引言：炒股就该两手抓，决定短期的是资金，决定长期的是价值
VBA代码新建函数公式
This Excel spreadsheet prices European options with both the standard Black-Scholes approach, and the Corrado & Su (1996) extension for excess skew and kurtosis (including the Brown & Robinson (2002) correction).
该Excel表格使用标准的Black-Scholes方法和Corrado&Su（1996）对过度偏斜和峰度的扩展（包括Brown&Robinson（2002）修正）对欧洲选项进行定价。
Learn about the Corrado & Su (1996) model for pricing options with excess skew and kurtosis, and get a pricing spreadsheet.
Corrado&Su（1996）发明了关于具有过度偏斜和峰度的期权定价模型。
The Black-Scholes option pricing model has several well-known deficiencies. Perhaps most significantly, Black-Scholes assumes that prices are log-normally distributed.
Black-Scholes期权定价模型有几个众所周知的缺陷。也许最重要的是，Black-Scholes假设价格是对数正态分布的。
In reality, howeer, investors see more extreme behavior than predicted by the normal distribution; in fact, extreme events occur 10 times more often than the normal distribution would have you assume.
然而，在现实中，投资者看到的极端行为比正态分布预测的要多；事实上，极端事件发生的频率是正态分布的10倍。
Extreme behavior in returns distributions can be described by two statistical quantities known as skew and kurtosis.
收益分布中的极端行为可以用两个统计量来描述，即偏斜和峰度。
Skewed returns distributions are not symmetric. If the returns distribution has positive skew, you should expect many smaller negative returns, and a few larger positive returns; your downside-risk is minimized.
偏斜的收益分布不是对称的。如果正态分布具有正偏斜，你应该期待许多较小的负回报，以及一些较大的正回报；您的下行风险降至最低。
negative skew, you should expect many smaller positive returns, and a few larger negative returns; this can be a real source of worry for risk-averse investors
负偏斜，你应该期待许多较小的正回报，和一些较大的负回报；对于规避风险的投资者来说，这可能是一个真正的风险来源
Kurtosis describes the relative “peakiness” or “flatness” of a returns distribution compared to the normal distribution. A peaky distribution has fat tails, with a lower probability of extreme behavior (this is also known as leptokurtic).
峰度描述了收益分布与正态分布相比的相对“峰值”或“平坦度”。尖峰分布有肥胖的尾巴，极端行为的概率较低（这也被称为黑天鹅）。
Corrado & Su (1996) extended the standard Black-Scholes scheme for option pricing by capturing the effect of skew and kurtosis. Their novel approach expanded the normal density function with a Gram-Charlier approach. This resulted in a pricing formula that was equal t
下面是VBA编程量化源代码
Function BlackScholes(OptionType, S, X, T, r, v, d)
dOne = (Log(S / X) + (r - d + 0.5 * v ^ 2) * T) / (v * (Sqr(T)))
NdOne = Exp(-(dOne ^ 2) / 2) / (Sqr(2 * Application.WorksheetFunction.Pi()))
dTwo = dOne - v * Sqr(T)
NdTwo = Application.NormSDist(dTwo)
If OptionType = "C" Then
BlackScholes = Exp(-d * T) * S * Application.NormSDist(dOne) - X * Exp(-r * T) * Application.NormSDist(dOne - v * Sqr(T))
ElseIf OptionType = "P" Then
BlackScholes = X * Exp(-r * T) * Application.NormSDist(-dTwo) - Exp(-d * T) * S * Application.NormSDist(-dOne)
End If
End Function
Function CorradoSu(OptionType, S, X, T, r, v, d, skew, kurt)
d1 = (Log(S / X) + (r - v) * T + ((v * Sqr(T)) ^ 2) / 2) / (v * Sqr(T))
nd1 = (1 / Sqr(2 * Application.WorksheetFunction.Pi)) * Exp(-(1 ^ 2) / 2)
NNd1 = Application.NormSDist(d1)
Q3 = 1 / 6 * S * Exp(-v * T) * v * Sqr(T) * ((2 * v * Sqr(T) - d1) * nd1 + v ^ 2 * T * NNd1)
Q4 = 1 / 24 * S * Exp(-v * T) * v * Sqr(T) * ((d1 ^ 2 - 1 - 3 * v * Sqr(T) * (d1 - v * Sqr(T))) * nd1 + v ^ 3 * T ^ (3 / 2) * NNd1)
If OptionType = "C" Then
CorradoSu = BlackScholes("C", S, X, T, r, v, d) + skew * Q3 + (kurt - 3) * Q4
ElseIf OptionType = "P" Then
CorradoSu = BlackScholes("P", S, X, T, r, v, d) + skew * Q3 + (kurt - 3) * Q4
End If
End Function
Corrado和Su（1996）通过捕捉偏斜和峰度的影响，扩展了期权定价的标准Black-Scholes方案。他们的新方法用Gram-Charlier方法扩展了正态密度函数。这导致了一个等于t的定价公式
The prices predicted by the Corrado & Su (1996) equations are equal to those predicted by Black-Scholes for a skew of 0 and kurtosis of 3.
Corrado和Su（1996）方程预测的价格等于Black-Scholes预测的偏斜为0和峰度为3的价格。
Brown and Robinson(2002) corrected an error in the Corrado & Su (1996) equations. The corrected equations are
Brown和Robinson（2002）修正了Corrado和Su（1996）方程中的一个错误。校正后的方程式为
Corrado Su (1997) equations for option pricing with skew and kurtosis
Corrado-Su（1997）具有偏斜和峰度的期权定价方程
where参数介绍K is the strike priceK是执行价格S0 is the asset priceS0是资产价格r is the risk-free rater是无风险利率σ is the volatilityσ是波动性T is the time to expiryT是到期时间CBS is the option price predicted by the Black-Scholes modelCBS是Black-Scholes模型预测的期权价格μ3 is the skewμ3是偏斜μ4 is the kurtosisμ4是峰度n(d) and N(d) are the standard normal density and the standard normal distributionn（d）和N（d）是标准正态密度和标准正态分布