Following the Crowd: Beginners Investors Guide to the Options Market

SMU Data Science Review SMU Data Science Review

Volume 7 Number 1 Article 7

Following the Crowd: Beginners Investors Guide to the Options Following the Crowd: Beginners Investors Guide to the Options

Market Market

Jeremy Dawkins

Southern Methodist University

, [email protected]

Alexy Morris

Southern Methodist University

, [email protected]

Jacob Gipson

Southern Methodist University

, [email protected]

Masoud Valizadeh

Northern Illinois University

, [email protected]

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Part of the Data Science Commons, and the Finance and Financial Management Commons

Recommended Citation Recommended Citation

Dawkins, Jeremy; Morris, Alexy; Gipson, Jacob; and Valizadeh, Masoud () "Following the Crowd: Beginners

Investors Guide to the Options Market,"

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: Vol. 7: No. 1, Article 7.

Available at: https://scholar.smu.edu/datasciencereview/vol7/iss1/7

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A warning and disclaimer to anyone expecting guaranteed rewards: this study does

not guarantee that someone will become wealthy from investing, but it will offer a

financial education tool to teach them how to invest their money.

Following the Crowd: Beginners Investors Guide to the

Options Market

Alexy Morris, Jacob Gipson2, Jeremy Dawkin3

Masoud Valizadeh4

Master of Science in Data Science, Southern Methodist University,

Dallas, TX 75275 USA

{jeremyd, alexym, gipsonj}@smu.edu

{[email protected]}

Abstract. While the options market may be intimidating for a beginner, having the right

tools can help improve the outcome of their investments. This project aims to develop a tool

that uses time-series analysis and forecasting to model the future demand of S&P 500 and

AAPL options contracts. The open interest of these contracts will be analyzed using various

models such as AR, ARIMA, Neural Networks, and VAR, along with the put-call ratio. The

goal is not to make buy or sell recommendations, but alert the user when money is flowing into

a security or index. Of all the models, the use of the ARMA model provides the best results for

predicting the open interest in contracts for these specific symbols.

1 Introduction

The world of financial opportunity has made way for individuals to take part and

make their fortune through investments, real estate, stock markets, options markets,

and many other ventures. Many individuals claim that participation in these ventures

requires wealth and success. However, this is not entirely true. Having the market

know-how can turn a small sum of money into a sizable profit with big rewards. This

holds true because everyday investors' awareness of their money helps them process

any potential risks and their possible yield results. When individuals can invest their

hard-earned money, diversifying their portfolio, it is safe to assume that they know

what they are doing. Why? Because of their experience in the financial market,

consistent investors can expand their portfolios. Future investors who want to invest

in the market are often left out, missing earnings that could help them.

One investment article state that "55% of Americans aren't investing…"

(Anderson, 2019, p. 1) because of investing ignorance, impatience with seeing a

profit, and fear. These factors deter individuals from placing their money somewhere

risky while waiting for it to grow. Most of the time, the easiest way to enter the world

of investing is either through the stock market, equity securities like Google and

Amazon, or indexes such as S&P 500 or DOW Jones. A minuscule amount of money

has the potential for gain within a certain period. When it comes to stock markets, one

must know what they are doing, who to invest in, when to invest, and how to keep up

with the current conditions of the American economy. There are even strategies used

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by investment firms or artificial intelligence advisors where they control or advise

individuals on which securities to invest in. An issue for someone with extra money

set aside in their savings account is that investing in the normal stock market takes too

long. Thus, many Americans who work normal jobs question why they should invest

in something that would take too long to see rewards.

Another issue preventing individuals from investing is a lack of education.

Financial Literacy is a plague for Americans only because there are few readily

available informational resources. American schools do not traditionally focus their

curriculum on finance. (Camberato, 2022, p. 1) Topics such as saving money,

calculating and filing taxes, or investing are left out of early education. When young

Americans attend college, many stay unaware of financial basics unless they are

business majors or decide to take extracurricular courses in business or finance.

Unfortunately, the gap between participation in this financially driven world and

comprehension of financial basics is growing. For example, when an individual gets

their first job and starts their career, one of the first onboarding tasks requires setting

up individual retirement accounts such as the Roth IRAs or 401ks. Many employees

complete these tasks with little understanding of personal investing; leading them to

teach themselves via the internet, friends, or other sources. One might mention that

the internet is accessible to all. However, it is difficult to scour through the time-

consuming and often complex subjects. The use of brokerage or investment firms

serves their purpose of helping individuals invest in the market. Still, with the many

vendors to choose from, the selection process can be overwhelming for some.

Another fear contributing to the lack of knowledge on investing is the mindset of

losing money due to a bear market or economic downturn. For example, during the

2007-08 financial crisis, the American market system took a downturn due to the

housing bubble's burst and mortgage crises. Simultaneously this resulted in people

losing their jobs, banks being in financial ruin, and even companies going bankrupt.

This led many to depend on individual savings or other income streams because the

market tanked, and Americans lost their money. Potential investors fear this repeating

and happening to them, but the fear lives mainly with the uninformed. Their lack of

skills in this specific area hinders them from making any money.

