Sunday, May 30, 2010

Options, Futures, & other Dirivatives : John C Hull

Options, Futures and Other 
Derivatives by John C. Hull
Designed to bridge the gap between theory and practice, this successful book is regarded as "the bible" in trading rooms throughout the world. The books covers both derivatives markets and risk management, including credit risk and credit derivatives; forward, futures, and swaps; insurance, weather, and energy derivatives; and more. For options traders, options analysts, risk managers, swaps traders, financial engineers, and corporate treasurers.

The author has written a nice, lively elementary text on mathematical finance. This book can serve as a excellent launching point into the topic. Hull starts out with several chapters on the basics of the derivative contracts in his study. The contracts introduced are forward and futures contracts, interest rate swaps, and equity options. The basic definitions of each contingency contract is given, as well as characteristics of the markets where these contracts trade. Some basic trading strategies are also studied.


This is a fantastic book. For people who wants to learn about derivatives and finantial markets it helps a lot, a classical book on Derivatives. A must read for anyone that is interested in learning how derivatives work and how to price them. The author masters in explaning it a lot of examples, comprehensive language and a lot of exercises. So if you're interesting about finance, go get this book!

Overview:
* Very in-depth treatment of derivative basics, e.g. call, puts, swaps, forwards, futures.
* Many, many examples to complement the material.
* Many good practice problems to help further your understanding.
* Covers binomial, Monte Carlo and Black Scholes pricing of options very well
* Industry standard textbook - all the professionals use it.

Hull starts out with several chapters on the basics of the derivative contracts in his study. The contracts introduced are forward and futures contracts, interest rate swaps, and equity options. The basic definitions of each contingency contract is given, as well as characteristics of the markets where these contracts trade. Some basic trading strategies are also studied.

The study of the option pricing model problem begins in earnest in Chapter 10. The section on one-step binomial tree model leads to a very intuitive description of risk-neutral valuation.

Chapter 11 introduces continuous time stochastic processes in a very intuitive setting. To avoid the hard-core Ito calculus, the author motivates the stochastic differential by considering difference equations. This is a nice technique and makes the material accessible to the beginner. The next highlight is a statement of Ito's lemma. This is not given in full generality, but only stated precisely as needed for Black-Scholes calculations. The appendix gives an intuitive motivation for Ito's lemma based on the multi-dimensional Taylor's formula.
This is a nice illustration as Taylor's formula is indeed a component of the formal semi-martingale based proof of Ito's rule. See for example Oksendal Stochastic Differential Equations: An Introduction with Applications Chapter 4, Karatzas & Shreve Brownian Motion and Stochastic Calculus Chapter 3, or Rogers and Williams Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus.

Chapter 12 is devoted to the Black-Scholes-Merton theory of option pricing. The famous Black-Scholes PDE is derived via Ito's rule and application of a delta hedge. The author doesn't directly solve this PDE (via the standard application of the Feyman-Kac formula). Instead a nice proof of the option pricing formula is established in the appendix based on a simple log-normal distribution argument.

Chapter 13 discusses option pricing in for other contingency contracts. In Chapter 14, we return to equity options by studying the Greek letters. The reader discovers the Greek letters can be thought of as coefficients of the Black-Scholes PDE and learns some elementary hedging techniques.

Chapter 15 discusses implied volatility and volatility smiles. It is here that the astute reader gets his first indication that the Black-Scholes theory for option pricing may not be as robust or "true to market" as the reader may have been lead to believe. (The folks at Long-Term Capital Management learned this hard lesson rather publicly.)

A survey of topics of interest follows in the next handful of chapters. The material on value at risk, the GARCH volatility model and exotic options is somewhat superficial. The careless reader will come away feeling he knows quite a bit more than he really does.

Martingale theory is touched on in 21 and the Girsanov Theorem is alluded to, but these topics are really too complex and require too many prerequisites for proper treatment in the context. A general multi-variate version of Ito's Rule is stated in the appendix of this chapter.

The next section of the book deals with term-structure models and their applications. One-factor models are discussed along with the various limitations of each of these models. This gives a nice historical treatment. The Heath-Jarrow-Morton and Libor Market Model k-factor term-structure frameworks are introduced. Without the supporting martingale theory, the analysis of these models presented here is very limited.

The last several chapters of the text are very survey-like and breezily touch on topics such as credit risk, credit derivatives and energy derivatives. There isn't a lot of theory in these chapters at all, but at least the reader is made aware of the existence of these kinds of contingencies.

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