Clear[S,k,r,δ,σ,T];d1[S_,k_,r_,δ_,σ_,T_]=(Log[S/k]+(r-δ+σ^2/2)T)/(σSqrt[T]);d2[S_,k_,r_,δ_,σ_,T_]=(Log[S/k]+(r-δ-σ^2/2)T)/(σSqrt[T]);[z_]=(1+Erf[z/Sqrt[2]])/2;BSPut[S_,k_,r_,δ_,σ_,T_]:=kE^(-rT)[-d2[S,k,r,δ,σ,T]]-SE^(-δT)[-d1[S,k,r,δ,σ,T]];BSPutDelta[S_,k_,r_,δ_,σ_,T_]=D[BSPut[S,k,r,δ,σ,T],S];ContourPlot[BSPutDelta[3000,k,.0175,.02,σ,.05],{k,1500.,3000.},{σ,0,1.5},ColorFunction->"BeachColors",PlotTheme->"Marketing",ImageSize->Large]