/// <summary>
/// 计算隐含波动率
/// </summary>
/// <param name="underlyingPrice"></param>
/// <param name="strikePrice"></param>
/// <param name="daysToMaturity"></param>
/// <param name="interestRate"></param>
/// <param name="marketPrice"></param>
/// <param name="optionType"></param>
/// <returns></returns>
public static double CalculateImpliedVolatilityBisection(double underlyingPrice, double strikePrice, int daysToMaturity, double interestRate, double marketPrice, OptionTypeEnum optionType)
{
double lower = 0;
double upper = 10;
double impliedVolatility = 0;
double impliedPrice = 0;
while (Math.Abs(upper - lower) > 0.000000001)
{
impliedVolatility = (lower + upper) / 2;
OptionPricingModelParams optionPricingModelParams = new OptionPricingModelParams(optionType,
underlyingPrice, strikePrice, interestRate, impliedVolatility, daysToMaturity);
OptionValue optionValue = OptionPricingModel.EuropeanBS(optionPricingModelParams);
if(impliedPrice == optionValue.Price)
{
break;
}
impliedPrice = optionValue.Price;
if (optionValue.Price >= marketPrice)
{
upper = impliedVolatility;
}
else
{
lower = impliedVolatility;
}
}
return impliedVolatility;
}
/// <summary>
/// 期权定价模型
/// </summary>
/// <param name="optionProperties"></param>
/// <returns></returns>
public static OptionValue EuropeanBS(OptionPricingModelParams optionProperties)
{
double sigmaTimesSqrtMaturity = optionProperties.Volatility * Math.Sqrt(optionProperties.Maturity);
double d1 = (Math.Log(optionProperties.UnderlyingPrice / optionProperties.StrikePrice) + (optionProperties.Volatility * optionProperties.Volatility / 2) *
optionProperties.Maturity) / sigmaTimesSqrtMaturity;
if (double.IsNaN(d1))
{
d1 = Double.PositiveInfinity;
}
double d2 = d1 - sigmaTimesSqrtMaturity;
double optionPrice = 0;
double delta = 0;
double gamma = 0;
double vega = 0;
double theta = 0;
double rho = 0;
switch (optionProperties.OptionType)
{
case OptionTypeEnum.call:
optionPrice = optionProperties.UnderlyingPrice * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * normdist(d1) -
normdist(d2) * optionProperties.StrikePrice * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity);
delta = Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * normdist(d1);
gamma = ((Math.Exp(-d1 * d1 / 2) / Math.Sqrt(2 * Math.PI)) * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity)) / (optionProperties.UnderlyingPrice * optionProperties.Volatility * Math.Sqrt(optionProperties.Maturity));
vega = (Math.Exp(-d1 * d1 / 2) / Math.Sqrt(2 * Math.PI)) * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * optionProperties.UnderlyingPrice * Math.Sqrt(optionProperties.Maturity);
theta = optionProperties.InterestRate * optionPrice - Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * optionProperties.UnderlyingPrice * (Math.Exp(-d1 * d1 / 2) / Math.Sqrt(2 * Math.PI)) * optionProperties.Volatility / (2 * Math.Sqrt(optionProperties.Maturity));
rho = -optionProperties.Maturity * optionPrice;
break;
case OptionTypeEnum.put:
optionPrice = -optionProperties.UnderlyingPrice * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * normdist(-d1) +
normdist(-d2) * optionProperties.StrikePrice * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity);
delta = Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * (normdist(d1) - 1);
gamma = ((Math.Exp(-d1 * d1 / 2) / Math.Sqrt(2 * Math.PI)) * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity)) / (optionProperties.UnderlyingPrice * optionProperties.Volatility * Math.Sqrt(optionProperties.Maturity));