Despite these concerns from the public, some still consider venturing into

investments to expand their income streams. This research focuses on targeting

people interested in investing in the market but lack the market knowledge to

effectively participate. It also is focused on people who do not have time to consider

these strategies deeply. It is not openly discussed that a great beginner market to tap

into for beginner investors is the options market. The options market can be risky but

can supply multiple advantages over the typical stock market, leading to less initially

invested money and potentially greater gains. Bearing this in mind, this research aims

to provide the fundamentals of the options market and what can be done with an

option contract. An investor would not need to know the intricate details of the

options market besides the basic knowledge provided in this research paper. The

options market supplies many opportunities in which one can make money quickly

compared to the stock market in a short amount of time. Allowing one to predict

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whether security will go up or down based on the market and a set date, one could see

profit no matter how big or small.

To further discuss the detailed part of this research paper, one must know what a

choice is and what calls and puts are. "Options are contracts that give the bearer the

right - but not the obligation to either buy or sell an amount of some underlying asset

at a predetermined price at or before the contract expires." (Downey, 2022, p. 1)

Many brokerage firms and investment banks offer these to individual investors in a

manner like the stock market. Many retail investors would say that people should

spread out their portfolio with some investments in the stock market and some in the

options market to help with offsetting losses that one can gain, this is called hedging.

One can hedge with options to reduce the amount of risk they take at a reasonable

cost to the investor. The option contracts allow the investor to predict future price

events of securities. They supply two key types of options contracts. One is the call

option which "gives the holder the right, but not the obligation, to buy the underlying

security at the strike price on or before expiration. A call option will become more

valuable as the underlying security rises in price" (Downey, 2022, p.1). An example

of this is allowing one to bet on if the price of Apple will go up soon before the set

expiration date of the contract. The other important contract choice is the put option

which is "Opposite to call options. A put gives the holder the right, but not the

obligation, to instead sell the underlying stock at the strike price on or before

expiration" (Downey, 2022, p.1). Continuing with the previous example, the put gains

value as the underlying price falls for Apple. Investors and corporations make billions

of dollars annually just from predicting price moves throughout the year on different

securities.

This research will serve as an opportunity to bridge the gap between novice retail

investors and experts in investing in the options market. Many scholars who supply

insights on the stock market or options market only present information to people who

are already knowledgeable on these topics. This allows them to keep expert investors

well-informed and to create strategies they could use to beat or outperform the

market. No techniques will be provided for predicting the price of a stock or

evaluating options but instead, a toolkit that could be used to help novice investors

with when to step into the market. The toolkit supplies an opportunity and freedom

for any investor who wants to continue learning about the options market. This study

will use data science and machine learning to discuss investment opportunities for

corporations and experts. Examining open interest for these specific securities over

time will create a time series discussion about timing and opportunities novices can

invest in.

This research intends to inform that a non-expert investor can predict open

interest in any security at any time. Can a time series model forecast open interest for

any type of security using exploratory data analysis and research? By supplying an

opportunity for evidence to support this hypothesis, one can introduce novice retail

investors into a new world of diversifying one's portfolios or streams of income. This

research will be valuable to the field by extending its findings to leading experts,

investment firms, or brokerages to pour resources into advertising for more

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consumers. This could also present a toolkit to be used as applications, or apps,

developed by firms who wish to expand accessibility to novice investors and inform

them on how the options industry works. Doing this makes way for entry into the

world of finance without significant knowledge of options but increased confidence in

one's ability to invest money.

2 Literature Review

2.1 Financial Literacy

Financial Literacy is a global problem that can seem far-off and intangible. For this

paper, Financial Literacy can be defined as the ability to use financial knowledge to

obtain a specific money-related goal. For example, opening a high-yield savings

account to eventually pay for a predictable high-cost expense, including a house, car,

further education, and more. There are many ways to quantify financial Literacy, with

one of the most prevalent being the Big 3, a series of questions created by Lusardi and

Mitchell (2014) in their research on financial Literacy in a global setting:

1. Suppose you had $100 in a savings account and the interest rate

was 2% per year. After five years, how much do you think you would

have in the account if you left the money to grow?

A. More than $102

B. Exactly $102

C. Less than $102

D. Do not know

E. Refuse to answer

2. Imagine that the interest rate on your savings account was 1%

per year, and inflation was 2 % per year. After one year, how much

would you be able to buy with the money in this account?

A. More than today

B. Exactly the same

C. Less than today

D. Do not know

E. Refuse to answer

3. Please tell me whether this statement is true or false. 'Buying a

single company's stock usually provides a safer return than a stock

mutual fund.'

A. True

B. False

C. Do not know

D. Refuse to answer. (p. 499)

These questions serve as a benchmark to determine an individual's understanding

of interest rates, inflation, and stocks. The answer choices for each question allow us

to easily categorize an individual into truly literate, moderately literate, and others for

those who withdrew from every question.

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One of the biggest examples of the need for Financial Literacy is how retirement

plans have changed in recent years. "In many countries, employer-sponsored defined

benefit (DB) pension plans are swiftly giving way to private defined contribution

(DC) plans, shifting the responsibility for retirement saving and investing from

employers to employees" (Lusardi, 2019, p. 1). In addition, the commonality of

targeted at younger citizens has increased tremendously; student loans and short-term

loan services have become much more easily accessible. Although short-term loan

services can be avoided, student loans have become a standard for those attending

further education. Unfortunately, this massive shift has not been met with an equal

increase in financial Literacy. This shows that there is ample space and a definite need

to create more tools and resources to further the average person's understanding of

and comfort with all forms of finances, including but certainly not limited to the stock

market.

Thus, Financial Literacy experiences wide-scale boosts, and tools that help these

endeavors along must be vital. In this day and age, "Financial literacy can be seen as

an investment in human capital" (Amagir et al. l, 2017, p. 57), and such investments

lead to advancements in the financial field.

