mafipy.function.black_payers_swaption_value_fhess_by_strike

mafipy.function.black_payers_swaption_value_fhess_by_strike(init_swap_rate, option_strike, swap_annuity, option_maturity, vol)

Second derivative of value of payer’s swaption with respect to strike under black model. See black_payers_swaption_value().

\[\frac{\partial^{2} }{\partial K^{2}} V_{\mathrm{payer}}(K; S, A, T, \sigma) = - A\phi(d_{2}(K)) d_{2}^{\prime}(K)\]

where \(S\) is init_swap_rate, \(K\) is option_strike, \(A\) is swap_annuity, \(T\) is option_maturity, \(\sigma\) is vol, \(d_{1}, d_{2}\) is defined in black_payers_swaption_value(), \(\Phi(\cdot)\) is c.d.f. of standard normal distribution, \(\phi(\cdot)\) is p.d.f. of standard normal distribution.

Parameters:

• init_swap_rate (float) – initial swap rate.
• option_strike (float) –
• swap_annuity (float) –
• option_maturity (float) –
• vol (float) – volatility. must be non-negative.

Returns:

value of derivative.

Return type:

float

Raises:

AssertionError – if volatility is not positive.