Derivatives analytics with python ---- Part 1

Market-based Valuation

This is a book that I think really helpful and practical to our quant work. But the python code in it is outdated, and some of them are missing the important parts, so from now on, I will use the mindmap to structure the knowledge in it and rewrite the codes in python 3.7. I hope this can help more people.

This is the overall structure of this book and it is also the information from the first chapter.

Mindmap

European Call Option Inner Value Plot

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rcParams['font.family'] = 'serif'

# Option Strike
K = 8000
# Graphical Output
S = np.linspace(7000, 9000, 100) # index level values
h = np.maximum(S - K, 0) # inner values of call option
plt.figure()
plt.plot(S, h, lw=2.5) # plot inner values at maturity
plt.xlabel('index level $S_t$ at maturity')
plt.ylabel('inner value of European call option')
plt.grid(True)

European Call Option Value Plot

# first, define the valuation formula for European Call option
import numpy as np
import scipy.stats as si
import sympy as sy
from sympy.stats import Normal, cdf
def BSM_call_value(S0, K, q, T, r, vol):
    # q denotes the dividend rate
    d1 = (np.log(S / K) + (r - q + 0.5 * vol ** 2) * T) / (vol * np.sqrt(T))
    d2 = (np.log(S / K) + (r - q - 0.5 * vol ** 2) * T) / (vol * np.sqrt(T))
    call = (S * np.exp(-q * T) * si.norm.cdf(d1, 0.0, 1.0) - K * np.exp(-r * T) * si.norm.cdf(d2, 0.0, 1.0))
    return call

import sys
sys.path.append('05_com')
# Model and Option Parameters
K = 8000 # strike price
T = 1.0 # time-to-maturity
r = 0.025 # constant, risk-less short rate
vol = 0.2 # constant volatility
# Sample Data Generation
S = np.linspace(4000, 12000, 150) # vector of index level values
h = np.maximum(S - K, 0) # inner value of option
C = [BSM_call_value(S0, K, 0, T, r, vol) for S0 in S][0]
# calculate call option values
# Graphical Output
plt.figure()
plt.plot(S, h, 'b-.', lw=2.5, label='inner value')
# plot inner value at maturity
plt.plot(S, C, 'r', lw=2.5, label='present value')
# plot option present value
plt.grid(True)
plt.legend(loc=0)
plt.xlabel('index level $S_0$')
plt.ylabel('present value $C(t=0)$')
plt.show()