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Options, Futures, and Other Derivatives with Disk

John C. Hull

posted on 15 March 2002

reviewed by Joe McCauley

Since this book is regarded as the bible of derivatives (it was also my first introduction) I will leave it to others to praise it and concentrate instead on what's wrong with it. First and foremost, one cannot learn how correctly to formulate solutions to stochastic differential equations from this text: eqns. (10.7,8), e.g., are not correct for arbitrary returns but are valid only as approxmations for small returns (Hull leads the reader to believe the opposite). The problem is that Ito's lemma is only stated, not proven, and it's the proof that shows one how to formulate correctly the stochastic integral equations that Hull calls 'stochastic difference equations'. When volatility depends on returns and/or time, then the errors made from following Hull's oversimplified treatment become serious.

My first impression of Baxter & Rennie's 'Financial Calculus' was that it was unnecessary and a waste of money. My opinion reversed completely after realizing (under prodding by a physics colleague who's an expert on sde's) how badly Hull's approach to sde's really is. Also, the systematic derivation of Black-Scholes from the assumption of a replicating, self-financing strategy in B&R is very nice. As Feynman said, we don't really understand a result until we can derive it from many different viewpoints. The method is not really different in principle from the standard short derivation given in Hull, but it does provide a nice, clear example of what is meant by replication and self-financing in the terminology of Brownian motion/sde's.