mafipy.function.black_scholes_call_value_fhess_by_strike

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

Second derivative of value of call option with respect to strike under black scholes model. See black_scholes_call_formula() and black_scholes_call_value_fprime_by_strike().

\[\begin{array}{ccl} \frac{\partial^{2}}{\partial K^{2}} c(0, S; T, K) & = & -e^{-rT} \phi(d_{2}(K)) d^{\prime}(K) \end{array}\]

where \(S\) is underlying, \(K\) is strike, \(r\) is rate, \(T\) is maturity, \(\sigma\) is vol, \(d_{1}, d_{2}\) is defined in black_scholes_call_formula(), \(\Phi(\cdot)\) is c.d.f. of standard normal distribution, \(\phi(\cdot)\) is p.d.f. of standard normal distribution.

Parameters:

• underlying (float) –
• strike (float) –
• rate (float) –
• maturity (float) – non-negative.
• vol (float) – volatility. non-negative.

Returns:

value of second derivative.

Return type:

float.