diff --git a/vnpy/pricing/black.py b/vnpy/pricing/black.py new file mode 100644 index 00000000..c3bd8a2a --- /dev/null +++ b/vnpy/pricing/black.py @@ -0,0 +1,137 @@ +# encoding: UTF-8 + +''' +Black76期权定价模型,主要用于标的物为期货的欧式期权的定价 + +变量说明 +f:标的物期货价格 +k:行权价 +r:无风险利率 +t:剩余到期时间(年) +v:隐含波动率 +cp:期权类型,+1/-1对应call/put +price:期权价格 + +出于开发演示的目的,本文件中的希腊值计算基于简单数值差分法, +运算效率一般,实盘中建议使用更高速的算法。 + +本文件中的希腊值计算结果没有采用传统的模型价格数值,而是采用 +了实盘交易中更为实用的百分比变动数值,具体定义如下 +delta:当f变动1%时,price的变动 +gamma:当f变动1%时,delta的变动 +theta:当t变动1天时,price的变动(国内交易日每年240天) +vega:当v涨跌1个点时,price的变动(如从16%涨到17%) +''' + + +from scipy import stats +from math import (log, pow, sqrt, exp) + +cdf = stats.norm.cdf + + +# 计算希腊值和隐含波动率时用的参数 +STEP_CHANGE = 0.001 +STEP_UP = 1 + STEP_CHANGE +STEP_DOWN = 1 - STEP_CHANGE +STEP_DIFF = STEP_CHANGE * 2 + +DX_TARGET = 0.00001 + + +#---------------------------------------------------------------------- +def calculatePrice(f, k, r, t, v, cp): + """计算期权价格""" + d1 = (log(f / k) + (0.5 * pow(v, 2) + r) * t) / (v * sqrt(t)) + d2 = d1 - v * sqrt(t) + price = cp * (f * cdf(cp * d1) - k * cdf(cp * d2) * exp(-r * t)) + return price + +#---------------------------------------------------------------------- +def calculateDelta(f, k, r, t, v, cp): + """计算Delta值""" + price1 = calculatePrice(f*STEP_UP, k, r, t, v, cp) + price2 = calculatePrice(f*STEP_DOWN, k, r, t, v, cp) + delta = (price1 - price2) / (f * STEP_DIFF) * (f * 0.01) + return delta + +#---------------------------------------------------------------------- +def calculateGamma(f, k, r, t, v, cp): + """计算Gamma值""" + delta1 = calculateDelta(f*STEP_UP, k, r, t, v, cp) + delta2 = calculateDelta(f*STEP_DOWN, k, r, t, v, cp) + gamma = (delta1 - delta2) / (f * STEP_DIFF) * pow(f, 2) * 0.0001 + return gamma + +#---------------------------------------------------------------------- +def calculateTheta(f, k, r, t, v, cp): + """计算Theta值""" + price1 = calculatePrice(f, k, r, t*STEP_UP, v, cp) + price2 = calculatePrice(f, k, r, t*STEP_DOWN, v, cp) + theta = (price1 - price2) * (t * STEP_DIFF * 240) + return theta + +#---------------------------------------------------------------------- +def calculateVega(f, k, r, t, v, cp): + """计算Vega值""" + price1 = calculatePrice(f, k, r, t, v*STEP_UP, cp) + price2 = calculatePrice(f, k, r, t, v*STEP_DOWN, cp) + vega = (price1 - price2) / (v * STEP_DIFF * 100) + return vega + +#---------------------------------------------------------------------- +def calculateGreeks(f, k, r, t, v, cp): + """计算期权的价格和希腊值""" + price = calculatePrice(f, k, r, t, v, cp) + delta = calculateDelta(f, k, r, t, v, cp) + gamma = calculateGamma(f, k, r, t, v, cp) + theta = calculateTheta(f, k, r, t, v, cp) + vega = calculateVega(f, k, r, t, v, cp) + return price, delta, gamma, theta, vega + +#---------------------------------------------------------------------- +def calculateImpv(price, f, k, r, t, cp): + """计算隐含波动率""" + # 检查期权价格必须为正数 + if price <= 0: + return 0 + + # 检查期权价格是否满足最小价值(即到期行权价值) + meet = False + + if cp == 1 and (price > (f - k) * exp(-r * t)): + meet = True + elif cp == -1 and (price > k * exp(-r * t) - f): + meet = True + + # 若不满足最小价值,则直接返回0 + if not meet: + return 0 + + # 采用Newton Raphson方法计算隐含波动率 + v = 0.2 # 初始波动率猜测 + + for i in range(50): + # 计算当前猜测波动率对应的期权价格和vega值 + p = calculatePrice(f, k, r, t, v, cp) + vega = calculateVega(f, k, r, t, v, cp) + + # 计算误差 + dx = (price - p) / vega + + # 检查误差是否满足要求,若满足则跳出循环 + if abs(dx) < DX_TARGET: + break + + # 计算新一轮猜测的波动率 + v += dx + + # 检查波动率计算结果非负 + if v < 0: + return 0 + + # 保留4位小数 + v = round(v, 4) + + return v + \ No newline at end of file