def test_prices(self):
while self.tdi.has_next():
row = self.tdi.next_row()
S, K, t, r, sigma = row['S'], row['K'], row['t'], row['R'], row[
'v']
self.assertTrue(
almost_equal(black_scholes('c', S, K, t, r, sigma),
row['bs_call'],
epsilon=.000001))
self.assertTrue(
almost_equal(black_scholes('p', S, K, t, r, sigma),
row['bs_put'],
epsilon=.000001))
def test_implied_volatility(self):
while self.tdi.has_next():
row = self.tdi.next_row()
S,K,t,r,sigma = row['S'],row['K'],row['t'],row['R'],row['v']
C,P = black_scholes('c', S, K, t, r, sigma), black_scholes('p', S, K, t, r, sigma)
try:
iv = implied_volatility(C, S, K, t, r, 'c')
self.assertTrue(almost_equal(sigma, iv, epsilon = .0001))
except:
print 'could not calculate iv for ', C, S, K, t, r, 'c'
iv = implied_volatility(P, S, K, t, r, 'p')
self.assertTrue(almost_equal(sigma, iv, epsilon = .001) or (iv ==0.0))
def test_prices(self):
while self.tdi.has_next():
row = self.tdi.next_row()
S,K,t,r,sigma = row['S'],row['K'],row['t'],row['R'],row['v']
self.assertTrue(
almost_equal(
black_scholes('c', S, K, t, r, sigma), row['bs_call'], epsilon=.000001
)
)
self.assertTrue(
almost_equal(
black_scholes('p', S, K, t, r, sigma), row['bs_put'], epsilon=.000001
)
)
def plot_numerical_vs_analytical(greek, flag):
"""Displays a plot comparing analytically and numerically
computed values of a given greek and option type.
:param flag: 'd','g','t','r', or 'v'
:type flag: str
:param flag: 'c' or 'p' for call or put.
:type flag: str
"""
f_analytical, f_numerical = {
'd':(delta,ndelta),
'g':(gamma,ngamma),
't':(theta,ntheta),
'v':(vega,nvega),
'r':(rho, nrho),
}[greek]
S_vals = numpy.linspace(10,250,2000)
K=100
t =.5
q =.05
sigma = 0.2
r = .01
price, analytical, numerical = [],[],[]
for S in S_vals:
analytical.append(f_analytical(flag, S, K, t, r, sigma))
numerical.append(f_numerical(flag, S, K, t, r, sigma))
price.append(black_scholes(flag, S, K, t, r, sigma))
plt.figure(1)
plt.subplot(211)
plt.plot(S_vals,analytical,label = 'Analytical')
plt.plot(S_vals,numerical, label = 'Numerical')
min_a, max_a = min(analytical), max(analytical)
h = max_a-min_a
plt.ylim(min_a - h*.05, max_a + h*.05)
plt.grid()
plt.legend(loc = 'best')
plt.subplot(212)
plt.plot(S_vals,price, label = 'Price')
plt.ylim(min(min(price),-10), max(max(price),10))
plt.grid()
plt.legend(loc = 'best')
plt.show()
#plot_numerical_vs_analytical('t','c')
def recalc(self,Scenario):
global r
S=self.underlying*(1+Scenario.fut/100.0)
t=(self.expiry-(self.valdate+dt.timedelta(days=Scenario.expiry_delta))).total_seconds()/(365.0*24*60*60)
sigma=self.vol+Scenario.vol/100.0
self.scenario_price=black_scholes(self.flag, S, self.strike, t, r, sigma)
self.PnL=100*(self.scenario_price-self.price)/self.price
return PnL(S,sigma,self.PnL)
def test_implied_volatility(self):
while self.tdi.has_next():
row = self.tdi.next_row()
S, K, t, r, sigma = row['S'], row['K'], row['t'], row['R'], row[
'v']
C, P = black_scholes('c', S, K, t, r,
sigma), black_scholes('p', S, K, t, r, sigma)
try:
iv = implied_volatility(C, S, K, t, r, 'c')
self.assertTrue(almost_equal(sigma, iv, epsilon=.0001))
except:
print('could not calculate iv for ', C, S, K, t, r, 'c')
iv = implied_volatility(P, S, K, t, r, 'p')
self.assertTrue(
almost_equal(sigma, iv, epsilon=.001) or (iv == 0.0))
def test_prices(self):
S = 100.0
for flag in ['c','p']:
for K in numpy.linspace(20,200,10):
for r in numpy.linspace(0,0.2,10):
for sigma in numpy.linspace(0.1,0.5,10):
for t in numpy.linspace(0.01,2,10):
for i in range(5):
val1 = black_scholes(flag, S, K, t, r, sigma)
val2 = python_black_scholes(flag, S, K, t, r, sigma)
results_match = abs(val1-val2)<epsilon
if not results_match:
print 'price mismatch:', flag, val1, val2
self.assertTrue(results_match)
def theoreticalPricer(algo_client):
calls = []
puts = []
given_strikes = [233500, 234000, 234500, 235000, 235500]
strikes = [
"C2335", "P2335", "C2340", "P2340", "C2345", "P2345", "C2350", "P2350",
"C2355", "P2355"
]
interest = .01
time_to_expiry = float(60 / 252)
greeks = Greeks(algo_client, "ESM7", given_strikes, .01, .24)
iv = greeks.return_implied_vol()
for x in xrange(1, 3):
