An Introduction to the Mathematics of Financial Derivatives, Second Edition, introduces the mathematics underlying the pricing of derivatives. The increased interest in dynamic pricing models stems from their applicability to practical with the freeing of exchange, interest rates, and capital controls, the market for derivative products has matured and pricing models have become more accurate. This updated edition has six new chapters and chapter-concluding exercises, plus one thoroughly expanded chapter. The text answers the need for a resource targeting professionals, Ph.D. students, and advanced MBA students who are specifically interested in financial derivatives. This edition is also designed to become the main text in first year masters and Ph.D. programs for certain courses, and will continue to be an important manual for market professionals and professionals with mathematical, technical, or physics backgrounds.
It's hard to think of a worse introduction to stochastic calculus than this. The exposition is illogical, disorganized and thoroughly unclear. The equations are full of errors (the available errata for the book runs to many pages) and the author uses symbols and formulas inconsistently, even within the same proof. The exercises seem to have been designed separately from the chapters and are of little value. I guess this is supposed to be a slow and gentle introduction but it just ends up a confusing, repetitive mess.
I can understand the appeal for this book. Coming from an MBA background, I needed an accessible introduction. I would argue the first 10 chapters of this book are fantastic! After that the author seems to skim over some details. I got an intuition behind the mathematics indeed, but was not able to solve the exercises easily!
The main issue with this approach to mathematics is that, you understand conceptually but applying it to problems is tricky. For that, you need more rigorous books.
I think this book can be a good stepping stone to more complex books like Shreve.