mafipy.function.black_scholes_call_value_third_by_strike¶
-
mafipy.function.
black_scholes_call_value_third_by_strike
(underlying, strike, rate, maturity, vol)[source]¶ Third derivative of value of call option with respect to strike under black scholes model. See
black_scholes_call_formula()
andblack_scholes_call_value_fprime_by_strike()
, andblack_scholes_call_value_fhess_by_strike()
.\[\begin{array}{ccl} \frac{\partial^{3}}{\partial K^{3}} c(0, S; T, K) & = & -e^{-rT} \left( \phi^{\prime}(d_{2}(K))(d^{\prime}(K))^{2} + \phi(d_{2}(K))d^{\prime\prime}(K) \right) \end{array}\]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 third derivative.
Return type: float.