From c320ce844f88d0df3a0774fc3065e7a5389db514 Mon Sep 17 00:00:00 2001 From: "vn.py" Date: Sun, 7 Jan 2018 12:34:46 +0800 Subject: [PATCH] =?UTF-8?q?[Add]=E6=96=B0=E5=A2=9ECRR=E6=9C=9F=E6=9D=83?= =?UTF-8?q?=E5=AE=9A=E4=BB=B7=E6=A8=A1=E5=9E=8B=EF=BC=8C=E9=92=88=E5=AF=B9?= =?UTF-8?q?=E5=9B=BD=E5=86=85=E7=BE=8E=E5=BC=8F=E5=95=86=E5=93=81=E6=9C=9F?= =?UTF-8?q?=E6=9D=83?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- vnpy/pricing/crr.py | 181 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 181 insertions(+) create mode 100644 vnpy/pricing/crr.py diff --git a/vnpy/pricing/crr.py b/vnpy/pricing/crr.py new file mode 100644 index 00000000..0f80591e --- /dev/null +++ b/vnpy/pricing/crr.py @@ -0,0 +1,181 @@ +# encoding: UTF-8 + +''' +Cox-Ross-Rubinstein二叉树期权定价模型，主要用于标的物为期货的美式期权的定价 + +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 +n: 二叉树高度 +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 __future__ import division + +import numpy as np +from math import (isnan, exp, sqrt, pow) + + +# 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 generateTree(f, k, r, t, v, cp, n): + """生成二叉树""" + dt = t / n + u = exp(v * sqrt(dt)) + d = 1 / u + a = exp(r * dt) + uTree = np.zeros((n+1,n+1)) + oTree = np.zeros((n+1,n+1)) + + # 计算风险平价概率 + p = (a - d) / (u - d) + p1 = p / a + p2 = (1 - p) / a + + # 计算标的树 + uTree[0, 0] = f + + for i in range(1, n+1): + uTree[0, i] = uTree[0, i-1] * u + for j in range(1, i+1): + uTree[j, i] = uTree[j-1, i-1] * d + + # 计算期权树 + for j in range(n+1): + oTree[j, n] = max(0, cp * (uTree[j, n]-k)) + + for i in range(n-1,-1,-1): + for j in range(i+1): + oTree[j, i] = max((p1 * oTree[j, i+1] + p2 * oTree[j+1, i+1]), # 美式期权存续价值 + cp * (uTree[j, i] - k)) # 美式期权行权价值 + + # 返回期权树和标的物树结果 + return oTree, uTree + +#---------------------------------------------------------------------- +def calculatePrice(f, k, r, t, v, cp, n=15): + """计算期权价格""" + oTree, uTree = calculatePrice(f, k, r, t, v, cp) + return oTree[0, 0] + +#---------------------------------------------------------------------- +def calculateDelta(f, k, r, t, v, cp, n=15): + """计算Delta值""" + price1 = calculatePrice(f*STEP_UP, k, r, t, v, cp, n) + price2 = calculatePrice(f*STEP_DOWN, k, r, t, v, cp, n) + delta = (price1 - price2) / (f * STEP_DIFF) * (f * 0.01) + return delta + +#---------------------------------------------------------------------- +def calculateGamma(f, k, r, t, v, cp, n=15): + """计算Gamma值""" + delta1 = calculateDelta(f*STEP_UP, k, r, t, v, cp, n) + delta2 = calculateDelta(f*STEP_DOWN, k, r, t, v, cp, n) + gamma = (delta1 - delta2) / (f * STEP_DIFF) * pow(f, 2) * 0.0001 + return gamma + +#---------------------------------------------------------------------- +def calculateTheta(f, k, r, t, v, cp, n=15): + """计算Theta值""" + price1 = calculatePrice(f, k, r, t*STEP_UP, v, cp, n) + price2 = calculatePrice(f, k, r, t*STEP_DOWN, v, cp, n) + theta = -(price1 - price2) / (t * STEP_DIFF * 240) + return theta + +#---------------------------------------------------------------------- +def calculateVega(f, k, r, t, v, cp, n=15): + """计算Vega值""" + vega = calculateOriginalVega(f, k, r, t, v, cp, n) / 100 + return vega + +#---------------------------------------------------------------------- +def calculateOriginalVega(f, k, r, t, v, cp, n=15): + """计算原始vega值""" + price1 = calculatePrice(f, k, r, t, v*STEP_UP, cp, n) + price2 = calculatePrice(f, k, r, t, v*STEP_DOWN, cp, n) + vega = (price1 - price2) / (v * STEP_DIFF) + return vega + +#---------------------------------------------------------------------- +def calculateGreeks(f, k, r, t, v, cp, n=15): + """计算期权的价格和希腊值""" + price = calculatePrice(f, k, r, t, v, cp, n) + delta = calculateDelta(f, k, r, t, v, cp, n) + gamma = calculateGamma(f, k, r, t, v, cp, n) + theta = calculateTheta(f, k, r, t, v, cp, n) + vega = calculateVega(f, k, r, t, v, cp, n) + return price, delta, gamma, theta, vega + +#---------------------------------------------------------------------- +def calculateImpv(price, f, k, r, t, cp, n=15): + """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 = 0.3 # 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, n) + + vega = calculateOriginalVega(f, k, r, t, v, cp, n) + + # 如果vega过小接近0，则直接返回 + if not vega: + break + + # 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