2.2 Individual Investors

The stock market is a slightly more tangible representation of a country’s economic

status, which means that one could argue that outside extreme circumstances a given

company’s stocks will remain constant quarterly. However, this assessment is

routinely proven false by the simple fact that human involvement is present in every

aspect of the marketplace. Investors can affect the market in a variety of ways; one of

the most common is done by what are called noise traders. These are individuals

taking part in the stock market without company backing or elevated levels of

experience. These traders are sensitive to outside influences, like the weather, news,

races, etc. Thus, it is possible to check these outside influences and gather them up

into a fear index that can predict when these noise traders are likely to sell off riskier

assets and the following, temporary, stock lowering. That said while the effect on the

stock market is always resolved around 20 days (about 3 weeks) after there is little

data showing that these same investors are coming back with the same consistency

(Kostopoulos et al, 2020). Looking at more experienced investors, usually with

company support, there is a higher degree of familiarity with the market that leads to

increased returns. Specifically, investors will typically see a higher and higher profit

margin as they grow in the industry. It is said that investors will see around a 20%

increase in profits from early portfolios to more recent ones (Nicolosi et al, 2009, p.

5). From this standpoint a machine learning model leveraging the knowledge of these

experienced investors would show similar profits and on average they did. Of course,

the limitations here are the need for a steady stream of data sourced from these

individuals (Pagliaro et al, 2021, p. 3). To get around this one can instead forget the

investor insights and create a model purely using market data both old and new. By

focusing on a single index, for instance the S&P 500, one can easily compare a

variety of models and thus decide the best strategy for predicting the stock market.

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The best is a supervised time series model (Soni et al, 2022, p.4). This paper will

continue from the ideas and strategy used here to create a more ideal solution. In this

paper, the focus will be on using the knowledge of novice and experienced investors

in more easily understood time series models to give everyday noise traders a solid

ground into more intricate stock strategies.

2.2 Using Machine Learning Techniques to Generate Returns in the Stock

Market

From historical data to 8-k filings, never has there been a time where more

information has been available to the average retail investor. With increasingly widely

available and real-time financial data, various machine-learning techniques have been

used to improve profits in the stock market. Sakarwala created a predictive model on

whether a stock moved up, down, or sideways based on the content of a

corresponding 8-k filing. Twenty thousand filings of S&P 500 companies were pulled

from the SEC (Securities and Exchange Commission) EDGAR website and were

combined with corresponding historical price data. The text was preprocessed, and

The Stanford NLP Wikipedia 2014 + Gigaword 100 dimensions were chosen for pre-

trained word embeddings under the assumption that it would carry information for

specialized, industry-specific words found in the texts since it was trained from the

Wikipedia corpus (Sakarwala et al., 2019, p.11). They then compared various deep

learning techniques (Multi-Layer Perceptron, Convolutional Neural Networks, and

Recurrent Neural Networks) in their ability to predict the stock's price action based on

the contents of the 8-k. They found that RNN (Recurrent Neural Networks) and RNN-

CNN performed the best. Now specifically about the options market, many studies

have been completed about using machine learning to perfect an options trading

strategy. Žabčić-Matić's paper looked at the use of neural networks to predict whether

the price of a stock will move, within the next trading day, by more or less than the

cost of its associated straddle option spread, with the expiry date set to be the next

trading day (Žabčić-Matić, 2019, p. 1). The stocks that were studied were the

following companies: Apple, IBM, Microsoft, Intel, Cisco, Qualcomm, Walmart,

General Electric, Goldman Sachs, and American Express. Many features were used

along with obvious ones like open, close, high, and low prices and daily volumes like

on-balance volume, accumulation/distribution line, and MACD. The results were

alarmingly good. The models did produce consistent profits and only very rarely

incurred a loss (Žabčić-Matić, 2019, p. 1). This shows that machine learning can lead

to profitable outcomes for the user, even in a volatile environment like the options

market.

Zeng explored using machine learning to predict the best timing of exercise

options. Specifically, they used a Q-learning algorithm to consider the early exercise

opportunity of American possibilities as a potential profit-generating source (The Q-

learning algorithm has two stages, an optimization, and an evaluation stage. In the

optimization stage, an iterative progressive hedging algorithm is used to find all

options' weights and exercise time at each time, where the Q-values are approximated

by regression (Zeng, 2017, p. 50). In the evaluation stage, real-time trading is used to

refine when to exercise the options for each simulated sample path (trajectory) given

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the weights from the optimization stage (Zeng, 2017, p. 54). In one of the evaluation

algorithms, they changed the Least Square Monte Carlo algorithm to evaluate their

performance in discovering the exercise time. Their model was successful because the

algorithms outperformed the LSMC about the utility gap from best and certainty

equivalent of return. This further proves that machine learning is beneficial in creating

profit in the options market.

Not only in the United States market that is being predicted but similar machine

learning algorithms have been used to predict across the world. Using machine

learning, Zhang and company studied market trends and prices in the Chinese stock

market. (Zhang et al., 2018, p. 54). They analyzed the Shanghai Stock Exchange

(SSE) Index stocks to decide to create a model to predict profitable patterns.

Techniques such as support vector machines, random forest, Naïve Bayes classifier,

and neural networks are compared to decide which model predicted future data using

the scoring metric of accuracy. From their conclusion, the neural network

outperformed all the other models in considering patterns in the index compared to

other deep learning techniques.

