In[]:=
d1[S_,k_,r_,δ_,σ_,T_]=(Log[S/k]+(r-δ+/2)T)σ/2)T)σ[d1[S,k,r,δ,σ,T]]-k[d2[S,k,r,δ,σ,T]];BSPut[S_,k_,r_,δ_,σ_,T_]:=k[-d2[S,k,r,δ,σ,T]]-S[-d1[S,k,r,δ,σ,T]];BSCallDelta[S_,k_,r_,δ_,σ_,T_]=D[BSCall[S,k,r,δ,σ,T],S];BSPutDelta[S_,k_,r_,δ_,σ_,T_]=D[BSPut[S,k,r,δ,σ,T],S];BSCallGamma[S_,k_,r_,δ_,σ_,T_]=D[BSCall[S,k,r,δ,σ,T],{S,2}];BSPutGamma[S_,k_,r_,δ_,σ_,T_]=D[BSPut[S,k,r,δ,σ,T],{S,2}];BSCallTheta[S_,k_,r_,δ_,σ_,T_]=-D[BSCall[S,k,r,δ,σ,T],T];BSPutTheta[S_,k_,r_,δ_,σ_,T_]=-D[BSPut[S,k,r,δ,σ,T],T];BSCallRho[S_,k_,r_,δ_,σ_,T_]=D[BSCall[S,k,r,δ,σ,T],r];BSPutRho[S_,k_,r_,δ_,σ_,T_]=D[BSPut[S,k,r,δ,σ,T],r];BSCallVega[S_,k_,r_,δ_,σ_,T_]=D[BSCall[S,k,r,δ,σ,T],σ];BSPutVega[S_,k_,r_,δ_,σ_,T_]=D[BSPut[S,k,r,δ,σ,T],σ];
2
σ
T
;d2[S_,k_,r_,δ_,σ_,T_]=(Log[S/k]+(r-δ-2
σ
T
;[z_]=1+Erfz2
2;BSCall[S_,k_,r_,δ_,σ_,T_]:=S-δT
-rT
-rT
-δT
In[]:=
Manipulate[Plot[BSHedge[S,k,r,δ,σ,t],{k,1500.,3000.},AxesLabel{"strike price","option sensitivity"},ImageSize400,ImagePadding{{25,30},{25,25}},AxesOrigin{Automatic,0}],{{BSHedge,BSCallDelta,"call sensitivities"},{BSCallDelta"call delta",BSCallGamma"call gamma",BSCallRho"call rho",BSCallVega"call vega",BSCallTheta"call theta"}},{{BSHedge,BSPutDelta,"put sensitivities"},{BSPutDelta"put delta",BSPutGamma"put gamma",BSPutRho"put rho",BSPutVega"put vega",BSPutTheta"put theta"}},{{S,3000.,"index price"},1500.,3000.},{{r,.0175,"interest rate"},.0025,.05},{{δ,.02,"dividend yield"},0.0,.05},{{σ,.3,"volatility"},.1,2.5},{{t,.01,"time to maturity"},.01,.1},SaveDefinitionsTrue,AutorunSequencing{4,6,7}]
Out[]=
