**ADVANCED OPTION PRICING MODELS:A SCIENTIFIC APPROACH
TO VALUING OPTIONS**

McGraw-Hill, 2005; ISBN 0071-4060-50; hardcover 437pp; List $70 U.S.

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Advanced Option Pricing Models

In this book, we apply the
same hard-edged, research-orientated approach used in *The
Encyclopedia of Trading Strategies* to the problem of evaluating
the worth of options. A variety of methods are investigated, from conditional
distributions and multivariate polynomial regressions (using Chebychev
polynomials) to hybridized neural networks. The studies demonstrate that
one can do much better than Black-Scholes when it comes to pricing options,
especially under certain market conditions. If you have a mathematical
bent, want the same kinds of technology that the market makers and institutional
traders have access to, and if you trade stocks or stock options, then
this book is for you.

*"An intriguing, in-depth
look at what really constitutes option pricing theory. Plus some interesting
thoughts on projecting and assessing volatility. A must read for those
who are looking for more advanced option modeling techniques*." --Lawrence
G. McMillan, author of *Options as a Strategic Investment* and *McMillan
on Options*

*"Refreshingly grounded in
empirical data and a spirit of numerical experimentation, this book also
succeeds at explaining the arcane mathematical concepts of options pricing
in straightforward, clear language. The reader will come away not just
with the accepted wisdom of the field, but also with a good sense of how
to test that wisdom against real data." * --William H. Press, senior
author of the* Numerical Recipes *book and software series; Harvard-Smithsonian
Center for Astrophysics; Senior Fellow, Los Alamos National Laboratory

*"Katz
and McCormick's rigorous data studies and their experiences as traders
lead to useful solutions for option modeling. In addition, their ability
to write in clear English should be studied by all financial authors*."
--Howard L. Simons, President, Rosewood Trading; contributing editor, *Futures*
magazine; author of *The Dynamic Option Selection System: Analyzing Models
and Managing Risk*.

**Chapter 1: A Review of Option
Basics.** Factors influencing option premium (from well-known factors
to skew, kurtosis, and cycles). Uses of options. Option pricing models.
The Greeks. The influence of various factors on option premium. Put-call
parity, conversions, and reversals. Synthetics and equivalent positions.

**Chapter 2: Fair Value and
Efficient Price.** Fair value and the efficient market. The context dependence
of fair value. Estimating fair value. Fair value and arbitrage. Fair value
and speculation. Estimating speculative fair value.

**Chapter 3: Popular Option
Pricing Models.** Cox-Ross-Rubinstein binomial model (specifying growth
and volatility, Monte Carlo pricing, pricing with binomial trees). Black-Scholes
(and forward expectation; versus binomial pricing). Means, medians, and
stock returns (empirical study).

**Chapter 4: Statistical Moments
of Returns.** The first four moments (their calculation and features).
Study 1: Moments and holding period (segmented analysis: statistical independence
and log-normality of returns, estimating standard errors; non-segmented
analysis: volatility and independence of returns, skew, kurtosis, and log-normality;
non-segmented analysis of two indices). Study 2: Moments and day of week.
Study 3: Moments and seasonality. Study 4: Moments and expiration.

**Chapter 5: Estimating Future
Volatility.** Measurement reliability. Model complexity and other issues.
Empirical studies of volatility (calculation of implied volatility). Study
1: Univariate historical volatility as predictor of future volatility (regression
to the mean, quadratic/nonlinear relationship, changing relationship with
changing volatility, straddle-based vs. standard future volatility, longer-term
historical volatility, raw data regressions). Study 2: Bivariate historical
volatility of future volatility (independent contributions, reversion to
long-term mean). Study 3: Reliability and stability of volatility measures.
Study 4: Multivariate prediction of volatility (using two measures of historical
volatility and three seasonal harmonics). Study 5: Implied volatility.
Study 6: Historical and implied volatility as related to future volatility
(regression results, correlational analysis, path analysis). Study 7: Reliability
of implied volatility.

