def BSM_theta(S0, K, T, r, sigma):
''' Black-Scholes-Merton THETA of European call option.
Parameters
==========
S0 : float
stock/index level at time t
K : float
strike price
T : time in year proportion
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
theta : float
European call option THETA
'''
d1 = d1f(S0, K, T, r, sigma)
d2 = d1 - sigma * math.sqrt(T)
theta_year = -(S0 * dN(d1) * sigma /
(2 * math.sqrt(T)) + r * K * math.exp(-r * (T)) * N(d2))
theta = theta_year / 365
return theta
def BSM_vega(S0, K, T, r, sigma):
''' Black-Scholes-Merton VEGA of European call option.
Parameters
==========
S0 : float
stock/index level at time t
K : float
strike price
T : time in year proportion
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
vega : float
European call option VEGA
'''
d1 = d1f(S0, K, T, r, sigma)
vega_full = S0 * dN(d1) * math.sqrt(T)
vega = vega_full / 100
return vega
def BSM_delta(S0, K, T, r, sigma):
''' Black-Scholes-Merton DELTA of European call option.
Parameters
==========
S0 : float
stock/index level at time t
K : float
strike price
T : time in year proportion
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
delta : float
European call option DELTA
'''
d1 = d1f(S0, K, T, r, sigma)
delta = N(d1)
return delta
def BSM_gamma(S0, K, T, r, sigma):
''' Black-Scholes-Merton GAMMA of European call option.
Parameters
==========
S0 : float
stock/index level at time t
K : float
strike price
T : time in year proportion
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
gamma : float
European call option GAMM and PUT GAMMA
'''
d1 = d1f(S0, K, T, r, sigma)
gamma = dN(d1) / (S0 * sigma * math.sqrt(T))
return gamma
def BSM_rho_put(S0, K, T, r, sigma):
''' Black-Scholes-Merton RHO of European call option.
# Parameters
# ==========
# S0 : float
# stock/index level at time t
# K : float
# strike price
# T : time in year proportion
# r : float
# constant, risk-less short rate
# sigma : float
# volatility
#
# Returns
# =======
# rho : float
# European call option RHO
# '''
d1 = d1f(S0, K, T, r, sigma)
d2 = d1 - sigma * math.sqrt(T)
rho = (K * (-T) * math.exp(-r * (T)) * N(-d2)) / 100
return rho