mafipy.function.black_scholes_call_theta

mafipy.function.black_scholes_call_theta(underlying, strike, rate, maturity, vol, today)

calculates black scholes theta.

\[\frac{\partial}{\partial t} c(t, S, K, r, T, \sigma) = - S * \phi(d_{1}) \left( \frac{\sigma}{2\sqrt{T - t}} \right) - r e^{-r(T - t)} K \Phi(d_{2})\]

where \(S\) is underlying, \(K\) is strike, \(r\) is rate, \(T\) is maturity, \(\sigma\) is volatility, \(\phi\) is standard normal p.d.f, \(d_{1}\) is defined in func_d1().

See black_scholes_call_value().

Parameters:

• underlying (float) –
• strike (float) –
• rate (float) –
• maturity (float) – must be non-negative.
• vol (float) – volatility. This must be positive.

Returns:

value of theta.

Return type:

float.