def calculate_weight(underlying, mtr, ATM_vol, K, K1, K2, K3):
b_s = BlackScholes(underlying, 0, 0, mtr)
vega_K = b_s.BS_vega(K, ATM_vol)
vega_K_1 = b_s.BS_vega(K1, ATM_vol)
vega_K_2 = b_s.BS_vega(K2, ATM_vol)
vega_K_3 = b_s.BS_vega(K3, ATM_vol)
weight_1 = (vega_K * np.log(K2 / K) * np.log(K3 / K)) / (vega_K_1 * np.log(K2 / K1) * np.log(K3 / K1))
weight_2 = (vega_K * np.log(K / K1) * np.log(K3 / K)) / (vega_K_2 * np.log(K2 / K1) * np.log(K3 / K2))
weight_3 = (vega_K * np.log(K / K1) * np.log(K / K2)) / (vega_K_3 * np.log(K3 / K1) * np.log(K3 / K2))
return [weight_1, weight_2, weight_3]
def SABR_vega(f, t, k, alpha, beta, rho, volvol):
b_s = BlackScholes(f, 0, 0, t)
atm_vol = ATM_vol(f, t, alpha, beta, rho, volvol)
strike_vol = 100 * lognormal_vol(k, f, t, alpha, beta, rho, volvol)
bs_vega = b_s.BS_vega(k, strike_vol)
vega = bs_vega * strike_vol / atm_vol
return vega
def SABR_delta_2(f, t, k, CallPut, alpha, beta, rho, volvol):
f2 = f * 1.01
b_s = BlackScholes(f, 0, 0, t)
SABR_vol = lognormal_vol(k, f, t, alpha, beta, rho, volvol) * 100
SABR_vol_shift = lognormal_vol(k, f2, t, alpha, beta, rho, volvol) * 100
bs_delta = b_s.BS_delta(k, SABR_vol, CallPut)
bs_vega = b_s.BS_vega(k, SABR_vol)
delta = bs_delta + bs_vega * (SABR_vol_shift - SABR_vol) / (f2 - f)
return delta
def SABR_delta_3(f, t, k, CallPut, alpha, beta, rho, volvol):
f2 = f * 1.01
b_s = BlackScholes(f, 0, 0, t)
SABR_vol = lognormal_vol(k, f, t, alpha, beta, rho, volvol) * 100
SABR_vol_shift = lognormal_vol(k, f2, t, alpha, beta, rho, volvol) * 100
bs_delta = b_s.BS_delta(k, SABR_vol, CallPut)
bs_vega = b_s.BS_vega(k, SABR_vol)
SABR_vol_alpha_shift = lognormal_vol(k, f, t, alpha * 1.01, beta, rho,
volvol) * 100
alpha_deri = (SABR_vol - SABR_vol_alpha_shift) / (alpha - 1.01 * alpha)
delta = bs_delta + bs_vega * ((SABR_vol_shift - SABR_vol) /
(f2 - f) + alpha_deri * (rho * volvol /
(f**beta)))
return delta
def get_greeks(row, greek):
b_s = BlackScholes(row['underlying_price'], 0, 0, row['mtr'])
if greek == 'gamma':
result = b_s.BS_gamma(row['Strike'], row['m_mid_vol'])
elif greek == 'theta':
result = b_s.BS_theta(row['Strike'], row['m_mid_vol'], row['CallPut'])
elif greek == 'vega':
result = b_s.BS_vega(row['Strike'], row['m_mid_vol'])
elif greek == 'delta':
result = b_s.BS_delta(row['Strike'], row['m_mid_vol'], row['CallPut'])
elif greek == 'vanna':
result = b_s.BS_vanna(row['Strike'], row['m_mid_vol'])
elif greek == 'volga':
result = b_s.BS_volga(row['Strike'], row['m_mid_vol'])
elif greek == 'gamma_deri':
result = b_s.BS_gamma_deri(row['Strike'], row['m_mid_vol'])
return result