2.3 ARIMA/ML Forecasting Modeling

Investment managers are always looking forward to the options market. That way,

they are prepared and can perfect a strategy to make money regardless of the current

market. In the aftermath of the 2008 financial crisis data, the Volatility Index (VIX)

outlook was trending downwards. An S&P 500 index options database involved

43,014 calls and 38,784 put premiums for 81,798 options traded on the CME (Rostan

et al., 2020). The calls and puts were collected over 60 months from January 2009

through December 2013. The strategy was to examine how an autoregressive

integrated moving average (ARIMA) model can be used to forecast calls and put

options with a comparison of the typical generalized autoregressive conditional

heteroskedasticity (GARCH) model. This paper only focused on European call-and-

put options contracts. After careful evaluation and exploratory analysis of the

contracts, the ARIMA model that proved to have impressive results was the ARIMA

forecasting model. When looking at the data, the researchers broke the data into two

pieces of calls and put and used ARIMA modeling techniques on them. From the

discovery, they could generate forecasts of the S&P 500 Composite Index obtained

from the ARIMA (1,1,1) model. When this is done, an options strategy is used,

allowing the investor to decide which direction they would like to go depending on

their call or selected choice. The ARIMA forecasting results in a being a much better-

produced result compared to the forecasting using the GARCH (1,1) model. The

authors assessed that there is more profit with call than put options when the economy

is in a bear market. They were able to see the intrinsic value of puts decrease (Rostan

et al., 2020, p. 4). Their research used the ARIMA model for forecasting calls and put

options to assess if dollar profit can be made based on undervalued or overvalued

performances. This strategy can be used today and improve on further research in a

bear market and discuss the feature importance of sentimental analysis. Alotaibi

discovered that an ARIMA (0,1,1) contributed to forecasting prediction returns for the

stock market (Alotaibi, 2022, p. 7). They examined the Willis Towers Watson

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company spanning from 2010 to 2016 and compared multiple linear regression and

ARIMA. With the S&P 500 Index being a popular security to examine, Sun studied

this index with an ARIMA and ETS model close price (Sun, 2020, p. 10). An ARIMA

(2,1,3) is the best model fitted using the year 2005 to 2014, which succeeded in

having a success of short-term predictions. There is the belief that even this current

model can be improved using deep learning techniques or hybrid models when

modeling the S&P 500 Index close prices.

Hedge fund managers examine VIX Futures due to the forecasting of predicting

market volatility around a certain time. This allows the managers to set up their

potential strategies to attack the market by investing. Hosker looks at the VIX Futures

forecasting using machine learning, comparing three existing financial models to six

machine/deep learning supervised regression methods. These six models generated

compared to the financial models will be analyzed and determined to present the

highest results showing lower mean absolute error (MAE), higher explained variance,

and higher correlation (Hosker, 2019, p. 3). To decide the best model, an accuracy

matrix was generated for every model displaying better overall accuracy.

2.4 Time Series Analytics and Deep Reinforcement Learning in Portfolio

Management

With so many people and corporations investing in the stock market, they hold

various securities in their portfolios that require management. Some would consider

stocks, options, ETFs, and bonds serious investments. For someone to see substantial

profit with their portfolio, managing these accounts requires a good knowledge of

markets and periodic adjustment of assets in the account (Chavin et al., 2021, p. 2).

With public market exchanges, individuals who want to invest in the market and have

limited assets are not afforded the same investment guidance level as those with

wealth managers supplying them with advice. People use many portfolios and

investment advisor tools to try to close the gap in smarter investing. With these

advisor tools being automated to an extent, one just needs to put their money in based

on personal preference and sit back and watch the artificial intelligence (AI) advisor

suggest securities for you automatically. Chavin's paper's sole focus is to use the

success of the AI/ML stock portfolio trade management research to date (Chavin et

al., 2021, p. 2). The portfolio management advisor implements various data science

techniques. This paper focuses on reinforcement learning (RL) algorithms (Q-

Learning & Policy Optimization) which use time series analysis. Investment firms are

always trying to improve their algorithms, allowing the advisor to make wiser

decisions so that the retail investor sees adequate results. Focusing on the RL

algorithm in advising allows the algorithm to learn and adjust its behavior while

interacting with a live environment. Many factors affect an economic influence that

the advisors consider, which is modeled using the Markov Decision Process (MDP).

This process uses a mathematical framework that helps with the decision-making of

economic influences of policy, war, supply, demand, etc. The data prepared in this

paper utilizes the DOW Jones Index using investment options DOW 30-day multi-

stock trading, DOW electronic trading fund single stock trading, and lastly, the DOW

30 portfolio rebalancing trading. An analytical approach is taken here, with models

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generated using the RL algorithm and presented with results that improve the

portfolio managers' advisor strategies. The RL approach generated multiple models

that can be averaged out on the dataset, which is considered the ensemble method.

They discovered that MDP and RL proved reputable evidence in the stock evidence in

the stock trading decision models in selecting which proper investment options to

select. The ensemble method produced the highest Sharpe Ratio and cumulative

portfolio final balance in their findings. This paper also contains a thorough use of

time series that contributed to a part of the selection environment and MDP. With the

advisor, this paper could use AI/ML techniques that can supply future aid to retail

investors who do not have time to manage their own investments or are not

knowledgeable compared to the wealthy and corporations.

