mafipy.function.black_payers_swaption_value

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

calculates value of payer’s swaptions under black model.

\[\begin{split}\begin{eqnarray} V_{\mathrm{payersswap}}(t) & = & A(t) \mathrm{E}_{t}^{A} \left[ (S(T) - K)^{+} \right] \\ & = & A(t)(S(t)N(d_{1}) - KN(d_{2})), \\ d_{1} & = & \frac{ \ln\left(\frac{S(t)}{K} \right) + \frac{1}{2}\sigma^{2}(T - t) }{ \sigma \sqrt{T - t} }, \\ d_{2} & = & \frac{ \ln\left(\frac{S(t)}{K} \right) - \frac{1}{2}\sigma^{2}(T - t) }{ \sigma \sqrt{T - t} } \end{eqnarray}\end{split}\]

where \(A(t)\) is swap_annuity, \(S(t)\) is init_swap_rate, \(K\) is option_strike, \(\sigma\) is vol.

Parameters:

• init_swap_rate (float) – initial swap rate.
• option_strike (float) – swaption strike.
• swap_annuity (float) – annuity of referencing swap
• option_maturity (float) – swaption maturity.
• vol (float) – volatilty. this must be positive.

Raises:

AssertionError – if volatility is not positive.