**Chapter 6: Pricing Options
with Conditional Distributions.** Degrees of freedom (problem of excessive
consumption, curve-fitting, use of rescaling to conserve degrees of freedom).
Study 1: Pricing options using conditional distributions with raw historical
volatility. Study 2: Pricing options using conditional distributions with
regression-estimated volatility (analytic method, deviant call premiums,
other deviant premiums, non-deviant premiums). Study 3: Re-analysis with
detrended distributions. Study 4: Skew and kurtosis as additional variables
when pricing options with conditional distributions (effect on out-of-the-money
calls, out-of-the-money puts, in-the-money options, at-the-money options).
Study 5: Effect of trading venue on option worth (out-of-the-money options,
detrended distributions; at-the-money options, detrended distributions;
out-of-the-money options, no detrending). Study 6: Stochastic crossover
and option value (out-of-the-money, detrended distributions; out-of-the-money,
raw distributions; at-the-money options).

**Chapter 7: Neural Networks,
Polynomial Regressions, and Hybrid Pricing Models.** Continuous nonlinear
functions. Construction of a pricing function. Polynomial regression models.
Neural network models. Hybrid models. Study 1: Neural networks and Black-Scholes
(can a neural network emulate Black-Scholes? test of a small neural network,
test of a larger neural network). Study 2: Polynomial regressions and Black-Scholes.
Study 3: Polynomial regressions on real-market data. Study 4: Basic neural
pricing models. Study 5: Pricing options with a hybrid model.

**Chapter 8: Volatility Revisited.**
Study 1: Volatility and historical kurtosis. Study 2: Volatility and historical
skew. Study 3: Stochastic oscillator and volatility. Study 4: Moving average
deviation and volatility. Study 5: Volatility and moving average slope.
Study 6: Range percent and volatility. Study 7: Month and volatility. Study
8: Real options and volatility.

**Chapter 9: Option Prices
in the Marketplace.** Study 1: Standard volatility, no detrending. Results
(calls on stocks with 30 percent historical volatility and with 90 percent
historical volatility, puts on stocks with 30 percent historical volatility
and with 90 percent historical volatility). Conclusion (discussion of issues,
suggestions for further study).

**Conclusion.** Defining
fair value. Popular models and their assumptions (strengths and weaknesses).
Volatility payoffs and distributions. Mathematical moments (moments and
holding periods, moments and distributions, moments and day of the week,
moments and seasonality, moments and expiration date). Volatility (standard
historical volatility as an estimator of future volatility, the reliability
of different measures of volatility, developing a better estimator of future
volatility, implied volatility). Conditional distributions (historical
volatility: conditional distributions vs. Black-Scholes; regression-estimated
volatility: conditional distributions vs. Black-Scholes; detrended distributions:
conditional distributions vs. Black-Scholes; distributions and the volatility
payoff; skew and kurtosis as variables in a conditional distribution; conditional
distributions and venue; technical indicators as conditioning variables).
Using nonlinear modeling techniques to price options (neural networks and
polynomial regressions vs. Black-Scholes, strengths and weaknesses of nonlinear
modeling techniques, hybrid models). Volatility revisited (the impact of
historical skew, kurtosis, and historical volatility on future volatility;
using technical indicators in the prediction of future volatility). Option
prices in the marketplace.

**Bibliography and Index**

Copyright © 2005. Scientific Consultant Services,Inc.

Revised - 2005.02.26 Home Page: www.scientific-consultants.com

E-Mail Jeffrey Owen Katz, Ph.D.: jeffkatz@scientific-consultants.com

E-Mail Donna McCormick: donnamccormick@scientific-consultants.com

Phone: 631-696-3333

Fax: 631-696-3333

Snail-Mail: 20 Stagecoach Road, Selden, NY 11784 (USA)