This paper will use previous research knowledge to focus on future investors. A

time series and multi-layer perceptron model will be used to analyze SPX and AAPL

open interest and forecast to predict future interest. Allowing someone to see how

open interest is moving throughout the year can give investors insight into what is

happening. The aim is to inform and stress the importance of allowing people who

want to invest in options an opportunity to do so despite their feelings that there is a

higher barrier to entry.

3 Methods

3.1 Background of Models

This research will use several diverse models to describe the open interest data for

SPY and AAPL: Autoregressive (AR), Moving Average (MA), ARMA, and ARIMA.

Stationary time series tend to be described by AR, MA, and ARMA models, while

nonstationary time series tend to be described by ARIMA models. It is safe to predict

that the type of model that best describes open interest data would be an ARIMA

model, as it is known that open interest is not stationary as the mean depends on the

window of time being observed.

The general form of an ARIMA (p, d, q) model is:

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Where fp are the autoregressive constants, qq are the moving average constants, Xt

is the value of the time series at time t, and at is the white noise component at time t.

The values of p and q indicate the number of autoregressive and moving average

constants are present in the model.

3.2 Data

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The data will be attained from The Options Clearing Corporation's website

(theocc.com), which is a clearing house that is the world's largest equity derivatives

clearing organization. The OCC provides data about the market integrity for options,

futures, and securities lending transactions.

A hypothesis testing will be conducted modeling open interest contract data using

the index SPY and the equity security Apple (AAPL). The hypothesis testing will

determine if the model is stationary or not using time series examining data provided

from the beginning of the year January 4, 2022, which is the first trading day of the

year through August 31st, 2022. A model will be created using a time series that will

prove the ability to forecast open interest for this upcoming fall of 2022 and winter of

2022. This forecasting will contribute to the ability of individual investors to where

money is being placed in the market during certain trading quarters that can be

beneficial to the investor.

An evaluation of different ARMA and ARIMA models that will be tested on the

data provided and provide detailed analysis with the equations provided. Creating a

time series model will be conducted using a five traditional step method, with step

one doing data preparation or preprocessing. A full examination of time series

decomposition, modeling, forecasting and the last is model evaluation.

3.3 Methods

The dataset that was used was open interest and put/call ratio data dating from

01/26/2021 to 09/22/2022 for both SPY and APPL tickers. Data until 07/13/2022 was

used to train our models, while the rest of the data was used to evaluate performance.

The cutoff was selected to evaluate predictions 50 trading days out. The primary

objective of the project was to model open interest, so the initial approach was to

analyze both tickers in a traditional univariate fashion before including the put-call

ratio as a potential regressor. This was done to establish the performance of the

univariate models as a baseline for comparison with more advanced models later.

Upon initial review of the realization plot of the SPY open interest data, wandering

behavior was observed. The lack of constant mean, independent of the section of the

time series, suggests that the series is not stationary. On the other hand, the AAPL

open interest data appeared to be stationary, with a constant mean and constant

variance that were independent of the time period, and the autocorrelation plot

showed signs of dampening. Although seasonality was suspected from the

autocorrelation plot, it was not confirmed through an overfitting test. For the sake of

completeness, both stationary and non-stationary models were explored as a single

realization is not always indicative of a variable’s stationarity.

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Figure 1: Realization of SPY open interest data from 01/26/2021 to 07/13/2022

Figure 2: Realization of AAPL open interest data from 01/26/2021 to 07/13/2022

First non-stationary models were explored. The wandering behavior was removed

from the data by first differencing. The aic.wge() function from the tswge package

was used to estimate the number of Autoregressive (AR) and Moving Average (MA)

components in the model. Both AIC and BIC were used as selection criteria to

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achieve the best fit while also placing value on model simplicity. For the SPY open

interest data, the same 3 models were selected using both criteria: ARIMA (1,1,1),

ARIMA (3,1,2), and ARIMA (4,1,1). The same strategy was applied to the AAPL

open interest data, and the following models were selected: ARIMA (5,1,6), ARIMA

(9,1,5), and ARIMA (1,1,1). The AR and MA components were estimated and

forecasted. Model performance was evaluated using 5, 10, and 50-day Mean Squared

Error (MSE) values, along with rolling window root mean squared errors (RWRMSE)

of the same window lengths.

Open interest data was also modeled using stationary models. A similar strategy

was taken except tTe aic.wge() function was used on non-differenced data. For SPY,

the AIC and BIC selection criteria favored an AR (2,0) and ARIMA (1,1), with

ARMA (1,2) as the only other model appearing on both lists of candidates. For

AAPL, the selected models were ARMA (6,8), ARMA (4,7), and AR (5). Forecasts

using these models and the same performance metrics were generated and can be seen

in the results.

Next, neural network models were fitted and compared to the traditional univariate

time series models. Multiple iterations were created for both SPY and AAPL data by

specifying lags, differencing order, and different numbers of hidden nodes, as well as

different selection strategies. The impact of daily put-call ratio on prediction accuracy

was also explored as a possible regressor.

Lastly, the introduction of the Vector Autoregressive (VAR) model is used to

investigate the relationship between the put-call ratio and open interest. The model is

intended to see how the two variables relate to each other or influence each other in

some way. The put-call ratio and open interest were combined to form a vector, which

was then modeled to fit an AR model. After determining the selected AR model, the

parameters were then used in a VAR model to determine the overall equation, which

produced a VAR (1). The two features, open interest, and put-call ratio were given a

weighted value by adding them together. From analyzing these two features, the

model produced a VAR (1) model, which was then used to forecast using the same

horizon as the previous models.

