def option_price(strike, vola, forward, r_counter, tau, is_call) \
-> Union[float, np.ndarray]:
"""Compute the Black-Scholes option price.
Vectorized for `strike` and `vola` to return output of the same
dimension as (strike * vola): e.g. if strike.shape == (1, 4) and
vola.shape == (2, 1), res.dim == (2, 4)
Parameters
----------
strike : float or numpy.ndarray
strikes prices
vola : float or numpy.ndarray
volatility, in (frac of 1) p.a.
forward : float
forward price of the underlying
r_counter : float
risk-free rate in the counter currency (continuously comp), in frac.
of 1 p.a.
tau : float
maturity, in years
is_call : bool or np.ndarray
True (False) to return prices of call (put) options
Returns
-------
res : float or numpy.ndarray
price, in domestic currency
"""
# +1 for call, -1 for put
omega = is_call * 2 - 1.0
res = omega * np.exp(-r_counter * tau) * (
forward * fast_norm_cdf(omega * d1(forward, strike, vola, tau)) -
strike * fast_norm_cdf(omega * d2(forward, strike, vola, tau)))
return res
def delta_pips_forward(forward, strike, vola, tau, is_call):
omega = is_call * 2 - 1
res = omega * fast_norm_cdf(omega * d1(forward, strike, vola, tau))
return res
def delta_premiumadj_spot(forward, spot, strike, vola, r_counter, tau,
is_call):
omega = is_call * 2 - 1
res = omega * np.exp(-r_counter * tau) * strike / spot * \
fast_norm_cdf(omega * d2(forward, strike, vola, tau))
return res
def delta_pips_spot(forward, strike, vola, r_base, tau, is_call):
omega = is_call * 2 - 1
res = omega * np.exp(-r_base * tau) * \
fast_norm_cdf(omega * d1(forward, strike, vola, tau))
return res
def delta_premiumadj_forward(forward, strike, vola, tau, is_call):
omega = is_call * 2 - 1
res = omega * strike / forward * \
fast_norm_cdf(omega * d2(forward, strike, vola, tau))
return res