def test_delta_greeks(self):
'''
Q: (Delta Greeks)
A future option, 6 month to expiry, the futures price is 105,
the strike strike price is 100, risk free interest rate is 10% per year,
volatility is 36% per year
A:
delta_call = 0.5946
delta_put = -0.3566
'''
bsg = BlackScholesGreeks('futures_option', 105, 100, 0.1, 0.5, 0.36)
self.assertEqual(0.5946, bsg.get_delta_greeks(OptionType.CALL))
self.assertEqual(-0.3566, bsg.get_delta_greeks(OptionType.PUT))
def test_delta_greeks(self):
'''
Q: (Delta Greeks)
A future option, 6 month to expiry, the futures price is 105,
the strike strike price is 100, risk free interest rate is 10% per year,
volatility is 36% per year
A:
delta_call = 0.5946
delta_put = -0.3566
'''
bsg = BlackScholesGreeks('futures_option', 105, 100, 0.1, 0.5, 0.36)
self.assertEqual(0.5946,
bsg.get_delta_greeks(OptionType.CALL))
self.assertEqual(-0.3566,
bsg.get_delta_greeks(OptionType.PUT))
def test_delta_greeks2(self):
'''
Q:
A commodity option with two years to expiration. The commodity price
is 90, the strike price is 40, the risk-free interest rate is 3% per year,
the cost-of-carry is 9% per year, and the volatility is 20%.
What's the delta of a call option?
A:
delta_call = 1.1273
This implies that the call option price will increase/decrease 1.1273 USD
if the spot price increase/decrease by 1 USD
'''
bsg = BlackScholesGreeks(None,
90,
40,
0.03,
2,
0.2,
cost_of_carry=0.09)
self.assertEqual(1.1273, bsg.get_delta_greeks(OptionType.CALL))
# For every 1 dollar increase/decrease of the spot price, the option price increase/decrease 1.1273
opt_price = BlackScholes(None,
90,
40,
0.03,
2,
0.2,
cost_of_carry=0.09).get_option_price(
OptionType.CALL)
self.assertAlmostEqual(
opt_price + 1.1273,
BlackScholes(None, 91, 40, 0.03, 2, 0.2,
cost_of_carry=0.09).get_option_price(OptionType.CALL),
3)
self.assertEqual(
round(opt_price - 1.1273, 4),
BlackScholes(None, 89, 40, 0.03, 2, 0.2,
cost_of_carry=0.09).get_option_price(OptionType.CALL))
def test_delta_greeks2(self):
'''
Q:
A commodity option with two years to expiration. The commodity price
is 90, the strike price is 40, the risk-free interest rate is 3% per year,
the cost-of-carry is 9% per year, and the volatility is 20%.
What's the delta of a call option?
A:
delta_call = 1.1273
This implies that the call option price will increase/decrease 1.1273 USD
if the spot price increase/decrease by 1 USD
'''
bsg = BlackScholesGreeks(None, 90, 40, 0.03, 2, 0.2, cost_of_carry=0.09)
self.assertEqual(1.1273,
bsg.get_delta_greeks(OptionType.CALL))
# For every 1 dollar increase/decrease of the spot price, the option price increase/decrease 1.1273
opt_price = BlackScholes(None, 90, 40, 0.03, 2, 0.2, cost_of_carry=0.09).get_option_price(OptionType.CALL)
self.assertAlmostEqual(opt_price + 1.1273,
BlackScholes(None, 91, 40, 0.03, 2, 0.2, cost_of_carry=0.09).get_option_price(OptionType.CALL),
3)
self.assertEqual(round(opt_price - 1.1273, 4),
BlackScholes(None, 89, 40, 0.03, 2, 0.2, cost_of_carry=0.09).get_option_price(OptionType.CALL))
plt.show()
'''
fig = plt.figure(figsize=plt.figaspect(0.5))
##### 1st subplot #####
X = np.arange(1, 180, 5) # days to maturity
lenX = len(X)
Y = np.arange(50, 150, 2) # spot price
lenY = len(Y)
X, Y = np.meshgrid(X, Y)
# Spot delta call: X = 100, r = 7%, b = 4%, vol= 30%
Z = [[
BlackScholesGreeks(None,
Y[i][j],
100,
0.07,
X[i][j] / 365.0,
0.3,
cost_of_carry=0.04).get_delta_greeks(
OptionType.CALL) for j in range(lenX)
] for i in range(lenY)]
ax = fig.add_subplot(121, projection='3d')
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet,
linewidth=0) #, antialiased=False)
#ax.plot_wireframe(X, Y, Z) # Draw a wireframe diagram without color
ax.set_zlim(0, 1)
ax.set_xlabel('Days to maturity')
ax.set_ylabel('Asset spot price')
ax.set_zlabel('Delta')
##### 2nd subplot ######
