mafipy.function.black_payers_swaption_value_third_by_strike¶
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mafipy.function.
black_payers_swaption_value_third_by_strike
(init_swap_rate, option_strike, swap_annuity, option_maturity, vol)[source]¶ Third derivative of value of payer’s swaption with respect to strike under black model. See
black_payers_swaption_value()
.\[\frac{\partial^{3} }{\partial K^{3}} V_{\mathrm{payer}}(K; S, A, T, \sigma) = - A \left( \phi^{\prime}(d_{2}(K)) (d_{2}^{\prime}(K))^{2} + \phi(d_{2}(K)) d_{2}^{\prime\prime}(K) \right)\]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) – strike of swaption.
- swap_annuity (float) – annuity of referencing swap.
- option_maturity (float) – maturity of swaption.
- vol (float) – volatility. must be non-negative.
Returns: value of derivative.
Return type: float
Raises: AssertionError – if volatility is not positive.