Derivative-security

This book is too simplistic for the real world.

When this book was written, it was somewhat current. Today, credit derivatives are a major factor in structured finance and dominate collateralized debt obligations which use bonds, MBS, and loans. This book neglects the recent explosive growth in these off-balance sheet products.

"Derivatives Demystified" is a real find. It explains this complex subject simply and thoroughly. Read it!

The authors provide the reader an excellent overview of equity derivatives and how they can be integrated into portfolio management. A great book for the novice and as a reference book for the more experienced professional. I find the way the authors describe the investment process and the derivatives process particularly useful and insightful.
The book is also easy to read and can be easily digested by the reader.

Wilmott's Derivatives is an accessible introduction to the partial differential equation (PDE) approach to mathematical finance.

The basis of mathematical finance is the observation by Black and Scholes that when pricing a derivative contract, for example a stock option, the randomness of the value of the underlying stock can be used to balance the randomness in value of the option in such a manner as to eliminate all randomness. A trader can thus by continually rebalancing his positions guarantee the price of an option. This price is the solution to the famous Black-Scholes equation. Thus the pricing of derivatives becomes a suprisingly rigourous branch of mathematics.

The Black-Scholes equation itself is not a particularly difficult equation -- indeed a few simple changes of variables transform it into the one-dimensional heat equation and a closed-form solution for the price of an option can be written down. The proof that it holds and the implications of the proof are however not so trivial and the book does well at explaining these.

Mathematical finance does not end with the Black-Scholes equation for two reasons. The first is that more and more complicated derivatives products are continually being innovated which require new mathematics to be invented. The second is that the equation is based on certain assumptions which while providing a reasonable first approximation are not perfect; the research of new more accurate models is therefore active and ongoing.

The author starts with the definitions of the basic financial instruments and gradually builds up to the Black-Scholes equation. He does so in a clear and detailed manner. He then goes on to discuss various generalizations to exotic options and more complicated models of stock price movements.

The principal defect of the book is that mathematical finance is not a branch of PDE theory or applied mathematics but rather a branch of probability theory. The probabilistic aspects of the subject are skimped on with only a brief coverage of binomial trees, and the concept of an equivalent martingale measure which is the fundamental concept of mathematical finance not discussed. Interest-rate options and many exotic stock options are more easily priced both practically and conceptually from a probabilitistic point of view and the PDE approach to them can become contrived.

To summarize, this book is worth buying but the reader should treat its contents with a pinch of salt and concentrate on the first two hundred pages. It should be read in parallel with another book, such as Baxter and Rennie, which concentrates on the probabilistic approach to the subject.

Financial engineering as a profession has exploded in the last 15 years, and has enlisted the minds of mathematicians, physicists, economists, engineers, as well as course everyday brokers and traders. This book is geared towards a mathematical audience, as one will need a background in the numerical solution of nonlinear partial differential equations and an understanding of stochastic processes (at the level of the Ito calculus). The author does devote a chapter to partial differential equations for readers who need it. Those readers with such a background will find the book very straightforward to read, especially those readers who are mathematicians or physicists, and are desiring to enter into the exciting field of financial engineering. The book is out of print, and an updated collection of books has been written by the author, but this one could still serve as an excellent introduction to the subject. In addition, this book has exercises, while the updated ones do not. Most of the results in the book can be used to develop practical trading strategies, and so the book qualifies more than being a mere academic exercise.

The author's approach is not always rigorous from a mathematical standpoint, but this is fine since the emphasis is on developing insight into the principles behind the subject, such as the principle of arbitrage, the idea of hedging, etc. Early on, the author shows what is involved in removing oneself from the Black-Scholes world, with clear explanations of jump conditions, time-dependent volatility, and path dependency. The discussion on the valuation of American style options using partial is illuminating considering this is typically done with Monte Carlo simulations. Another interesting part of the book is the derivation of the partial differential equation for the market price of volatility risk. In addition, the author gives an overview of how to speculate with options, a topic that is truly removed from the Black-Scholes world, but of course is taken up with enthusiasm by many traders the world over. This discussion is very interesting, in that it sheds light on just how subjective preferences enter into options trading; but it also shows that such preferences can be treated quantitatively. Assuming the asset price follows a random walk, the author derives an equation for the present value of the expected payoff, an equation that differs from the Black-Scholes equation in having the drift rate rather than the interest rate in the delta term. This risk-neutral valuation is dealt with in more detail in the author's discussion on portfolio management.

The author uses spreadsheets and Visual Basic to perform some of the numerical calculations, with many included on the accompanying CD. This is done no doubt to maintain the connection with practical trading. All of the mathematics and numerical studies could be done more efficiently though with a high-level programming language, such as Mathematica or Maple. The graphical capabilities of these languages will allow the reader to view the results of the calculations on-the-fly.

Some omissions in the book include discussions on energy and weather derivatives, but these are covered, although in not too much detail, in the author's more recent books. Also omitted is any discussion on bandwidth markets or derivatives trading in network capacity. This is also a new area, but one that is growing rapidly. Discussion of it will no doubt be included in future books on derivatives.

This is actually a wonderful introduction to the theory of derivatives and personally I find it to be a little humorous on occasion as well. There is definitely some ego here but it does not interfere with the author's sincere attempt to present the material in such a way that it can be understood easily by anyone with the required math background. That of course is the problem for some: this book requires a fairly extensive math background to be really understood. Fakers may try, but the successful will have a pretty good background in mathematics. That said, the discussion of stochastic calculus is better than many have led the casual onlooker to believe. It is not rigorous but is perfectly sufficient for the subject matter at hand. A good understanding of the material in this book will make the reader truly dangerous in the realms of the PDE theory of derivatives.