# P. Derivative of function with embedded functions // Black Scholes Formula

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 Hi all, I'm having a hard time computing the Delta of a European Put option using Mathematica. For those not in finance, i'm basically trying to computer a partial derivative of a function containing two other functions. I am setting the appropriate functions but once I try to compute it is not working.Any help will be greatly appreciated! I am trying to get this answer by calculating the partial derivative S from this function: From this functionOnce again I need to calculate: Here is my code dplus[S_, [Sigma]_, q_, r_, t_, T_, k_] := ((T - t) (r - q + [Sigma]^2/2) + Log[S/k])/( Sqrt[T - t] [Sigma]) dminus[S_, [Sigma]_, q_, r_, t_, T_, k_] := dplus[S, [Sigma], q, r, t, T, k] - [Sigma] Sqrt[-t + T] D[dplus[S, [Sigma], q, r, t, T, k ], S] D[dminus[S, [Sigma], q, r, t, T, k ], S] funtime[S_] := ( Se^(-q (T - t)) [CapitalPhi] (dplus[S, [Sigma], q, r, t, T, k ])) - (Ke^(-r (T - t)) [CapitalPhi] (dminus[S, [Sigma], q, r, t, T, k ])) D[funtime[S], S] But I am getting: (Se^(-q (-t + T)) [CapitalPhi])/(S Sqrt[-t + T] [Sigma]) - Ke^(-r (-t + T)) !(*SuperscriptBox[([CapitalPhi]dminus), TagBox[ RowBox[{"(", RowBox[{"1", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None])[S, [Sigma], q, r, t, T, k] Can anyone explain what is going on? I can successfully get partial derivatives from the first 2 parameters (Dplus and Dminus), but once I try to get the partial derivative from my function, "funtime", it's not coming together. Any help will be greatly appreciated! I have attached my mathematica file for anyone trying to help.Thanks! Attachments:
 Bill Simpson 2 Votes Replace funtime[S_]:= (Se^(-q(T-t))\[CapitalPhi](dplus[S,\[Sigma],q,r,t,T,k]))-(Ke^(-r(T-t))\[CapitalPhi](dminus[S,\[Sigma],q,r,t,T,k])) with funtime[S_]:= (S*E^(-q(T-t))\[CapitalPhi](dplus[S,\[Sigma],q,r,t,T,k]))-(K*E^(-r(T-t))\[CapitalPhi](dminus[S,\[Sigma],q,r,t,T,k])) I am also seeing phi' in Mathematica's result, but there are no ' in your pasted image at the top of your post, but that may just be typesetting or my misunderstanding of their notation.