def div_rho_BS(S, K, r, d, v, T, p):
if T <= 0:
return 0
else:
if p == "call":
return K * T * exp(-r * T) * norm_cdf(d_j(2, S, K, r, d, v, T))
elif p == "put":
return -K * T * exp(-r * T) * norm_cdf(-d_j(2, S, K, r, d, v, T))
def div_delta_BS(S, K, r, d, v, T, p):
if T <= 0:
if p == "call":
return max(0, S - K) / max(0.0001, S - K)
elif p == "put":
return -max(0, K - S) / max(0.00001, K - S)
else:
if p == "call":
return norm_cdf(d_j(1, S, K, r, d, v, T))
elif p == "put":
return -norm_cdf(-d_j(1, S, K, r, d, v, T))
def div_theta_BS(S, K, r, d, v, T, p):
if T <= 0:
return 0
else:
if p == "call":
return (S * v * norm_pdf(d_j(1, S, K, r, d, v, T))) / (
2 * T**0.5) - r * K * exp(-r * T) * norm_cdf(
d_j(2, S, K, r, v, T))
elif p == "put":
return -(S * v * norm_pdf(d_j(1, S, K, r, d, v, T))) / (
2 * T**0.5) + r * K * exp(
-r * T) * norm_cdf(-d_j(2, S, K, r, d, v, T))
def div_price_BS(S, K, r, d, v, T, p):
if T <= 0:
if p == "call":
return max(0, S - K)
elif p == "put":
return max(0, K - S)
else:
if p == "call":
return S * exp(-d * T) * norm_cdf(d_j(
1, S, K, r, d, v, T)) - K * exp(-r * T) * norm_cdf(
d_j(2, S, K, r, d, v, T))
elif p == "put":
return -S * exp(
-d * T) * norm_cdf(-d_j(1, S, K, r, d, v, T)) + K * exp(
-r * T) * norm_cdf(-d_j(2, S, K, r, d, v, T))
def vanilla_put_prices(S, K, r, v, T):
return -S * norm_cdf(-d_j(1, S, K, r, v, T)) + \
K*exp(-r*T) * norm_cdf(-d_j(2, S, K, r, v, T))
def vanilla_call_prices(S, K, r, v, T):
return S * norm_cdf(d_j(1, S, K, r, v, T)) - \
K*exp(-r*T) * norm_cdf(d_j(2, S, K, r, v, T))