mafipy.function.black_scholes_call_volga

mafipy.function.black_scholes_call_volga(underlying, strike, rate, maturity, vol)

black_scholes_call_volg calculates black scholes volga.

\[\frac{\partial^{2}}{\partial \sigma^{2}} c(S, K, r, T, \sigma) S \phi^{\prime}(d_{1}(\sigma)) \frac{ (\frac{1}{2} \sigma^{2} - r)T }{ \sigma^{2} }\]

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 volga.

Return type:

float.