def bear_test():
'''
test the vaild of bull test: the class bull
input paramter:
short_Call： p=5.39 k=45 maturity=30 European
long_Call: p=0.45 k=55 maturity=30 European
output parameter:
if S=35
then portfolio.value_at_maturity()=4.69
if S=65
then portfolio.value_at_maturity()=-0.31
'''
import matplotlib.pyplot as plt
short = option.Call(5.39, 45, 30, 'E')
long = option.Call(0.45, 55, 30, 'E')
portfolio = bear.bear(short, long, 'C')
print('S=35:', portfolio.value_at_maturity(35))
print('S=65:', portfolio.value_at_maturity(65))
plt.figure('Call Bear')
portfolio.plot_value_at_maturity()
'''
test the vaild of bull test: the class bull
input paramter:
short_Put： p=0.02 k=40 maturity=30 European
long_Put: p=9.96 k=60 maturity=30 European
output parameter:
if S=35
then portfolio.value_at_maturity()=10.06
if S=65
then portfolio.value_at_maturity()=-9.94
'''
short = option.Put(0.02, 40, 1 / 12, 'E')
long = option.Put(9.96, 60, 1 / 12, 'E')
portfolio = bear.bear(short, long, 'P')
print('S=35:', portfolio.value_at_maturity(35))
print('S=65:', portfolio.value_at_maturity(65))
plt.figure('Put Bear')
portfolio.plot_value_at_maturity()
'''
plot the probability of spot price at maturity
Y axis: pdf(normed(log(ST/S0)))
X axis: S
'''
plt.figure('probability')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3))
'''
Calculate the expected return follow the formula
sum{return(i)*prob(i)*interval(i)}
test validity
if S0=80
then expected return is around -9.90
if S0=35
then expected return is around 10.00
'''
print('expected_profit:', portfolio.expectated_profit(35, 0.1, 0.3))
print('expected_profit:', portfolio.expectated_profit(80, 0.1, 0.3))
def diagonal_spreads_test():
'''
test the validity of diagonal_spreads.
input parameter:
short_early_Call_k1: p=0.34 k=50 maturity=30/360 European
long_late_Call_k2：p=0.51 k=55 maturity=93/360 European
mu=0.1
sigma=33.33%
q=0
r=0.015
output parameters:
if S=50
then portfolio.value_at_maturity()=0.93
if S=60
then portfolio.value_at_maturity()=-3.76
if S=35
then portfolio.value_at_maturity()=around -0.20
if S=51.35
then portfolio.value_at_maturity()=0
if S=44.04
then portfolio.value_at_maturity()=0
'''
import matplotlib.pyplot as plt
short_early_Call_k1 = option.Call(0.34, 50, 30 / 360, 'E')
long_late_Call_k2 = option.Call(0.51, 55, 93 / 360, 'E')
portfolio = diagonal_spreads.diagonal_spreads(short_early_Call_k1,
long_late_Call_k2, 'C', 'P',
'bear')
print('S=50:', portfolio.value_at_maturity(50, 0.015, 0.3333, 0))
print('S=60:', portfolio.value_at_maturity(60, 0.015, 0.3333, 0))
print('S=35:', portfolio.value_at_maturity(35, 0.015, 0.3333, 0))
print('S=51.35:', portfolio.value_at_maturity(51.35, 0.015, 0.3333, 0))
print('S=44.04:', portfolio.value_at_maturity(44.04, 0.015, 0.3333, 0))
plt.figure('Profit_diagonal_spreads')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.grid()
plt.figure('probability_diagonal_spreads')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
def calendar_option_test():
'''
test the vaild of calendar_option : the class calendar_option
input paramter:
short_early_Call：p=1.98 k=50 maturity=30/360 European
long_late_Call: p=2.91 k=50 maturity=65/360 European
mu=0.1
sigma=33.33%
q=0
r=0.015
output parameter:
if S=50
then portfolio.value_at_maturity()=1.17
if S=40
then portfolio.value_at_maturity()=-0.90
if S=47.19
then portfolio.value_at_maturity()=0
if S=53.35
