def BSM_gamma(St, K, t, T, r, sigma):
''' Black-Scholes-Merton GAMMA of European call option.
Parameters
==========
St : float
stock/index level at time t
K : float
strike price
t : float
valuation date
T : float
date of maturity/time-to-maturity if t = 0; T > t
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
gamma : float
European call option GAMM
'''
d1 = d1f(St, K, t, T, r, sigma)
gamma = dN(d1) / (St * sigma * math.sqrt(T - t))
return gamma
def BSM_theta(St, K, t, T, r, sigma):
''' Black-Scholes-Merton THETA of European call option.
Parameters
==========
St : float
stock/index level at time t
K : float
strike price
t : float
valuation date
T : float
date of maturity/time-to-maturity if t = 0; T > t
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
theta : float
European call option THETA
'''
d1 = d1f(St, K, t, T, r, sigma)
d2 = d1 - sigma * math.sqrt(T - t)
theta = -(St * dN(d1) * sigma /
(2 * math.sqrt(T - t)) + r * K * math.exp(-r * (T - t)) * N(d2))
return theta
def BSM_theta(St, K, t, T, r, sigma):
''' Black-Scholes-Merton THETA of European call option.
Parameters
==========
St : float
stock/index level at time t
K : float
strike price
t : float
valuation date
T : float
date of maturity/time-to-maturity if t = 0; T > t
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
theta : float
European call option THETA
'''
d1 = d1f(St, K, t, T, r, sigma)
d2 = d1 - sigma * math.sqrt(T - t)
theta = -(St * dN(d1) * sigma / (2 * math.sqrt(T - t)) +
r * K * math.exp(-r * (T - t)) * N(d2))
return theta
def BSM_gamma(St, K, t, T, r, sigma):
''' Black-Scholes-Merton GAMMA of European call option.
Parameters
==========
St : float
stock/index level at time t
K : float
strike price
t : float
valuation date
T : float
date of maturity/time-to-maturity if t = 0; T > t
r : float
constant, risk-less short rate
sigma : float
volatility
Returns
=======
gamma : float
European call option GAMM
'''
d1 = d1f(St, K, t, T, r, sigma)
gamma = dN(d1) / (St * sigma * math.sqrt(T - t))
return gamma
def BSM_vega(St, K, t, T, r, sigma):
d1 = dlf(St, K, t, T, r, sigma)
vega = St * dN(d1) * math.sqrt(T - t)
return vega
def BSM_theta(St, K, t, T, r, sigma):
d1= dlf(St, K, t, T, r, sigma)
d2 = d1 - sigma * math.sqrt(T - t)
theta = -(St * dN(d1) * sigma / (2 * math.sqrt(T-t)) + r * K * math.exp(-r * (T - t) * N(d2)))
return theta
def BSM_gamma(St, K, t, T, r, sigma):
gamma = dN(d1) / (St * sigma * math.sqrt(T - t))
return gamma
