Python code for Chapter 6

QID-1143-SFEgamma/Metainfo.txt

@@ -10,6 +10,8 @@ See also: SFEvanna, SFEvolga, SFEdelta, SFEvega, SFEtheta, SFEspeed, SFEcharmcal
 
 Author: Wolfgang K. Haerdle
 
+Author[Python]: David Schulte
+
 Submitted: Mon, November 24 2014 by Awdesch Melzer
 
 Example: 'For given [lower, upper] bound of Asset price S like [50,150] and [lower, upper] bound of time to maturity tau like [0.01, 1] a plot of the Gamma of a call option is produced.'

QID-1143-SFEgamma/SFEgamma.py

@@ -0,0 +1,38 @@
+import numpy as np
+from scipy.stats import norm
+from matplotlib import pyplot as plt
+from matplotlib import cm
+
+# parameter settings
+save_figure = True
+S_min = 50          # lower bound of Asset Price
+S_max = 150         # upper bound of Asset Price
+tau_min = 0.05      # lower bound of Time to Maturity
+tau_max = 1         # upper bound of Time to Maturity
+K = 100             # exercise price
+r = 0.1             # riskfree interest rate
+sig = 0.25          # volatility
+d = 0.2             # dividend rate
+steps = 60          # steps
+
+tau = np.linspace(tau_min, tau_max, steps)
+S = np.linspace(S_max, S_min, steps)
+
+
+def get_gamma(tau, S, K, r, d, sig):
+    y = (np.log(S/K) + (r - d - sig**2/2) * tau)/(sig * np.sqrt(tau))
+
+    return np.exp(-d*tau)*norm.pdf(y+sig*np.sqrt(tau))/(S * sig * np.sqrt(tau))
+
+
+X, Y = np.meshgrid(tau, S)
+fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
+ax.plot_surface(X, Y, get_gamma(X, Y, K, r, d, sig), cmap=cm.viridis)
+ax.set_title('Dependence of Gamma on Stock Price and Time to Maturity')
+ax.set_xlabel('Time to Maturity')
+ax.set_ylabel('Stock Price')
+ax.set_zlabel('Gamma')
+plt.show()
+
+if save_figure:
+    fig.savefig('SFEgamma.png', transparent=True)

QID-1389-SFEBSCopt2/SFEBSCopt2.py

@@ -0,0 +1,17 @@
+import numpy as np
+from scipy.stats import norm
+
+# input variables
+K = 100
+S = 98
+r = 1/20
+b = 1/20
+tau = 20/52
+sig = 1/5
+
+# main computation
+y = (np.log(S/K) + (b - (sig**2)/2) * tau)/(sig * np.sqrt(tau))
+c = np.exp(-(r - b) * tau) * S * norm.cdf(y + sig * np.sqrt(tau)) - np.exp(-r * tau) * K * norm.cdf(y)
+
+# output
+print("The call price is {}".format(c))

QID-1414-SFEtheta/Metainfo.txt

@@ -10,6 +10,8 @@ See also: SFEvanna, SFEvolga, SFEdelta, SFEgamma, SFEvega, SFEspeed, SFEcharmcal
 
 Author: Ekaterina Ignatieva, Ying Chen, Christian M. Hafner
 
+Author[Python]: David Schulte
+
 Submitted: Sun, December 04 2011 by Dedy Dwi Prastyo
 
 Example: 'For given [lower, upper] bound of Asset price S like [50,150] and [lower, upper] bound of time to maturity tau like [0.05, 1] a plot of the Theta of a call option is produced.'

QID-1414-SFEtheta/SFEtheta.py

@@ -0,0 +1,38 @@
+import numpy as np
+from scipy.stats import norm
+from matplotlib import pyplot as plt
+from matplotlib import cm
+
+# parameter settings
+save_figure = True
+S_min = 50          # lower bound of Asset Price
+S_max = 150         # upper bound of Asset Price
+tau_min = 0.05      # lower bound of Time to Maturity
+tau_max = 1         # upper bound of Time to Maturity
+K = 100             # exercise price
+r = 0.1             # riskfree interest rate
+sig = 0.25          # volatility
+d = 0.2             # dividend rate
+steps = 60          # steps
+
+tau = np.linspace(tau_min, tau_max, steps)
+S = np.linspace(S_max, S_min, steps)
+
+
+def get_theta(tau, S, K, r, d, sig):
+    y = (np.log(S/K) + (r - d - sig**2/2) * tau)/(sig * np.sqrt(tau))
+
+    return -np.exp(-d*tau)*sig*S/(2*np.sqrt(tau))*norm.pdf(y+sig*np.sqrt(tau)) - r*K*np.exp(-r*tau)*norm.cdf(y)
+
+
+X, Y = np.meshgrid(tau, S)
+fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
+ax.plot_surface(X, Y, get_theta(X, Y, K, r, d, sig), cmap=cm.viridis)
+ax.set_title('Dependence of Theta on Stock Price and Time to Maturity')
+ax.set_xlabel('Time to Maturity')
+ax.set_ylabel('Stock Price')
+ax.set_zlabel('Theta')
+plt.show()
+
+if save_figure:
+    fig.savefig('SFEtheta.png', transparent=True)

QID-1428-SFEvega/Metainfo.txt

@@ -10,6 +10,8 @@ See also: SFEvanna, SFEvolga, SFEdelta, SFEgamma, SFEtheta, SFEspeed, SFEcharmca
 
 Author: Ying Chen, Christian M. Hafner
 
+Author[Python]: David Schulte
+
 Submitted: Tue, July 01 2014 by Petra Burdejova
 
 Example: 'For given [lower, upper] bound of Asset price S like [50,150] and [lower, upper] bound of time to maturity tau like [0.01, 1] a plot of the Vega of a call option is produced.'