4 Results

SPY Open Interest

Model

Day

MSE*

day

MSE*

day

MSE*

5 day

RWRMSE

10 day

RWRMSE

50 day

RWRMSE

Ljung-Box test p-

values

K = 24

K = 48

SMU Data Science Review, Vol. 7 [], No. 1, Art. 7

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ARIMA

(1,1,1)

0.844

1.31

1.04

4.21

4.94

5.42

0.0678

ARIMA

(4,1,1)

0.987

1.39

1.06

4.33

5.11

5.48

0.274

0.229

ARIMA

(3,1,2)

0.844

1.26

1.03

3.70

4.44

4.97

0.071

0.0643

ARMA

(1,1)

0.673

0.604

1.24

2.49

2.72

3.01

0.11

0.065

ARMA

(1,2)

0.682

0.604

1.24

2.50

2.72

3.02

0.095

0.063

AR (2)

0.678

0.603

1.24

2.50

2.72

3.02

0.12

0.077

Univariate

0.631

0.596

1.21

2.49

2.71

3.02

N/A

Multivariate

0.636

0.624

1.17

N/A

* X 10

**X 10

Figure 7: Summary of performance metrics for candidate models for SPY Open

Interest

All non-neural network models failed to reject at the 95% confidence level when

conducting the Ljung-box test on the residuals, indicating that the models do not show

a lack of fit. Only the ARIMA (1, 1, 1), ARIMA (4, 1, 1), and ARMA (1, 2) failed to

reject at a 90% confidence level using two different maximum lags (K). The

stationary models outperformed the non-stationary candidates significantly in all

measures except for the 50-day MSE. In the end, the ARMA (1, 1, 1) model was

selected as the top performing univariate model, as it scored the best or second best in

all 6 metrics and passed the Ljung-box test at the 95% confidence level. The model

can be seen below:



  







 







  







where 



    



(3)

The top performing neural network (NN) model was made up of 5 hidden nodes

and one input, a univariate lag of 1. It can be seen below:

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Figure 3: $SPX Multi Layered Perceptron model diagram

It performed similarly or slightly better than the previous AR (2) model in all

metrics. Another NN model was trained using the put-call ratio data, but it did not

improve performance and, in fact, the 10-day MSE worsened.

AAPL Open Interest

Model

5 day

MSE

day

MSE

day

MSE

5 day

RWRMSE

10 day

RWRMSE*

50 day

RWRMSE

Ljung-Box test p-

values

K = 24

K = 48

ARIMA

(5,1,6)

3.06

4.77

7.22

1.32

1.57

2.06

0.038

0.35

ARIMA

(9,1,5)

2.46

4.80

6.46

1.19

1.39

1.92

0.38

0.72

ARIMA

(1,1,1)

4.65

4.79

8.15

1.23

1.37

1.65

0.0032

0.0027

ARMA (6,8)

3.06

7.84

6.49

0.95

1.01

1.14

0.46

0.79

ARMA (4,7)

2.56

7.34

6.21

0.95

1.01

1.15

0.77

0.89

AR (5)

3.52

7.38

6.51

0.89

0.96

1.09

0.70

0.67

Univariate

3.27

6.28

6.44

0.87

0.94

1.08

N/A

Multivariate

3.63

4.61

7.30

N/A

* X 10

** X 10

Figure 4: Summary of performance metrics for candidate models for AAPL Open

Interest

SMU Data Science Review, Vol. 7 [], No. 1, Art. 7

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The Ljung-Box failed to reject all the models at a 95% confidence level except for

the ARIMA (1,1,1) model, which was eliminated from consideration. The non-

stationary ARIMA models all outperformed the other models in the 5 and 10 day

MSE scores, but underperformed in the other 4 metrics. The ARMA (4, 7) model had

a very high 10 day MSE score, but the low 5 day MSE score in conjunction with the

lowest RWRMSE scores gave us the most confidence in selecting it as the best

performing non-neural network model. The equation for the model is shown below:



    



 



 









 



 



    



 



 



 



 



 









where





    



(4)

The univariate neural network model that had the best performance had 5 hidden

nodes and 2 inputs, univariate lags at 1 and 4. Its performance was an improvement

over the AR (5) model in all four metrics. A diagram of the model can be seen below:

Figure 5: $AAPL Multi Layered Perceptron model

Unlike the SPY neural network model, incorporating put-call ratio as a regressor

significantly improved the 10-day MSE, but also increased the 5 and 50 day MSE.

A Vector Auto-Regressive (VAR) model was created for SPY and AAPL put-call

ratio. This is a widely used measurement to understand how the equity or index is

moving and to predict if there will soon be a bull or bear market. A training and test

set is created to train the model and test its forecasting prediction. With the VAR

model, the interrelationships between open interest and put-call ratio are considered to

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use all variables. The correlation between variables is leveraged to improve fitting and

forecasting.

There is a relationship between open interest and put and call options that

influences investors to buy or sell certain contracts. A cross-correlation between the

put-call ratio and open interest for SPY is shown:

Figure 6: Autocorrelation Function of PCR and Open Interest for SPY

As shown in the graph, the PCR and the open interest of SPY produced the greatest

autocorrelation at lag 1, with lag 3 closed behind. The VAR select process,

considering a maximum lag is 3, was used. The VAR selects used the AIC, which

picked lag 3, and the BIC picked lag 1. To reduce the number of parameters, the BIC

selection was used, and the parameter estimation is created by considering the lag at

1. A summary of the VAR model produced the following equation:

        (5)

The forecasting of the last 50 dates of options trading is then used to display how

well the model is performing on the test set. The forecast of the VAR (1) model is

shown, displaying its performance of future dates.

