markets01_lecture

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markets01_lecture.pdf
%A L. Ingber
%T Statistical Mechanics of Financial Markets (SMFM): Applications to Trading Indicators and Options
%R SMFM Lecture Plates
%I Lester Ingber Research
%D 2001
%O URL http://www.ingber.com/markets01_lecture.pdf

 COVER PAGE
CONTENTS-1
CONTENTS-2
MATHEMATICAL PHYSICS
Nonlinear Nonequilibrium Multivariate Stochastic Aggregation
Stochastic Differential Equation (SDE)
Partial Differential Equation (PDE)
Lagrangian Probability Distribution Function (PDF)
Path-Integral Riemannian Geometry
Statistical Mechanics of Financial Markets (SMFM) -- Microscopic Agents
SMFM-- Market Dynamics
Information
Transformations Without Ito Calculus
Intuitive Variables
Euler-Lagrange Variational Equations
Canonical Momenta Indicators (CMI)
NUMERICAL ALGORITHMS
Adaptive Simulated Annealing (ASA)
Hills and Valleys
Outline of ASA Algorithm
Numerical Path Integration (PATHINT)
Outline of PATHINT Algorithm
Mesh Limitations
Probability Tree (PATHTREE)
Standard Binomial Tree
Deficiency of Standard Algorithm to Order dt
Problems Generalizing The Standard Tree
Probability PATHTREE
Construction of PATHTREE
Direct Calculation of Probability
Numerical Derivatives of Expectation of Probability
Alternative First Derivative Calculation of Probability
PATHTREE vs PATHINT
Black-Scholes (BS) and Ornstein-Uhlenbeck (OU) Examples
APPLICATIONS TO INTEREST RATE PRODUCTS
2-Factor Interest-Rate Model
Lagrangian Representation
ASA Fits
Bond PDE/PATHINT
APPLICATIONS TO TRADING INDICATORS
S&P Interday Futures-Cash
Inner-Shell Dynamic Model
Outer-Shell Trading Model
Recursive ASA Fits
Tick Resolution CMI Trading
Intuitive Value of CMI
Multiple Local Minima
Use of CMI
Data Processing
Inner-Shell Optimization
Trading Rules (Outer-Shell) Recursive Optimization
CMI Neutral Line
Training -> Testing
Alternative Algorithms
Slippage
Money Management
Example: Data Used
Example: Derived CMI
Example: Long-Averaged Derived CMI
Main Features
APPLICATIONS TO OPTIONS
Eurodollar Volatility Modeling
Eurodollar Volatility of Historical Volatility
Eurodollar Volatility of Implied Volatility
Power-Law Model
Stochasticity: Volatility vs Exponent
Multi-Factor Volatility Model
x Market Indicators
PATHINT
PATHINT Two-Factor
BS vs CRR vs PATHINT
Portfolios of Options

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Lester Ingber <[email protected]>
Copyright © 2001-2012 Lester Ingber. All Rights Reserved.

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