I personally believe this is one of the best books on stochastic calculus for finance applications. It is accessible for anyone who has a background in calculus, probability, algebra and finance. If you want to go beyond the Neftci level, you should use this textbook. This book is the volume II of Shreve's two volume series of stochastic calculus for finance. Volume I is Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. The difference betwen the two volumes is that first discusses discrete-time models while the second discusses continuous-time models. Shreve has been writing his book for many years dated back to 1980s when option pricing theory was getting popular. He cofounded Carnegie Mellon University's Master’s program in Computational Finance and this book evolves from the class he taught there over ten years. Over the time, he distributed the draft freely to many quantitative finance students who have benefited a lot from his notes. The volume II is good enough for a quant to learn suffice stochastic calculus. Chapter 1, 2 3 present basic background in probability theory such as probability measure, conditional expectation and sigma-algebra, abstract concept for information. Chapter 4 discusses stochastic calculus, including Brownian motion, quadractic variation, Ito Integral, Ito's lemma, stochastic differential equation (SDE) and derivation of famous Black-Scholes-Merton equation etc. Chapter 5 discusses risk neutral measure, Girsanov theorem and chapter 6 discusses Feyman-Kac theorem which relates risk-neutral measure to partial differential equations. Chapter 7-11 discusses exotic options, American options, change of numeriaire, term structure of interest rate and jump diffusion process. A quant should finish the first six chapters to have a solid background in stochastic calculus. A quant would better finish the exercises in the book as well. A collection of answers to the exercises is going to be available soon, please check back later. If you want to take a preview of Shreve's book, click here to download his draft free!(Back to Top)

    This book is between introductory and intermediate level. You will get a better understanding of the text if you have read through John Hull's book before. The author writes clearly in his view of quantitative finance. He starts from risk, arbitrage and presents the simple binomial tree to price option. The good thing is that the author then points out the practical shortcomings of the theoretically perfect pricing method. Later, the author begins to discuss stochastic calculus and risk-neutral and uses them to price exotic options. Some advanced quantitative finance have been discussed such as volatility smile, jump-diffusion etc. I like the chapter on static replication, which is seldom discussed on other quantitative finance books. Since replication is the bedrock for the option pricing, it should desire more attentions than other pricing methods although many other books ignore the issue intentionally or unintentionally. At some points, where beginners normally ignore, the author gives great presentations of what things should look like. It's rather a practical book than conceptual. Many examples are very practical and away from ideal theoretical world. One more worthmention is that at the end of the book there are some programming projects which are useful for anyone who wants to practice their knowledge and programm skills in finance applications. You should try to finish the projects and put them on your resume if you don't have better words to brag yourself. There are also exercises at the end of each chapter, which can be used to examine your knowledge of finance.