SMU Data Science Review, Vol. 7 [], No. 1, Art. 7

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Figure 7: Forecast of the VAR Model for SPY

Then RMSE for the model came out to be around 0.33, which is small and suggests

that the model did a decent job at predicting the put-call ratio.

A VAR model was then examined with similar settings but with the AAPL equity.

The cross-correlation of the PCR and the open interest was analyzed in this equity.

From the chart below, there appear to be significant differences around lag – 2 and

around lag 16.

Figure 8: Autocorrelation Function of PCR and Open Interest of AAPL

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The maximum lag to capture any of the trading days is lag 20. Considering the

increase at lag 16, the AIC selects a lag of 5, and the BIC selects a lag of 1. To

minimize the parameters of the model, the BIC selection of lag 1 was used. The

equation for the VAR model with lag 1 is shown below:

         (6)

The RMSE from the prediction forecast of the last 50 dates was compared to

what the VAR model produced, resulting in an RMSE of 0.38. The testing set of the

last 50 dates was close to what was predicted.

A prediction of the last 50 dates is used and plotted with the training data, as shown

below:

Figure 9: Forecast of the VAR of AAPL

5 Discussion

5.1 Discussion

The results discovered in this report show that the ability to forecast open interest

is immense. It could provide insight into how the market is trending day-to-day and

SMU Data Science Review, Vol. 7 [], No. 1, Art. 7

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the possibility of predicting what comes next. Since the options market constantly

moves up and down based on trends or business, and many outside influences, our top

performing models for each ticker displayed accurate results in predicting the

forecast. The 10 and 50-day forecasts for each ticker using their corresponding top

performing, non-neural network model can be seen below:

Figure 10: 10-day forecast for $SPX Open Interest using ARMA (1, 1) model

Figure 11: 50-day forecast for $SPX Open Interest using ARMA (1, 1) model

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Figure 12: 10-day forecast for $AAPL Open Interest using ARMA (4, 7) model

Figure 12: 50-day forecast for $AAPL Open Interest using ARMA (4,7) model

We can see in our foreasts that our short term forecasts are more valuable than our

long term (50 day) forecasts. The short term (10 day) forecasts mimic the behavior of

the open interest data, while the 50-day forecast just converges to the mean open

interest value. This makes conceptual sense as what we know today can make better

predictions for tomorrow, but 50 days out would not be helpful in this case due to the

nature of the markets and the lack of knowledge about what may happen in the short

term. The uncertainty of these predictions is compounded the longer the time horizon

is for the predictions. The short-term look into the future is usually the best, allowing

one to be a proactive member of the market, rather than just having a contract expire.

The SPY and AAPL symbols move differently from each other since the SPY

represents the S&P 500, which combines multiple companies from different

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industries, whereas AAPL is just one technology company. Apple is a very volatile

company, so its open interest contracts are abundant and constantly changing daily.

The SPY contract open interest contracts tend to vary based on any market impact,

which could change open interest drastically.

A Vector Autoregressive model is examined to see if the put-call ratio somehow

correlates to open interest. PCR does have and had in determining how options are

moving from day to day, but the VAR model did not show accurate results when it

came to predicting open interest. From this aspect, PCR is useful as a tool alongside

open interest. With PCR, one could see if more puts or calls are being used for certain

symbols, they are interested in investing in. The use of open interest can be used as a

tool and a guide for new investors as well as people who want to invest more who try

their hand at options trading. With this tool, a possible investment company that has

mobile applications or trading platforms could provide a tool like this to be of service

to attract newcomers.

5.2 Ethical Discussion

This research is believed to not contain any violations of ethical standards imposed

on the paper by the affiliated institutions. The data used to create the previously

discussed models was obtained through legal channels and does not contain any

information that can be regarded as outside of the public domain. For full

transparency, the specific data used here was acquired from a specific company's

database, but the exact same information can be gained from a multitude of publicly

accessible sources.

That said, the models and any results-based discussion presented in this research

paper are not intended to be taken as actionable recommendations. This is strictly

intended as an educational tool, and the authors, nor any affected institutions, can be

held responsible for any effects of implementing this work.

Lastly, because of the nature of this research paper, it does not violate any ethical

standards set by the financial industry. Specifically, the paper is not susceptible to

common financial ethical dilemmas such as insider trading, conflicts of stakeholder

interest, or improper investment management.

6 Conclusion

Overall, the ARMA model provided outstanding results on the S&P 500 (SPY) and

Apple's (AAPL) symbols. With contracts, there are expiration dates attached to them,

so depending on the investor's intention, it can be monumental. This provides a

different aesthetic not only to them but allows one to potentially make money at a bit

of a faster pace than traditional stocks. This also introduces investors to help alleviate

risks in their portfolios and not keep all their money in one venture. The models used

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here are just the beginning, and other models could prove to be a bit more accurate.

One could continue this work to possibly look at Long Short-Term Memory or

Convolutional Networks as well. One could also advance this research by taking into

consideration sentiment analysis as well. The market does not just thrive on numbers

but many outside influences, so other factors could be added to the data to emphasize

these features.

The market, in general, is very difficult to navigate and predict due to these factors,

so the challenge itself of looking at non-stationary models comes into play. Other

tools could be used in hand with open interest and the put-call ratio as well, which

could benefit in predicting. The ability to educate people in financial literacy and

provide an avenue for them to learn about other investing options is important. As

technology continues to improve, many things will begin to become more

streamlined, which could indeed help people catch up and be active players.