then portfolio.value_at_maturity()=0
if S=60
then portfolio.value_at_maturity()=around -0.5
'''
import matplotlib.pyplot as plt
short_early_Call = option.Call(1.98, 50, 30 / 360, 'E')
long_late_Call = option.Call(2.91, 50, 65 / 360, 'E')
portfolio = calendar_option.calendar_option(short_early_Call,
long_late_Call, 'P')
print('S=50:', portfolio.value_at_maturity(50, 0.015, 0.3333, 0))
print('S=40:', portfolio.value_at_maturity(40, 0.015, 0.3333, 0))
print('S=47.19:', portfolio.value_at_maturity(47.19, 0.015, 0.3333, 0))
print('S=53.35:', portfolio.value_at_maturity(53.35, 0.015, 0.3333, 0))
print('S=60:', portfolio.value_at_maturity(60, 0.015, 0.3333, 0))
plt.figure('Profit')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.figure('probability')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
'''
def option_compound_test():
import matplotlib.pyplot as plt
'''
input parameters:
spread1:
Call_Positive bear spread
short_early_call_k1: p=0.45, k1=55, t=30/360
long_late_call_k2: p=0.38, k2=60, t=65/360
spread2:
Put_Positive bull spread
long_late_put_k1: p=0.85, k1=45, t=65/360
short_early_put_k2: p=1.89, k2=50, t=30/360
output parameters:
if S=50
then portfolio.value_at_maturity()=1.54
if S=60
then portfolio.value_at_maturity()=-3.28
if S=43.51
then portfolio.value_at_maturity()=0
if S=52.06
then portfolio.value_at_maturity()=0
'''
short_early_Call_k1 = option.Call(1.98, 50, 30 / 360, 'E')
long_late_Call_k2 = option.Call(1.16, 55, 65 / 360, 'E')
long_late_put_k1 = option.Put(0.15, 40, 65 / 360, 'E')
short_early_put_k2 = option.Put(0.31, 45, 30 / 360, 'E')
option_list_short = [short_early_Call_k1, short_early_put_k2]
option_list_long = [long_late_Call_k2, long_late_put_k1]
portfolio = option_compound.option_compound(option_list_short,
option_list_long)
print('S=50:', portfolio.value_at_maturity(50, 0.015, 0.3333, 0))
print('S=60:', portfolio.value_at_maturity(60, 0.015, 0.3333, 0))
print('S=43.51:', portfolio.value_at_maturity(43.51, 0.015, 0.3333, 0))
print('S=52.06:', portfolio.value_at_maturity(52.06, 0.015, 0.3333, 0))
plt.figure('Profit_double_spreads with positive bear')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.grid()
plt.figure('probability_double_spreads with positive bear')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
'''
input parameter:
call: p=0.45 k=55 maturity=30/360 European
put：p=0.31 k=45 maturity=30/360 European
mu=0.1
sigma=33.33%
q=0
r=0.015
output parameters:
if S=50
then portfolio.value_at_maturity()=-0.76
if S=65
then portfolio.value_at_maturity()=9.42
if S=44.24
then portfolio.value_at_maturity()=0
if S=55.76
then portfolio.value_at_maturity()=0
'''
call = option.Call(0.45, 55, 30 / 360, 'E')
put = option.Put(0.31, 45, 30 / 360, 'E')
option_list_short = []
option_list_long = [call, put]
portfolio = option_compound.option_compound(option_list_short,
option_list_long)
print('S=50:', portfolio.value_at_maturity(50, 0.015, 0.3333, 0))
print('S=65:', portfolio.value_at_maturity(65, 0.015, 0.3333, 0))
print('S=44.24:', portfolio.value_at_maturity(44.24, 0.015, 0.3333, 0))
print('S=55.76:', portfolio.value_at_maturity(55.76, 0.015, 0.3333, 0))
plt.figure('Profit_strangle')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.grid()
plt.figure('probability_strangle')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
def straddle_test():
'''
test the validity of diagonal_spreads.
