*The Business Professor*, updated February 10, 2020, last accessed October 20, 2020, https://thebusinessprofessor.com/lesson/amplitude-definition/.

### Amplitude Definition

Amplitude is a measure of a change in a variable over a period of time, it also measures the degree of difference between the extreme values of a variable. In the context of securities or asset. Amplitude is the measure of the difference in the price of a security over a period of time. There are different definitions of amplitude as used in different contexts, this term can be used on physics to measure displacement.

### A Little More on What is Amplitude

Generally, amplitude measures the movement of price from bottom to top (Peak) or from its wave cycle trough to the crest. Through this measurement, traders can determine the extent of the volatility of a security’s price. The positivity or negativity of the amplitude shows the level of volatility present.

The volatility of the price of security gives insight into the degree of risk entailed in the underlying security. When the amplitude is positive, it means the calculation is done from trough to peak (bottom to top), this is done when calculating bullish retracement in the market. On the other hand, when the amplitude is positive, a bearish retracement is being calculated.

### What Constitutes a Peak or Trough

Simply put, a peak is the highest price a security can reach during a period of time, while trough refers to the lowest amount a security’s price at that same time. A single security can have a different peak and trough at different periods. While the peak is associated with periods of the market boom, the trough is associated with periods of depression in the market. An accurate understanding of peak and trough is crucial to help us know how an amplitude functions.

### Determining Amplitude as Related to Peaks and Troughs

Amplitude is the measure of the difference between the midpoints of a peak and trough within a period of time. It finds out the displacement between the extreme ends of a variable, that is, the extent to which the midpoint of the peak and that of the trough are displaced. Usually, the midpoint of the peak and the midpoint of the trough signifies a zero point which means they can either make an upward movement (positive) or downward movement (negative). The midpoint of a security’s price is the mean price.

### Calculating Amplitude as a Formula

Amplitude is calculated differently depending on what retracement is being calculated. For bearish retracement, the formula for calculating amplitude is; c – b = a,

This formula should be used where b precedes c on the x-axis.

For bullish retracement, the formula is; b – c = a,

This formula should be used where c precedes b on the x-axis.

### Reference for “Amplitude”

https://www.investopedia.com › Trading › Trading Strategy

https://financial-dictionary.thefreedictionary.com/amplitude

https://amplitude.com/customers/financial-services

https://www.green-acres.fr/en/prog_directory_details-rf-155529.html

https://www.glassdoor.com › San Francisco

### Academics research on “Amplitude”

**[PDF]** Jump-diffusion stock return models in **finance**: Stochastic process density with uniform-jump **amplitude**, **Hanson, F. B., & Westman, J. J. (2002, August). Jump-diffusion stock return models in finance: Stochastic process density with uniform-jump amplitude. In ***Proc. 15th International Symposium on Mathematical Theory of Networks and Systems*** (Vol. 7).**

Modeling the stylized facts in **finance **through simple nonlinear adaptive systems, **Hommes, C. H. (2002). Modeling the stylized facts in finance through simple nonlinear adaptive systems. ***Proceedings of the National Academy of Sciences***, ***99***(suppl 3), 7221-7228.v**Recent work on adaptive systems for modeling financial markets is discussed. Financial markets are viewed as evolutionary systems between different, competing trading strategies. Agents are boundedly rational in the sense that they tend to follow strategies that have performed well, according to realized profits or accumulated wealth, in the recent past. Simple technical trading rules may survive evolutionary competition in a heterogeneous world where prices and beliefs co-evolve over time. Evolutionary models can explain important stylized facts, such as fat tails, clustered volatility, and long memory, of real financial series.

Power laws in economics and **finance**: some ideas from physics, **Bouchaud, J. P. (2001). Power laws in economics and finance: some ideas from physics.v**We discuss several models in order to shed light on the origin of power-law *distributions* and power-law *correlations* in financial time series. From an empirical point of view, the exponents describing the tails of the price increments distribution and the decay of the volatility correlations are rather robust and suggest universality. However, many of the models that appear naturally (for example, to account for the distribution of wealth) contain some multiplicative noise, which generically leads to *non-universal exponents*. Recent progress in the empirical study of the volatility suggests that the volatility results from some sort of multiplicative cascade. A convincing ‘microscopic’ (i.e. trader based) model that explains this observation is however not yet available. It would be particularly important to understand the relevance of the pseudo-geometric progression of natural human time scales on the long-range nature of the volatility correlations.

Quantum **finance**, **Schaden, M. (2002). Quantum finance. ***Physica A: Statistical Mechanics and Its Applications***, ***316***(1-4), 511-538.v**Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding securities and cash is taken as the basis of the Hilbert space of market states. The temporal evolution of an isolated market is unitary in this space. Linear operators representing basic financial transactions such as cash transfer and the buying or selling of securities are constructed and simple model Hamiltonians that generate the temporal evolution due to cash flows and the trading of securities are proposed. The Hamiltonian describing financial transactions becomes local when the profit/loss from trading is small compared to the turnover. This approximation may describe a highly liquid and efficient stock market. The lognormal probability distribution for the price of a stock with a variance that is proportional to the elapsed time is reproduced for an equilibrium market. The asymptotic volatility of a stock in this case is related to the long-term probability that it is traded.

Discovering structure in **finance **using independent component analysis, **Back, A. D., & Weigend, A. S. (1998). Discovering structure in finance using independent component analysis. In ***Decision Technologies for Computational Finance*** (pp. 309-322). Springer, Boston, MA.v**Independent component analysis is a new signal processing technique. In this paper we apply it to a portfolio of Japanese stock price returns over three years of daily data and compare the results obtained using principal component analysis. The results indicate that the independent components fall into two categories, (i) infrequent but large shocks (responsible for the major changes in the stock prices), and (ii) frequent but rather small fluctuations (contributing little to the overall level of the stocks). The small number of major shocks indicate turning points in the time series and when used to reconstruct the stock prices, give good results in terms of morphology. In contrast, when using shocks derived from principal components instead of independent components, the reconstructed price does not show the same results at all. Independent component analysis is shown to be a potentially powerful method of analysing and understanding driving mechanisms in financial time series.