# Weiner Process and Ito's Lemma

I am reading weiner process and Ito’s lemma to quench my thrist for understanding whats happening beneath the BSM blackbox. I am using John C Hull’s Options, Futures, and Other Derivatives. I am still a little uncomfortable with all the overwhelming mathematics and ambiguous concepts. Can you please refer an alternative source or a better material or book to understand it better? thanks

Stochastic Calculus for Finance II (Continous-Time Models) by Steven E. Shreve

^ That’s my fav, but at a higher math level than Hull so if Hull is overwhelming, Shreve would be very difficult. Even Shreve doesn’t give all the gory details of the proof of Ito’s lemma, for example.

Of course maybe you could post your questions here, thuogh the format really sucks for presenting math.

yeah i was going to say that for me, all the other texts and articles were much more math-intensive and hard to understand than hull for wiener processes, ito’s lemma, brownian motion.

Definitely agree with above posters. Hull is a rather user-friendly text in comparison to many others. The Shreve texts were helpful in exploring topics further in-depth. Although I can’t imagine trying to learn these topics independently. That’s very impressive - I don’t think I could have managed outside of the classroom.

thanks for your suggestions … I will definitely post questions here JDV, once I get through the material. For now: How do you integrate dS/S = u dt to S(T) =S(o)e^(uT) b/w time 0 and T subscripts are in ()

i read Hull and i liked it, although i lack math background to understand Ito derivation. I understood general concept and theory behind it. I need to learn more math

basically you want to solve partial def equation dS/dt = uS, so question is what function is the function which derivatives is multiple of itself time constant? turns out it is C*e^(t*u)

madanalyst Wrote: ------------------------------------------------------- > thanks for your suggestions … I will definitely > post questions here JDV, once I get through the > material. > > For now: How do you integrate > > dS/S = u dt > > to > > S(T) =S(o)e^(uT) > b/w time 0 and T > > subscripts are in () That’s standard calc, not stochastic calc - Int(ds/S) = ln(s) + C

You might want to start with Mathematics for Economists by Simon & Blume.

The book Stochastic Calculus Steven E. Shreve is in an alien langugae … I cant understand a word… How do I go about understanding this kind of exotic material in finance ? I have taken some calculus courses in undergrad but knowledge is rusty. I am starting myself on calculus … and I welcome your feedback. How I got into this? ------------------------- I am studying for FRM and I have put a lid on lot of details and now my sack is full and I cant put no more lids… I want to know the real stuff… since I just dont want to pass the exam and know a little thats why I am now digging … no matter how long it will take and how hard it is.