function s = Derivative


syms S0 V0 s c F r d m std TF vb

Derivative='V0 - [(1-s)*c*F]/r - ([s*c]/r + d*([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])) * F*(V0/(([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F))^(-((r - m )/(std^2)- 0.5)-((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) - (1 - c/r)*F* ([1-exp(-r*TF)] / [r*TF] - (1/(r*TF)*(([(V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F))^(-((r - m )/(std^2)- 0.5)+((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))] * normcdf([-log(V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F)) - ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*(TF)] / [std*((TF)^0.5)]) + [(V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F))^(-((r - m )/(std^2)- 0.5)-((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))] * normcdf([-log(V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F)) + ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*(TF)] / [std*((TF)^0.5)]))-exp(-r*TF)*(normcdf([-log((V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F))) - ((r - m )/(std^2)- 0.5)*(std^2)*(TF)] / [std * ((TF)^0.5)]) +[(V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F))^(-2*((r - m )/(std^2)- 0.5))] * normcdf([-log(V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F)) + ((r - m )/(std^2)- 0.5)*(std^2)*(TF)] / [std * ((TF)^0.5)]))))) - ((1-d)*([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))]) - c/r)*F*(1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))*[(- (V0/( ([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F))^(-((r - m )/(std^2)- 0.5)+((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)))*normcdf([-log(V0/(([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F)) - ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*(TF)] / [std*((TF)^0.5)])*([-log(V0/(([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F)) - ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*(TF)] / [std*((TF)^0.5)]) + (V0/(([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F))^(-((r - m )/(std^2)- 0.5)-((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))] * normcdf([-log(V0/(([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F)) + ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*(TF)] / [std*((TF)^0.5)])*([-log(V0/(([(c/r) * ((2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -   2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*  normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF))))- (2*((r - m )/(std^2)- 0.5)*exp(-r*TF) * normcdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) -     2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5)) -2/(std * (TF^0.5)) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * std * (TF^0.5)) + 2* exp(-r*TF)/(std*(TF^0.5)) * normpdf(((r - m )/(std^2)- 0.5)*std*(TF^0.5)) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)))/(r*TF) - (((r - m )/(std^2)- 0.5)+((((((r - m )/     (std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2))*((s*c)/r)]/     [1+ d*(((r - m )/(std^2)- 0.5)+ ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)) -     (1-d)*(-((2*((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) + 2/     (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*TF))) *     normcdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*std*(TF^0.5))- (2/(std*(TF^0.5))) * normpdf(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) *std*TF^0.5) + (((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)-((r - m )/(std^2)- 0.5)) + (1/(((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2) * (std^2)*TF)))])*F)) + ((((((r - m )/(std^2)- 0.5) * std^2)^2 + 2*r*(std^2))^0.5)/std^2)*(std^2)*(TF)] / [std*((TF)^0.5)]))'

diff(Derivative,'V0')

 clear