mafipy.function.black_scholes_call_vega_fprime_by_strike

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

calculates derivative of black scholes vega with respect to strike. This is required for sabr_pdf().

\[\frac{\partial}{\partial K} \mathrm{Vega}{\mathrm{BSCall}}(S, K, r, T, \sigma) = S\phi^{\prime}(d_{1}(S, K, r, T, \sigma)) \frac{1}{\sigma K}\]

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) – if maturity <= 0.0, this function returns 0.
• vol (float) – volatility. This must be positive.

Returns:

derivative of vega with respect to strike.

Return type:

float.