input parameter:
call: p=1.98 k=50 maturity=30/360 European
put：p=1.89 k=50 maturity=30/360 European
mu=0.1
sigma=33.33%
q=0
r=0.015
output parameters:
if S=50
then portfolio.value_at_maturity()=-3.87
if S=60
then portfolio.value_at_maturity()=6.32
if S=46.13
then portfolio.value_at_maturity()=0
if S=53.87
then portfolio.value_at_maturity()=0
'''
import matplotlib.pyplot as plt
call = option.Call(1.98, 50, 30 / 360, 'E')
put = option.Put(1.89, 50, 30 / 360, 'E')
portfolio = straddle.straddle(call, put)
print('S=50:', portfolio.value_at_maturity(50))
print('S=60:', portfolio.value_at_maturity(60))
print('S=46.13:', portfolio.value_at_maturity(46.13))
print('S=53.87:', portfolio.value_at_maturity(53.87))
plt.figure('Profit')
portfolio.plot_value_at_maturity()
plt.grid()
plt.figure('probability')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:', portfolio.expectated_profit(40, 0.1, 0.3333))
print('expected_profit:', portfolio.expectated_profit(50, 0.1, 0.3333))
print('expected_profit:', portfolio.expectated_profit(60, 0.1, 0.3333))
'''
input parameter:
call: p=0.45 k=55 maturity=30/360 European
put：p=0.31 k=45 maturity=30/360 European
mu=0.1
sigma=33.33%
q=0
r=0.015
output parameters:
if S=50
then portfolio.value_at_maturity()=-0.76
if S=65
then portfolio.value_at_maturity()=9.42
if S=44.24
then portfolio.value_at_maturity()=0
if S=55.76
then portfolio.value_at_maturity()=0
'''
call = option.Call(0.45, 55, 30 / 360, 'E')
put = option.Put(0.31, 45, 30 / 360, 'E')
portfolio = straddle.straddle(call, put)
print('S=50:', portfolio.value_at_maturity(50))
print('S=65:', portfolio.value_at_maturity(65))
print('S=44.24:', portfolio.value_at_maturity(44.24))
print('S=55.76:', portfolio.value_at_maturity(55.76))
plt.figure('Profit_strangle')
portfolio.plot_value_at_maturity()
plt.grid()
plt.figure('probability_strangle')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:', portfolio.expectated_profit(40, 0.1, 0.3333))
print('expected_profit:', portfolio.expectated_profit(50, 0.1, 0.3333))
print('expected_profit:', portfolio.expectated_profit(60, 0.1, 0.3333))
def double_diagonal_test():
import matplotlib.pyplot as plt
'''
input parameters:
spread1:
Call_Positive_bear spread
short_early_call_k1: p=0.45, k1=55, t=30/360
long_late_call_k2: p=0.38, k2=60, t=65/360
spread2:
Put_Positive_bull spread
long_late_Put_k1: p=0.15, k1=40, t=65/360
short_early_Put_k2: p=0.31, k2=45, t=30/360
output parameters:
if S=45
then portfolio.value_at_maturity()=around 0.50
if S=55
then portfolio.value_at_maturity()=0.91
if S=44.43
then portfolio.value_at_maturity()=0
if S=56.22
then portfolio.value_at_maturity()=0
if S=40
then portfolio.value_at_maturity()=-3.16
if S=60
then portfolio.value_at_maturity()=around -2.10
'''
short_early_Call_k1 = option.Call(0.45, 55, 30 / 360, 'E')
long_late_Call_k2 = option.Call(0.38, 60, 65 / 360, 'E')
long_late_Put_k1 = option.Put(0.15, 40, 65 / 360, 'E')
short_early_Put_k2 = option.Put(0.31, 45, 30 / 360, 'E')
spread1 = diagonal_spreads.diagonal_spreads(short_early_Call_k1,
long_late_Call_k2, 'C', 'P',
'bear')
spread2 = diagonal_spreads.diagonal_spreads(long_late_Put_k1,
short_early_Put_k2, 'P', 'P',
'bull')
portfolio = diagonal_spreads.double_diagonal(spread1, spread2)
print('S=45:', portfolio.value_at_maturity(45, 0.015, 0.3333, 0))
print('S=55:', portfolio.value_at_maturity(55, 0.015, 0.3333, 0))
print('S=44.43:', portfolio.value_at_maturity(44.43, 0.015, 0.3333, 0))
print('S=56.22:', portfolio.value_at_maturity(56.22, 0.015, 0.3333, 0))
print('S=40:', portfolio.value_at_maturity(40, 0.015, 0.3333, 0))
print('S=60:', portfolio.value_at_maturity(60, 0.015, 0.3333, 0))
plt.figure('Profit_double_spreads')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.grid()
