mafipy.replication.make_pdf_fprime_black_scholes¶
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mafipy.replication.make_pdf_fprime_black_scholes(underlying, rate, maturity, vol)[source]¶ make_pdf_fprime_black_scholes_model return first derivative of p.d.f. of black scholes. See
make_pdf_black_scholes().\[\Phi_{S}^{\prime}(k) := \frac{\partial}{\partial K^{2}} c(0, S; T, K)\]where \(S\) is underlying, \(T\) is maturity, \(K\) is strike, \(\Phi_{S}(k)\) is p.d.f. of \(S\), \(c(0, S; T, K)\) is value of call option with strike \(K\) and \(T\) maturity at time 0.
Parameters: - underlying (float) –
- rate (float) –
- maturity (float) – non-negative.
- vol (float) – volatility. non-negative.
Returns: first derivative of p.d.f. of call price under black scholes model as a function of strike.
Return type: