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from math import log,exp,sqrtfrom scipy import statsimport pandas as pdimport numpy as npimport pyecharts





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ÆÚȨBS¶¨¼ÛÄ£ÐÍd1 = (ln(st/k)+(r+1/2*sigma)*T)/(sigma*sqrt(T))d2 = d1 - sigma*sqrt(T)call = st *N(d1)-k *exp(-r *T) *N(d2)put = k*exp(-r*T)*N(-d2)-st*N(-d1)

In [16]:

def call(st,k,r,T,sigma):    '''    st,k,r,T,sigma(TÒÔÄêΪµ¥Î»£¬ÌìÊýÓ¦¸Ã³ýÒÔ365)    '''    d1 = (log(st/k)+(r+1/2*sigma)*T)/(sigma*sqrt(T))    d2 = d1-sigma*sqrt(T)    call = st*stats.norm.cdf(d1)-k*exp(-r*T)*stats.norm.cdf(d2)    return calldef put(st,k,r,T,sigma):    '''    st,k,r,T,sigma(TÒÔÄêΪµ¥Î»£¬ÌìÊýÓ¦¸Ã³ýÒÔ365)    '''    d1 = (log(st/k)+(r+1/2*sigma)*T)/(sigma*sqrt(T))    d2 = d1-sigma*sqrt(T)    put = k*exp(-r*T)*stats.norm.cdf(-1*d2)-1*st*stats.norm.cdf(-1*d1)    return put





Deltacall :delta = N(d1)put :delta = N(-d1)

In [19]:

def delta(st,k,r,T,sigma,n=1):    '''    nĬÈÏΪ1¿´ÕÇÆÚȨµÄdelta    nΪ-1Ϊ¿´µøÆÚȨµÄdelta    '''    d1 = (log(st/k)+(r+1/2*sigma)*T)/(sigma*sqrt(T))    delta = n*stats.norm.cdf(n*d1)    return delta





Gammagamma = N£§(d1)/(st*sigma*sqrt(T))

In [37]:

def gamma(st,k,r,T,sigma):    d1 = (log(st/k)+(r+1/2*sigma)*T)/(sigma*sqrt(T))    gamma = stats.norm.pdf(d1)/(st*sigma*sqrt(T))    return gamma





Thetacall: theta = -1*(st*N£§(d1)*sigma)/(2*sqrt(T))-r¡Ák*exp(-r *T)*N(d2)put:theta = -1*(st*N£§(d1)*sigma)/(2*sqrt(T))+r¡Ák*exp(-r *T)*N(-1*d2)

In [22]:

def theta(st,k,r,T,sigma,n=1):    '''    nĬÈÏΪ1¿´ÕÇÆÚȨµÄdelta    nΪ-1Ϊ¿´µøÆÚȨµÄdelta    '''    d1 = (log(st/k)+(r+1/2*sigma)*T)/(sigma*sqrt(T))    d2 = d1-sigma*sqrt(T)    theta = -1*(st*stats.norm.pdf(d1)*sigma)/(2*sqrt(T))-n*r*k*exp(-r*T)*stats.norm.cdf(n*d2)    return theta





Vegavega = st*sqrt(T)*N£§(d1)

In [23]:

def vega(st,k,r,T,sigma):    d1 = (log(st/k)+(r+1/2*sigma)*T)/(sigma*sqrt(T))    vega = st*sqrt(T)*stats.norm.pdf(d1)    return vega





Ï£À°×Öĸ»­Í¼

In [40]:

#»­Í¼º¯Êýfrom pyecharts import Surface3Ddef create_surface3d_data(func,st,k,r,T,sigma):    for t0 in T:        y = t0        for t1 in k:            x = t1            z = func(st,t1,r,t0,sigmas)            yield [x, y, z]def plots(func,strs,st,k,r,T,sigma):    range_color = [    "#313695",    "#4575b4",    "#74add1",    "#abd9e9",    "#e0f3f8",    "#ffffbf",    "#fee090",    "#fdae61",    "#f46d43",    "#d73027",    "#a50026",    ]    _data = list(create_surface3d_data(func,st,k,r,T,sigma))    surface3d = Surface3D(strs, width=1200, height=600)    surface3d.add(        "",        _data,        is_visualmap=True,        visual_range_color=range_color,        visual_range=[-70,0 ],        grid3d_rotate_sensitivity=1,        xaxis3d_min=80,    )    return surface3d

