnnualTimePerStep) * tmp1;
tTreeOptionPrice[i] = Math.Max((tTreeAssetPrice[i] - info.ExercisePrice) * OptionType, tmp2);
if (cnt == level + 1) //本层遍历结束
{
cnt = 0;
level--;
}
}
#endregion
}
/// <summary>
/// 获取Rho
/// </summary>
public double GetRho()
{
double epsilon = 0.00001;
AmericanOptionInfo info2 = AmericanOptionInfo.Clone(Info);
info2.r += epsilon;
double tu = 0, td = 0, tp = 0, tpNegative = 0;
double[] tTreeAssetPrice = null;
double[] tTreeOptionPrice = null;
Calc(info2, out tu, out td, out tp, out tpNegative, out tTreeAssetPrice, out tTreeOptionPrice);
if (tTreeOptionPrice == null || tTreeOptionPrice.Length < 1)
{
throw new Exception("获取Rho失败");
}
return((tTreeOptionPrice[0] - TreeOptionPrice[0]) / epsilon * OptionType * 0.01);
}
static void Main(string[] args)
{
try
{
//double test3 = 40927.52 * 100;
//double test6 = (double)((decimal)40927.52 * 100);
//double test9 = (double)((decimal)40927.525 * 100);
//double test10 = Math.Floor(test9) / 100;
//double test11 = (double)Math.Floor((decimal)40927.525 * 100) / 100;
//double test7 = (float)40927.52 * 100;
//double test2 = -40927.52 * 100;
//double test1 = -Math.Abs(40927.52) * 100;
//double test = Math.Ceiling(-Math.Abs(40927.52) * 100) / 100;
//double test4 = -Math.Ceiling(Math.Abs(40927.52) * 100) / 100;
//double test8 = -Math.Ceiling(Math.Abs(40927.5199) * 100) / 100;
double test5 = Math.Floor(40927.52 * 100) / 100;
double test12 = (double)Math.Floor((decimal)40927.52 * 100) / 100;
#region 美式期权
//某美式期权信息
AmericanOptionInfo americanOptionInfo = new AmericanOptionInfo()
{
OptionType = -1,
N = 2,
AssetPrice = 3.061,
ExercisePrice = 3.12,
MarketPrice = -0.0833,
StartDate = new DateTime(2019, 12, 1),
EndDate = new DateTime(2020, 1, 22),
sigma = 0.1105,
r = 0.0303,
q = 0
};
Stopwatch sw1 = Stopwatch.StartNew();
//美式期权计算器初始化
AmericanOptionCalc americanOptionCalc = new AmericanOptionCalc(americanOptionInfo);
sw1.Stop();
Console.WriteLine(string.Format("初始化用时：{0}秒", sw1.Elapsed.TotalSeconds));
Stopwatch sw2 = Stopwatch.StartNew();
//获取理论价格
double TheoreticalPrice = americanOptionCalc.GetTheoreticalPrice();
//获取理论价格%
double TheoreticalPricePer = americanOptionCalc.GetTheoreticalPricePercent();
double Delta = americanOptionCalc.GetDelta();
double Gamma = americanOptionCalc.GetGamma();
double Vega = americanOptionCalc.GetVega();
double Theta = americanOptionCalc.GetTheta();
double Rho = americanOptionCalc.GetRho();
double IntriValue = americanOptionCalc.GetIntriValue();
double TimeValue = americanOptionCalc.GetTimeValue();
double DueProfit = americanOptionCalc.GetDueProfit();
double CurrentProfit = americanOptionCalc.GetCurrentProfit();
sw2.Stop();
Console.WriteLine(string.Format("获取结果用时：{0}秒\r\n共{1}秒", sw2.Elapsed.TotalSeconds, sw1.Elapsed.TotalSeconds + sw2.Elapsed.TotalSeconds));
#endregion
#region 概率图
Stopwatch sw3 = Stopwatch.StartNew();
//样本价格序列S0
List <double> S0 = new List <double>()
{
3, 2, 3, 4, 5, 6, 7, 8, 7
};
//当前标的价格
double AssetPrice = 3;
//盈亏平衡点
List <double> BalancePoints = new List <double>()
{
4, 6
};
ProbabilityCalc probabilityCalc = new ProbabilityCalc(S0);
//概率图点集（步骤八）
List <Node> ProbabilityMap = probabilityCalc.GetProbabilityMap(AssetPrice, BalancePoints);
//各区间概率大小（步骤七）
List <double> IntervalProbability = probabilityCalc.GetIntervalProbability(BalancePoints);
sw3.Stop();
//各区间概率和越接近1，区间概率结果越精确
Console.WriteLine(string.Format("概率图用时：{0}秒，各区间概率和：{1}", sw3.Elapsed.TotalSeconds, IntervalProbability.Sum()));
#endregion
Console.WriteLine("Hello World!");
}
catch (Exception ex)
{
Console.WriteLine(ex.Message);
}
}