Nftion[x_]:=CDF[NormalDistribution[],x]

Nftion[0]

S0=100; r=0.04; σ=0.25; T=1; K=100

done[s_,t_]:=(Log[s/K]+(r+σ^2/2)*(T-t))/σ/Sqrt[T-t]

dtwo[s_,t_]:=done[s,t]-σ*Sqrt[T-t]

Call[s_,t_]= s*Nftion[done[s,t]]-K*E^(-r(T-t))*Nftion[dtwo[s,t]]

Call[100,0]

Plot3D[Call[x,y],{x,0,200},{y,0,1}]

Plot[Call[100,y],{y,0,1}]

EuroPut[s_,t_]:= K*E^(-r(T-t))*Nftion[-dtwo[s,t]]-s*Nftion[-done[s,t]]

EuroPut[100,0]

Plot3D[EuroPut[x,y],{x,0,200},{y,0,1}]

Plot[EuroPut[80,y],{y,0,1}]

ΔC[s_,t_]=D[Call[s,t],s]

Plot3D[ΔC[x,y],{x,0,200},{y,0,1}]

ΘC[s_,t_]=D[Call[s,t],t]

Plot3D[ΘC[x,y],{x,0,200},{y,0,1}]

Plot[ΘC[x,0],{x,0,200}]

ΘP[s_,t_]=D[EuroPut[s,t],t]

Plot3D[ΘP[x,y],{x,0,200},{y,0,1}]

Plot[ΘP[x,0],{x,0,200}]

Clear[s,t,σ,r,δ]

doneAll[s_,t_,σ_,r_,δ_]= (Log[s/100]+(r-δ+σ^2/2)*(1-t))/σ/Sqrt[1-t]

dtwoAll[s_,t_, σ_, r_, δ_]= doneAll[s,t,σ,r,δ]-σ*Sqrt[1-t]

Together[%]

Simplify[%]

CallAll[s_,t_,σ_,r_,δ_]= s*E^(-δ*(1-t))*Nftion[doneAll[s,t,σ,r,δ]]-100*E^(-r*(1-t))*Nftion[dtwoAll[s,t,σ,r,δ]]

ΔCallAll[s_,t_,σ_,r_, δ_] = Simplify[D[CallAll[s,t,σ,r,δ],s],Assumptions->{s>0, 0<t, t<1, σ>0}]

Plot[ΔCallAll[x,0,0.25,0.04,0.01],{x,0,200}]

VegaCallAll[s_,t_,σ_,r_,δ_]=D[CallAll[s,t,σ,r,δ],σ]

Plot[VegaCallAll[s,0,0.25,0.04,0.01],{s,0,200}]

ρCallAll[s_,t_,σ_,r_,δ_]=D[CallAll[s,t,σ,r,δ],r]

Plot[ρCallAll[s,0,0.25,0.04,0.01],{s,0,200}]

ψCallAll[s_,t_,σ_,r_,δ_]=D[CallAll[s,t,σ,r,δ],δ]

Plot[ψCallAll[s,0,0.25,0.04,0.01],{s,0,200}]

PutAll[s_,t_,σ_,r_,δ_]= -s*E^(-δ*(1-t))*Nftion[-doneAll[s,t,σ,r,δ]]+100*E^(-r*(1-t))*Nftion[-dtwoAll[s,t,σ,r,δ]]

ΔPutAll[s_,t_,σ_,r_, δ_] = D[PutAll[s,t,σ,r,δ],s]

Plot[ΔPutAll[s,0,0.25,0.04,0.01],{s,0,200}]

ρPutAll[s_,t_,σ_,r_,δ_]=D[PutAll[s,t,σ,r,δ],r]

Plot[ρPutAll[s,0,0.25,0.04,0.01],{s,0,200}]

ψPutAll[s_,t_,σ_,r_,δ_]=D[PutAll[s,t,σ,r,δ],δ]

Plot[ψPutAll[s,0,0.25,0.04,0.01],{s,0,200}]