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Financial Calculus : An Introduction to Derivative Pricing

Martin Baxter, Andrew Rennie

posted on 20 March 2002

reviewed by J. McCauley

I was put off by the formalism until I realized just how badly stochastic differential equations and stochastic integration are treated in Hull's popular book Option, Futures, and other Derivatives. The problem with Hull 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 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. The problem with the book, clearly, is that one must first learn the rudiments of options elsewhere (Hull, Bodie & Merton): this is not a text for beginners.