mafipy.replication.make_pdf_fprime_black_swaption

mafipy.replication.make_pdf_fprime_black_swaption(init_swap_rate, swap_annuity, option_maturity, vol)

return first derivative of p.d.f. of black swaption. See make_pdf_black_swaption().

\[\Phi_{S}^{\prime}(k) := \frac{\partial^{3}}{\partial K^{3}} V_{\mathrm{payers}}(0, S; K, A, T)\]

where \(S\) is init_swap_rate, \(S\) is swap_annuity, \(T\) is option_maturity, \(K\) is option_strike, \(\Phi_{S}(k)\) is p.d.f. of \(S\), \(V_{\mathrm{payers}}(0, S; K, A, T)\) is value of call option with strike \(K\) and \(T\) maturity at time 0.

Parameters:

• init_swap_rate (float) – initial swap rate.
• swap_annuity (float) – annuity of referencing swap.
• option_maturity (float) – maturity of swaption.
• vol (float) – volatility. non-negative.

Returns:

first derivative of p.d.f. of black swaption model as a function of strike.

Return type:

function

Raises:

AssertionError – if volatility is not positive.