References

1. Alotaibi, R. (2022). Arima model for stock market prediction. 2022 8th International

Conference on Computer Technology Applications.

https://doi.org/10.1145/3543712.3543723

2. Amagir, A., Groot, W., Maassen van den Brink, H., & Wilschut, A. (2017). A review

of financial-literacy education programs for children and adolescents. Citizenship,

Social and Economics Education, 17(1), 56–80.

https://doi.org/10.1177/2047173417719555

3. Anderson, J. (2019, October 14). This is why 55% of Americans aren't investing.

GOBankingRates. Retrieved October 31, 2022, from

https://www.gobankingrates.com/investing/strategy/this-is-why-55-of-americans-

arent-investing/

4. Camberato, J. (2022, October 12). Council post: Should schools teach

financial literacy classes? Forbes. Retrieved December 1, 2022, from

https://www.forbes.com/sites/forbesfinancecouncil/2022/10/11/should-

schools-teach-financial-literacy-classes/?sh=7be75a8d4633

5. Chavan, S., Kumar, P., & Gianelle, T. (n.d.). Intelligent Investment Portfolio

Management using time-series analytics and deep reinforcement learning. SMU

Scholar. Retrieved September 18, 2022, from

https://scholar.smu.edu/datasciencereview/vol5/iss2/7/

6. Downey, L. (2022, August 23). Essential Options Trading Guide. Investopedia.

Retrieved October 31, 2022, from https://www.investopedia.com/options-basics-

tutorial

7. Faulkner, A. (2021). Financial Literacy around the world: What we can learn from

the national strategies and contexts of the top ten most financially literate nations.

The Reference Librarian, 63(1-2), 1–28.

https://doi.org/10.1080/02763877.2021.2009955

8. Hosker, J., Djurdjevic, S., Nguyen, H., & Slater, R. (n.d.). Improving VIX futures

forecasts using machine learning methods. SMU Scholar. Retrieved September 18,

2022, from https://scholar.smu.edu/datasciencereview/vol1/iss4/6/

SMU Data Science Review, Vol. 7 [], No. 1, Art. 7

https://scholar.smu.edu/datasciencereview/vol7/iss1/7

9. Kostopoulos, D., Meyer, S., & Uhr, C. (2020). Google search volume and individual

investor trading. Journal of Financial Markets, 49, 100544.

https://doi.org/10.1016/j.finmar.2020.100544

10. Lusardi, A. (2019). Financial Literacy and the need for financial education: Evidence

and implications. Swiss Journal of Economics and Statistics, 155(1).

https://doi.org/10.1186/s41937-019-0027-5

11. Lusardi, A., & Mitchell, O. S. (2014). The economic importance of Financial

Literacy: Theory and Evidence. Journal of Economic Literature, 52(1), 5–44.

https://doi.org/10.1257/jel.52.1.5

12. Nicolosi, G., Peng, L., & Zhu, N. (2009). Do individual investors learn from

their trading experience? Journal of Financial Markets, 12(2), 317–336.

https://doi.org/10.1016/j.finmar.2008.07.001

13. Pagliaro, C., Mehta, D., Shiao, H.-T., Wang, S., & Xiong, L. (2021). Investor

behavior modeling by analyzing financial advisor notes. Proceedings of the Second

ACM International Conference on AI in Finance.

https://doi.org/10.1145/3490354.3494388

14. Rostan, P., Rostan, A., & Nurunnabi, M. (2020). Options trading strategy based on

ARIMA forecasting. PSU Research Review, 4(2), 111-127. 10.1108/PRR-07-2019-

0023

15. Sakarwala, M. A., & Tanaydin, A. (n.d.). Use advances in Data Science and

computing power to invest in stock market. SMU Scholar. Retrieved September 18,

2022, from https://scholar.smu.edu/datasciencereview/vol2/iss1/17/

16. Soni, P., Tewari, Y., & Krishnan, D. (2022). Machine learning approaches in stock

price prediction: A systematic review. Journal of Physics: Conference Series,

2161(1), 012065. https://doi.org/10.1088/1742-6596/2161/1/012065

17. Sun, Z. (2020). Comparison of trend forecast using Arima and ETS models for

S&P500 Close Price. 2020 The 4th International Conference on E-Business and

Internet. https://doi.org/10.1145/3436209.3436894

18. The Options Clearing Corporation. (n.d.). OCC - the Foundation for secure markets -

theocc.com. Retrieved September 19, 2022, from https://www.theocc.com/.

19. Zabcic-Matic, T. F. (2019). One Step Back, Two Steps Forward - a Machine

Learning-Powered Options Trading Strategy (thesis). Retrieved September 18, 2022,

from https://dash.harvard.edu/handle/1/37364632.

20. Zeng, Y. (2017). Machine Learning in Option Markets Available from Dissertation

Abstracts International

http://www.pqdtcn.com/thesisDetails/A3ABA5AA9895B956AF8603F237954168

21. Zhang, C., Ji, Z., Zhang, J., Wang, Y., Zhao, X., & Yang, Y. (2018). Predicting

Chinese stock market price trend using machine learning approach. Proceedings of

the 2nd International Conference on Computer Science and Application Engineering

- CSAE '18. https://doi.org/10.1145/3207677.3277966

Appendix

Use if needed for additional information

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