plt.figure('probability_double_spreads')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
'''
input parameters:
spread1:
Call_Positive_bear spread
short_early_call_k1: p=0.45, k1=55, t=30/360
long_late_call_k2: p=0.38, k2=60, t=65/360
spread2:
Put_Positive_bull spread
long_late_Put_k1: p=0.15, k1=40, t=65/360
short_early_Put_k2: p=0.31, k2=45, t=30/360
output parameters:
if S=50
then portfolio.value_at_maturity()=2.77
if S=40
then portfolio.value_at_maturity()=-2.94
if S=60
then portfolio.value_at_maturity()=-2.25
if S=46.95
then portfolio.value_at_maturity()=0
if S=53.59
then portfolio.value_at_maturity()=0
'''
short_early_Call_k1 = option.Call(1.98, 50, 30 / 360, 'E')
long_late_Call_k2 = option.Call(1.16, 55, 65 / 360, 'E')
long_late_Put_k1 = option.Put(0.85, 45, 65 / 360, 'E')
short_early_Put_k2 = option.Put(1.89, 50, 30 / 360, 'E')
spread1 = diagonal_spreads.diagonal_spreads(short_early_Call_k1,
long_late_Call_k2, 'C', 'P',
'bear')
spread2 = diagonal_spreads.diagonal_spreads(long_late_Put_k1,
short_early_Put_k2, 'P', 'P',
'bull')
portfolio = diagonal_spreads.double_diagonal(spread1, spread2)
print('S=50:', portfolio.value_at_maturity(50, 0.015, 0.3333, 0))
print('S=40:', portfolio.value_at_maturity(40, 0.015, 0.3333, 0))
print('S=60:', portfolio.value_at_maturity(60, 0.015, 0.3333, 0))
print('S=46.95:', portfolio.value_at_maturity(46.95, 0.015, 0.3333, 0))
print('S=53.59:', portfolio.value_at_maturity(53.59, 0.015, 0.3333, 0))
plt.figure('Profit_double_spreads with same strikes')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.grid()
plt.figure('probability_double_spreads with same strikes')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
'''
input parameters:
spread1:
Call_Positive bear spread
short_early_call_k1: p=0.45, k1=55, t=30/360
long_late_call_k2: p=0.38, k2=60, t=65/360
spread2:
Put_Positive bull spread
long_late_put_k1: p=0.85, k1=45, t=65/360
short_early_put_k2: p=1.89, k2=50, t=30/360
output parameters:
if S=55
then portfolio.value_at_maturity()=1.84
if S=40
then portfolio.value_at_maturity()=-3.69
if S=48.14
then portfolio.value_at_maturity()=0
if S=57.55
then portfolio.value_at_maturity()=0
'''
short_early_Call_k1 = option.Call(0.45, 55, 30 / 360, 'E')
long_late_Call_k2 = option.Call(0.38, 60, 65 / 360, 'E')
long_late_put_k1 = option.Put(0.85, 45, 65 / 360, 'E')
short_early_put_k2 = option.Put(1.89, 50, 30 / 360, 'E')
spread1 = diagonal_spreads.diagonal_spreads(short_early_Call_k1,
long_late_Call_k2, 'C', 'P',
'bear')
spread2 = diagonal_spreads.diagonal_spreads(long_late_put_k1,
short_early_put_k2, 'P', 'P',
'bull')
portfolio = diagonal_spreads.double_diagonal(spread1, spread2)
print('S=55:', portfolio.value_at_maturity(55, 0.015, 0.3333, 0))
print('S=40:', portfolio.value_at_maturity(40, 0.015, 0.3333, 0))
print('S=48.14:', portfolio.value_at_maturity(48.14, 0.015, 0.3333, 0))
print('S=57.55:', portfolio.value_at_maturity(57.55, 0.015, 0.3333, 0))
plt.figure('Profit_double_spreads with positive bull')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.grid()
plt.figure('probability_double_spreads with positive bull')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
'''
input parameters:
spread1:
Call_Positive bear spread
short_early_call_k1: p=0.45, k1=55, t=30/360
long_late_call_k2: p=0.38, k2=60, t=65/360
spread2:
Put_Positive bull spread
long_late_put_k1: p=0.85, k1=45, t=65/360
short_early_put_k2: p=1.89, k2=50, t=30/360
output parameters:
if S=50
then portfolio.value_at_maturity()=1.54
if S=60
then portfolio.value_at_maturity()=-3.28
if S=43.51
then portfolio.value_at_maturity()=0
if S=52.06
then portfolio.value_at_maturity()=0
'''
short_early_Call_k1 = option.Call(1.98, 50, 30 / 360, 'E')
long_late_Call_k2 = option.Call(1.16, 55, 65 / 360, 'E')
long_late_put_k1 = option.Put(0.15, 40, 65 / 360, 'E')