In [43]:

#deltak = np.linspace(80,120,100)T = np.linspace(0.01,1,100)st = 100r = log(1+0.065)sigma = 0.4plots(delta,'delta',st,k,r,T,sigma)

Out[43]:

In [44]:

plots(gamma,'gamma',st,k,r,T,sigma)

Out[44]:

In [45]:

plots(vega,'vega',st,k,r,T,sigma)

Out[45]:

In [46]:

plots(theta,'theta',st,k,r,T,sigma)

Out[46]:

ÆÚȨ×éºÏËðÒæͼ

In [92]:

def line_op(kind,x,y,name):    kind.add(name,x,y,is_label_show=True)    return kind

In [93]:

#ËðÒæ¼ÆËãdef buy(st,k,qlj,n=1):    '''    n=1 call    n=-1 put    '''    lists = []    for i in st:        profit = max(n*(i-k)-qlj,-qlj)  #max(k-st-qlj,-qlj)        lists.append(profit)    return listsdef sell(st,k,qlj,n=1):    '''    n=1 call    n=-1 put    '''    lists = []    for i in st:        profit = -1*max(n*(i-k)-qlj,-qlj)  #max(k-st-qlj,-qlj)        lists.append(profit)    return lists





Áì×ÓÆÚȨ

In [148]:

#1.ÂòÈëÒ»·Ý±êµÄ×ʲúp1#2.ÂòÈëÐéÖµ¿´µøp2#3.Âô³öÐéÖµ¿´ÕÇp3s1 = 100  c_k = 105p_k = 95r = 0.05T = 30/365sigma = 0.4st = np.linspace(80,120,100)c = call(s1,c_k,r,T,sigma)p = put(s1,p_k,r,T,sigma)p1 = []for i in st:    p1.append(i-s1)p2 = buy(st,p_k,p,-1)p3 = sell(st,c_k,c)sum_p = []for i in range(len(p1)):    sum_p.append(p1+p2+p3)    import matplotlib.pyplot as pltimport matplotlib as mpl%matplotlib inlinempl.rcParams['font.sans-serif']=['FangSong'] #ÓÃÀ´Õý³£ÏÔʾÖÐÎıêÇ©mpl.rcParams['axes.unicode_minus']=False #ÓÃÀ´Õý³£ÏÔʾ¸ººÅplt.figure(figsize=(12,7))plt.plot(st/100-1,p1,label='±êµÄ',alpha=0.4,linestyle='--')plt.plot(st/100-1,p2,label='ÂòÈëÐéÖµ¿´µø',alpha=0.4,linestyle='--')plt.plot(st/100-1,p3,label='Âô³öÐéÖµ¿´ÕÇ',alpha=0.4,linestyle='--')plt.plot(st/100-1,sum_p,linewidth=3,label='×éºÏÊÕÒæ')plt.grid(True)ax = plt.gca()ax.spines['bottom'].set_position(('data', 0))ax.spines['left'].set_position(('data', 0))ax.legend()

Out[148]:

<matplotlib.legend.Legend at 0x12d9ab70>

In [156]:

#pyecharts »­µÄͼÉÏ´«ºóÎÞ·¨ÏÔʾ Õâ±ßÓÃmatplotlibÔÙ»­Ò»´Îdef matplot_op(func,st,k,T,r,sigma):    fig = plt.figure()    ax = Axes3D(fig)    z = np.zeros((len(k),len(T)))    for j in range(len(k)):        for i in range(len(T)):            z[i,j] = func(st,k[j],r,T,sigma)    k,T = np.meshgrid(k,T)    ax.plot_wireframe(k,T,z)from mpl_toolkits.mplot3d import Axes3Dk = np.linspace(80,120,100)T = np.linspace(0.01,1,100)st = 100r = log(1+0.065)sigma = 0.4matplot_op(delta,st,k,T,r,sigma)plt.title('delta');

In [158]:

matplot_op(vega,st,k,T,r,sigma)plt.title('vega');

In [162]:

matplot_op(gamma,st,k,T,r,sigma)plt.title('gamma');

In [161]:

matplot_op(theta,st,k,T,r,sigma)plt.title('theta');