This book seems very odd to me in a way similar many other text books I have read over the years. The author tries to convince the reader that the prerequisites are minimal. However, the problem sets appear more difficult than the author lets on. For example, if you really need to be remined of the integration by parts formula, can you actually complete the problem #9 in chapter 3 without getting frustated and quiting. Also, I have taken calculus through real analysis and simple measure theory. Without this background, I would think the problem sets would be very difficult or unenlightening. with the background suggested by Neftci, I would be surprised if you really leaned anything, rather than being tricked into thinking you learned something.



That being said, in my humble opinion, I feel the only way you would learn anything from Neftci is by studying a more difficult book by Steele or Shreve and then go back and learn the many intutive insights Neftci provides. If you do not have the background for those books, are you really getting anything from Neftci anyways?



To sum it up, Neftci provides excellent intuition. After leaning Stochastic Calculus from a more rigorous book, Neftci's book would be a nice "extremely quick" read where you wouldn't have to work out one equation, and gain a lot of useful intuition. However, if you try to start with Neftci and go to Steele you will start from nearly ground zero and have learn everything as if you have never seen it before. So, Steele and Shreve will completely eliminate the work you will have to do to benefit from Neftci, but if you do all the hard work to memorize and trick yourself into thinking you are learning, you will have to do all the work over again to actually learn stochastic calculus from another book. Also, after Steele and Shreve you can move through more advanced text books more quickly.



Neftci: Excellent intuition, but you cannot really "learn" anything from this book that will move you through more advanced treatments the way other slightly more difficult text books will.