short_early_put_k2 = option.Put(0.31, 45, 30 / 360, 'E')
spread1 = diagonal_spreads.diagonal_spreads(short_early_Call_k1,
long_late_Call_k2, 'C', 'P',
'bear')
spread2 = diagonal_spreads.diagonal_spreads(long_late_put_k1,
short_early_put_k2, 'P', 'P',
'bull')
portfolio = diagonal_spreads.double_diagonal(spread1, spread2)
print('S=50:', portfolio.value_at_maturity(50, 0.015, 0.3333, 0))
print('S=60:', portfolio.value_at_maturity(60, 0.015, 0.3333, 0))
print('S=43.51:', portfolio.value_at_maturity(43.51, 0.015, 0.3333, 0))
print('S=52.06:', portfolio.value_at_maturity(52.06, 0.015, 0.3333, 0))
plt.figure('Profit_double_spreads with positive bear')
portfolio.plot_value_at_maturity(0.015, 0.3333, 0)
plt.grid()
plt.figure('probability_double_spreads with positive bear')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3333))
plt.grid()
print('expected_profit:',
portfolio.expectated_profit(40, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(50, 0.1, 0.3333, 0.015, 0))
print('expected_profit:',
portfolio.expectated_profit(60, 0.1, 0.3333, 0.015, 0))
def butterfly_test():
'''
test the vaild of bull test: the class bull
input paramter:
short_Call_1： p=1.98 k=50 maturity=30 European
short_Call_2: p=1.98 k=50 maturity=30 European
long_Call_1: p=0.45 k=55 maturity=30 European
long_Call_2: p=5.39 k=45 maturity=30 European
output parameter:
if S=40
then portfolio.value_at_maturity()=-1.88
if S=60
then portfolio.value_at_maturity()=-1.88
if S=50
then portfolio.value_at_maturity()=3.12
if S=46.88
then portfolio.value_at_maturity()=0
if S=53.12
then portfolio.value_at_maturity()=0
'''
import matplotlib.pyplot as plt
short_1 = option.Call(1.98, 50, 30, 'E')
short_2 = option.Call(1.98, 50, 30, 'E')
long_1 = option.Call(0.45, 55, 30, 'E')
long_2 = option.Call(5.39, 45, 30, 'E')
portfolio = butterfly.butterfly(short_1, short_2, long_1, long_2, 'C')
print('S=40:', portfolio.value_at_maturity(40))
print('S=60:', portfolio.value_at_maturity(60))
print('S=50:', portfolio.value_at_maturity(50))
print('S=46.88:', portfolio.value_at_maturity(46.88))
print('S=53.12:', portfolio.value_at_maturity(53.12))
plt.figure('Call Butterfly')
portfolio.plot_value_at_maturity()
'''
test the vaild of bull test: the class bull
input paramter:
short_Put： p=0.02 k=40 maturity=30 European
long_Put: p=9.96 k=60 maturity=30 European
output parameter:
if S=40
then portfolio.value_at_maturity()=-18.9
if S=60
then portfolio.value_at_maturity()=-18.9
if S=50
then portfolio_value_at_maturity()=3.11
if S=46.89
then portfolio_value_at_maturity()=0
if S=53.11
then portfolio_value_at_maturity()=0
'''
short_1 = option.Put(1.89, 50, 1 / 12, 'E')
short_2 = option.Put(1.89, 50, 1 / 12, 'E')
long_1 = option.Put(5.36, 55, 1 / 12, 'E')
long_2 = option.Put(0.31, 45, 1 / 12, 'E')
portfolio = butterfly.butterfly(short_1, short_2, long_1, long_2, 'P')
print('S=40:', portfolio.value_at_maturity(40))
print('S=60:', portfolio.value_at_maturity(60))
print('S=50:', portfolio.value_at_maturity(50))
print('S=46.89:', portfolio.value_at_maturity(46.89))
print('S=53.11:', portfolio.value_at_maturity(53.11))
plt.figure('Put Butterfly')
portfolio.plot_value_at_maturity()
'''
plot the probability of spot price at maturity
Y axis: pdf(normed(log(ST/S0)))
X axis: S
'''
plt.figure('probability')
plt.plot(portfolio.S, portfolio.prob_value_at_maturity(50, 0.1, 0.3))
'''
Calculate the expected return follow the formula
sum{return(i)*prob(i)*interval(i)}
test validity
if S0=80
then expected return is around -9.90
if S0=35
then expected return is around 10.00
'''
print('expected_profit:', portfolio.expectated_profit(40, 0.1, 0.3))
print('expected_profit:', portfolio.expectated_profit(50, 0.1, 0.3))
print('expected_profit:', portfolio.expectated_profit(60, 0.1, 0.3))