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Stochastic Calculus and Financial Applications

J. Michael Steele

posted on 03 September 2002

reviewed by Joe McCauley

Good intro to stochastic calculus and sde's, can compare roughly with Baxter and Rennie in readability. However, the book unnecessarily
propagates ideology. First, it makes excuses for the fact that the empirically wrong notion of utility ('maximizing behavior') is totally disconnected
from the Black-Scholes model. Second, the text propagates Black and Schole's original mistaken claim that CAPM produces the same option
pricing pde as does the delta hedge. A careful and correct calculation shows that this claim is wrong, that with the wrong assumption made by
B-S the fractions invested in both the stock and the option are zero! For the correct result, including the difference in option pricing via delta hedge
and CAPM, see my recent paper "An Empirical Model for Volatiliy of Returns and Option Pricing' with Gunaratne. A third criticism is that only
Gaussian returns are discussed in this text, but the empiciral distribution is far from Gaussian and is approximately exponential, with nontrivial
volatility.

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