calls.append(iv[given_strikes[x - 1]][0])
puts.append(iv[given_strikes[x - 1]][1])
theoreticalPrice = {}
x = 0
while x < 5:
theoreticalPrice[strikes[x]] = b_s.black_scholes(
'c', 9830, given_strikes[x / 2], .24, .01, calls[x / 2])
theoreticalPrice[strikes[x + 1]] = b_s.black_scholes(
'p', 9830.5, given_strikes[x / 2], .24, .01, puts[x / 2])
x += 2
return theoreticalPrice
def test_prices(self):
S = 100.0
for flag in ['c','p']:
for K in numpy.linspace(20,200,10):
for r in numpy.linspace(0,0.2,10):
for sigma in numpy.linspace(0.1,0.5,10):
for t in numpy.linspace(0.01,2,10):
for i in range(5):
val1 = black_scholes(flag, S, K, t, r, sigma)
val2 = python_black_scholes(flag, S, K, t, r, sigma)
results_match = abs(val1-val2)<epsilon
if not results_match:
print 'price mismatch:', flag, val1, val2
self.assertTrue(results_match)
def plot(self, x_vector, date, r, iv):
'''
Creates a risk graph for the calendar spread
inputs:
x_vector -> vector of underlying prices where Black-Scholes must
be calculated
date -> date to be plotted
r -> interest rate on a 3-month U.S. Treasury bill or similar
iv -> implied volatility of the underlying
returns:
y -> Black-Scholes solution to given x_vector and parameters
'''
y = np.zeros(len(x_vector))
# Create the discrete values of P/L to plot against xrange
for opt in self.options_list:
t = (opt.expiration - date).days / 365.
y += np.array([opt.multiplier * opt.amount * (bs.black_scholes(
opt.right, x, opt.strike, t, r, iv) -
opt.get_debit()) for x in x_vector])
return y
def corp1(ss, k1, k2, r, T, vol, callput):
return k1-bls.black_scholes(callput, ss, k2, T, r, vol)
def vol_lib(x_vector, K, r, t, iv):
return [vol_bs.black_scholes('c', x, K, t, r, iv) for x in x_vector]
def bs_price(cp_flag,S,K,T,v,r,q=0.0):
price = black_scholes(cp_flag, S, K, T, r, v)
return price
def function_to_minimize(sigma):
return price - black_scholes(flag, S, K, t, r, sigma)
def function_to_minimize(sigma):
return price - black_scholes(flag, S, K, t, r, sigma)
def optPrice(curVol, price, S0, T):
return (price-bls.black_scholes('c', S0, K, T, r, curVol))
def plot_risk_graph(options_list,
t_list,
risk_free_rate,
iv,
show_plot=False,
save_png=False):
'''
Creates a risk graph for the combination of options provided
in the input list of options for the different times to
expiration provided
inputs:
options_list -> list of options composing the strategy. It is important
to provide this list ordered by near-term expiries first
t_list -> dates to be plotted (in datetime)
risk_free_rate -> interest rate on a 3-month U.S. Treasury bill or similar
iv -> implied volatility of underlying
show_plot -> determines if the plot is shown in a window (default False)
save_png -> determines if the plot is saved as a PNG file (default False)
returns:
list of tuples (x, (datetime, y))
'''
# First get the graph bounds, 10% apart from the min and max
# strikes
min_strike = None
max_strike = None
for opt in options_list:
if (min_strike is None) or (opt.strike < min_strike):
min_strike = opt.strike
if (max_strike is None) or (opt.strike > max_strike):
max_strike = opt.strike
# Prices
x_vector = np.linspace(min_strike * 0.7, max_strike * 1.3, 500)
# Now plot the risk graph for the different time values provided
return_values = []
y = []
for t in t_list:
y.append(np.zeros(len(x_vector)))
# Create the discrete values of P/L to plot against xrange
for opt in options_list:
t_exp = (opt.expiration - t).days / 365.
y[-1] += np.array([
opt.multiplier * opt.amount *
(bs.black_scholes(opt.right, x, opt.strike, t_exp,
risk_free_rate, iv / 100.) - opt.get_debit())
for x in x_vector
])
# Get the number of days to expiration from today for plot's legend
days_to_expire = (options_list[0].expiration - t).days
plt.plot(x_vector, y[-1], label='t: ' + str(days_to_expire))
return_values.append((t, y[-1]))
plt.legend()
plt.xlabel('Price')
plt.ylabel('P/L')
# Save the plot as a PNG if required, or show plot in a window
if save_png:
plt.savefig(datetime.today().strftime('%d%b%y ') + '.png')
else:
# Show the plot
plt.show()
# Return the values calculated TODO for what? to calculate breakevens?
return (x_vector, return_values)