Finance question: delta confidence interval

[mkkrnfoo85]

Hi, if I have the confidence interval for the point estimate of an option price A which was found through simulation, can I also find a confidence interval for delta (dA/dS), where S is underlying asset price, without further simulation?

thanks,

sl

 

[Enuma_Elish]

You can approximate dA(t)/dS(t) as (ΔA/Δt)/(ΔS/Δt), e.g. (A(t)-A(t-1))/(S(t)-S(t-1)) where t indexes successive simulation outputs.