Mak D.K Mathematical Techniques in Financial Market Trading

Singapore: World Scientific Publishing Company, 2006. - 322 p.
The present book contains much more materials than the author's previous book The Science of Financial Market Trading. Spectrum analysis is again emphasized for the characterization of technical indicators employed by traders and investors. New indicators are created. Mathematical analysis is applied to evaluate the trading methodologies practiced by traders to execute a trade transaction. In addition, probability theory is employed to appraise the utility of money management techniques. The book: identifies the faultiness of some of the indicators used by traders and accentuates the potential of wavelets as a trading tool; describes the scientific evidences that the market is non-random, and that the non-randomness can vary with respect to time; demonstrates the validity of the claim by some traders that, with good money management techniques, the market is still profitable even if it were random; and analyzes why a popular trading tactic has a good probability of success and how it can be improved.Log-Normal Distribution of Stock Market Data.
Tsallis Entropy.
Random Walk Hypothesis and Efficient Market Hypothesis.
Variance-Ratio Test.
Long-Range Dependence?
Log-Periodicity Phenomenological Model.
Omori Law.
Ideal Causal Trending Indicator.
Exponential Moving Average.
Butterworth Filters.
Sinc Function n = 2.
Sinc Function n = 4.
Adaptive Exponential Moving Average.
"Zero-lag" EMA (ZEMA).
Modified EMA (MEMA) with a Skip 1 Cubic Velocity.
Modified EMA (MEMA) with a Skip 2 Cubic Velocity.
Modified EMA (MEMA) with a Skip 3 Cubic Velocity.
Computer Program for Modified EMA (MEMA).
Causal Wavelet Filters.
Mexican Hat Wavelet.
Causal Mexican Hat Wavelet.
Discrete Fourier Transform.
Calculation of Zero Phase Frequencies.
Signal with Frequency π/4.
Signal with Frequency π/32.
Signal with Frequencies π/4 and π/32.
Limitations of Mexican Hat Wavelet Filters.
Instantaneous Frequency.
Calculation of Frequency ( 4 data points).
Examples using 4 Data Points.
Alternate Calculation of Frequency ( data points).
Example with a Frequency Chirp.
Example with Real Financial Data.
Example with Real Financial Data (more stringent condition).
Phase.
Relation between the Real and Imaginary Parts of the Fourier Transform of a Causal System.
Calculation of the Frequency Response Function H(w).
Example - The Two Point Moving Average.
Computer Program for Calculating H(w) and h(n) of a Causal System.
Example O(w) = -w/3.
Example O(w) = ASIN(w).
Derivation of HR(w) in Terms of HI(w) for a Causal System.
Causal High Pass Filters.
The Slope.
The Filter.
Filtering Smoothed Data.
The Filters.
Filtering Smoothed Data.
The Filters.
Filtering Smoothed Data.
The Filters.
Filtering Smoothed Data.
The Filters.
Filtering Smoothed Data.
Velocity and Acceleration Indicator Responses on Smoothed Data.
Frequency Response of a Convolution.
Frequency Response of a Skipped Convolution.
Skipped Exponential Moving Average.
Skipped Convolution and Downsampled Signal.
Velocity Divergence.
MACD Line.
MACD-Histogram.
MACD-Histogram Divergence.
Exponential Moving Average of an Exponential Moving Average.
Multiple Timeframes.
Long-Term Timeframe.
Multiple Screen Trading System.
Examples of a Trading System.
Triple Screen Trading system.
Test of a Trading System.
Money Management - Time Independent Case.
Probability Distribution of Price Variation.
Probability of Being Stopped Out in a Trade.
Expected Value of a Trade.
Experiment and the Sample Space.
Events.
Independent Events.
Trailing Stop-Loss.
Probability and Expected Value.
Total Probability and Total Expected Value.
Total Expected Value/Average Time.
Probability and Expected Value.
Total Probability and Total Expected Value.
Total Expected Value/Average Time.
Record-Keeping.
Money Management.
Probability Theory and Money Management.
A Coefficients of the Sinc Function with n = 2.
A Coefficients of the Sinc Function with n = 4.
A "Zero-lag" Exponential Moving Average.
A Modified EMA (MEMA) with a Skip 1 Cubic Velocity.
A Modified EMA (MEMA) with a Skip 2 Cubic Velocity.
A Modified EMA (MEMA) with a Skip 3 Cubic Velocity.
A Derivation of Frequency (4 points).
A Derivation of Frequency (5 points).
A Error Calculation of Frequency (4 points).
A Computer Program for Calculating Frequency.
A Computer Programs for Calculating Wave Velocity and Wave Acceleration.
A Quartic Velocity Indicator.
A Quartic Acceleration Indicator.
A Quintic Velocity Indicator.
A Quintic Acceleration Indicator.
A Sextic Velocity Indicator.
A Sextic Acceleration Indicator.
A Trailing Stop-Loss Program.
A Fixed Stop-Loss Program.