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KaistLectureKaistLecture
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final practice
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‎new Season/bank_account_sol.py‎

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@@ -44,5 +44,30 @@ def sdf_Tree(r0,dr,n,p):
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print(Rstr)
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plt.plot(i,R,'s-')
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b = np.array([100,50]).reshape((2,1))
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a1 = [np.exp(0.1+0.11), np.exp(0.1+0.09)]
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a1 = np.array(a1).reshape((2,1))
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a1 = np.ones((2,1))*np.exp(0.1)*np.exp(
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np.array([0.11,0.09])).reshape(2,1)
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a2 = np.ones((2,1))*np.exp(R[1]*2)
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A = np.hstack([a1,a2])
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x = np.linalg.inv(A).dot(b)
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price = x.sum()
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price2 = (100*np.exp(
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-0.11)*0.6 + 50*np.exp(-0.09)*0.4)*np.exp(-0.1)
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print(price)
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print(price2)
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‎new Season/exam_practice.py‎

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d = dict()
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for i in range(2,13):
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d[i] = []
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for i in range(1,7):
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for j in range(1,7):
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d[i+j].append((i,j))
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for x in d:
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print(x,d[x])
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#%%
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import numpy as np
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n = 10000
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x = np.random.random((n,10))
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y = np.random.random((n,10))
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#length = np.zeros((n,1))
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length = []
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for i in range(n):
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s = 0
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for j in range(10):
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if j==9:
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s += np.sqrt((x[i,j]-x[i,0])**2+(y[i,j]-y[i,0])**2)
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else:
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s += np.sqrt((x[i,j]-x[i,j+1])**2+(y[i,j]-y[i,j+1])**2)
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length.append(s)
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length = np.array(length)
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'''
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dx = np.diff(x, axis=1)
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dy = np.diff(y, axis=1)
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length = np.sqrt(dx**2 + dy**2).sum(axis=1)
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'''
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import matplotlib.pyplot as plt
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plt.hist(length,bins=30)
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print(length.mean())
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print(length.std())
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‎new Season/practice5.docx‎

67.8 KB
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‎new Season/vix_data.xlsx‎

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‎new Season/vix_sol.py‎

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import pandas as pd
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import numpy as np
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import matplotlib.pyplot as plt
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data = pd.read_excel("vix_data.xlsx")
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data.index = data.pop("DATE")
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data.dropna(inplace=True)
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data["SP500"] = np.log(data["SP500"])
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r = data.diff()
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fig, ax = plt.subplots(1,1,figsize=(6,4))
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ax.scatter(x=r["SP500"], y=r["VIXCLS"],marker='+')
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model = pd.ols(x=r["SP500"], y=r["VIXCLS"])
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alpha = model.beta.intercept
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beta = model.beta.x
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x = np.array([-0.15,0.15])
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y = alpha + beta*x
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ax.plot(x,y,'r-')
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ax.text(0,20,r"$\Delta VIX_t ={0:0.3f}+{1:0.3f}\Delta logS_t$".format(alpha, beta), fontsize=15)
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ax.set_xlabel(r"$\Delta log S_t$")
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ax.set_ylabel(r"$\Delta VIX_t$")
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fig.show()
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rv = pd.rolling_std(r["SP500"], window=20) * np.sqrt(252)
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model1 = pd.ols(x=data["VIXCLS"]/100.0, y=rv)
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alpha1 = model1.beta.intercept
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beta1 = model1.beta.x
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x1 = np.array([0,0.9])
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y1 = alpha1 + beta1*x1
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fig1, ax1 = plt.subplots(1,2,figsize=(10,4))
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ax1[0].scatter(x=data["VIXCLS"]/100.0,y=rv,marker=".")
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ax1[0].plot(x1,y1,'r-')
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ax1[0].set_xlabel("VIX")
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ax1[0].set_ylabel("Historical Vol")
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ax1[0].text(-0.15,1.0,r"$Y ={0:0.3f}+{1:0.3f}X+\epsilon$".format(alpha1, beta1), fontsize=15)
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ax1[1].plot(data["VIXCLS"]/100.0)
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ax1[1].plot(rv)
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