vega = (Math.Exp(-d1 * d1 / 2) / Math.Sqrt(2 * Math.PI)) * Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * optionProperties.UnderlyingPrice * Math.Sqrt(optionProperties.Maturity);
theta = optionProperties.InterestRate * optionPrice -
Math.Exp(-optionProperties.InterestRate * optionProperties.Maturity) * optionProperties.UnderlyingPrice * (Math.Exp(-d1 * d1 / 2) / Math.Sqrt(2 * Math.PI)) * optionProperties.Volatility / (2 * Math.Sqrt(optionProperties.Maturity));
rho = optionProperties.Maturity * optionPrice;
break;
default:
break;
}
switch (GlobalValues.TimeMeasurementType)
{
case TimeMeasurementTypeEnum.交易日:
theta /= GlobalValues.TradingDaysPerYear;
break;
case TimeMeasurementTypeEnum.日历日:
theta /= GlobalValues.GeneralDaysPerYear;
break;
default:
break;
}
return new OptionValue(optionPrice, delta, gamma, vega / 100, theta, rho / 100, optionProperties.Maturity);
}
/// <summary>
/// 有行情到来时的处理逻辑
/// </summary>
/// <param name="md"></param>
private void MD_OnTick(ThostFtdcDepthMarketDataField md)
{
if (this.option.InstrumentID == md.InstrumentID)
{
this.option.LastMarket = md;
//计算期权理论价格
OptionPricingModelParams optionPricingModelParams = new OptionPricingModelParams(this.option.OptionType,
MainForm.Future.LastMarket.LastPrice, this.option.StrikePrice, GlobalValues.InterestRate, GlobalValues.Volatility,
StaticFunction.GetDaysToMaturity(this.option.InstrumentID));
this.option.OptionValue = OptionPricingModel.EuropeanBS(optionPricingModelParams);
////计算隐含波动率
if (MainForm.Future.LastMarket != null)
{
this.option.ImpliedVolatility = StaticFunction.CalculateImpliedVolatilityBisection(MainForm.Future.LastMarket.LastPrice, this.option.StrikePrice,
StaticFunction.GetDaysToMaturity(this.option.InstrumentID), GlobalValues.InterestRate, md.LastPrice, this.option.OptionType);
string[] updateDateTimeString = md.UpdateTime.Split(':');
DateTime updateDateTime = new DateTime();
updateDateTime = updateDateTime.AddHours(double.Parse(updateDateTimeString[0]));
updateDateTime = updateDateTime.AddMinutes(double.Parse(updateDateTimeString[1]));
updateDateTime = updateDateTime.AddSeconds(double.Parse(updateDateTimeString[2]));
if ((updateDateTime - lastUpdateDateTime).TotalSeconds > this.ReplaceOrderDuration)
{
//撤单
this.CancelOrder();
//计算报价
double[] quote = this.CalculateQuote();
if (isRunning)
{
this.ReplaceOrderDuration = 11;
this.lastUpdateDateTime = updateDateTime;
this.PlaceOrder(quote);
}
else if (hasForQuote)
{
this.ReplaceOrderDuration = 11;
this.lastUpdateDateTime = updateDateTime;
hasForQuote = false;
this.PlaceOrder(quote);
}
}
}
}
}
/// <summary>
/// Put行情更新时该方法被调用
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
void put_MarketUpdated(object sender, EventArgs e)
{
//计算期权相关值
if (put.MarketData != null && underlying.MarketData != null)
{
//计算期权理论价格
OptionPricingModelParams optionPricingModelParams = new OptionPricingModelParams(this.put.OptionType,
this.underlying.MarketData.LastPrice, this.put.StrikePrice, GlobalValues.InterestRate, GlobalValues.Volatility,
StaticFunction.GetDaysToMaturity(this.put.Contract.InstrumentID));
this.put.OptionValue = OptionPricingModel.EuropeanBS(optionPricingModelParams);
//计算隐含波动率
this.put.ImpliedVolatility = StaticFunction.CalculateImpliedVolatilityNewton(this.underlying.MarketData.LastPrice,
this.put.StrikePrice, StaticFunction.GetDaysToMaturity(this.put.Contract.InstrumentID),
GlobalValues.InterestRate, this.put.MarketData.LastPrice, this.put.OptionType);
}
}
