Hi everyone, this is Rob. I'm a senior systems developer, and I'm also working on a second master's degree at Tufts University in mathematics, after completing one in computer science. This will be my third degree from Tufts overall, as I also completed my undergraduate degree in mathematics here. I have been auditing graduate courses in economics and philosophy (spring 2025).
As an undergraduate, I was focused on pure mathematics, also spending several years in Tufts' Russian department with the intention of studying the works of Russian mathematicians in analysis and topology, and in 2015 I published a paper in number theory on p-adic dynamical systems, A p-adic Perron-Frobenius Theorem. I also enjoyed set theory, type theory, category theory, and logic.
I am now focused on computer science–implementating algorithms for efficient systems operations and machine learning–and applied mathematics–the foundations of machine learning and financial analysis. This site below contains a list of resources I've been compiling on financial analysis, quantitative methods, and automated trading. Let me know if you're interested in collaborating.
A lot of what happens at the hedge funds doing quantitative analysis is quite secretive, but the "word on the street" (Wall Street) is that Hidden Markov Models are quite useful in modeling finance trends. I am hoping to work on making some finance models more accessible, including strategies for online and semisupervised learning algorithms, while keeping some of the code I develop still a secret between my collaborators. Here is some published literature on portfolio analysis and hedging, and see the below section for more recent research.
- For a modern guide to technical analysis, take a look at John Murphy's Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications (1999).
- Darrell Duffie wrote a widely referenced 2001 book on Dynamic Asset Pricing Theory, as well as a 2002 survey of Intertemporal Asset Pricing Theory.
- Tufts President Sunil Kumar, who told me about the above book at a February 2025 Hackathon, has a background in probability theory and published a 2006 paper on Multidimensional portfolio optimization with proportional transaction costs.
This is primarily research I encountered at JMM 2025.
- Predicting stock market index using LSTM
- Predicting NEPSE index price using deep learning models
- Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis
- The Distribution Builder: A Tool for Inferring Investor Preferences
- Analysis of Investment Returns as Markov Chain Random Walk
- Can We See the Next Recession Coming? Deep Learning in Economic Forecasting.
- FOREX Prediction Using Deep Learning
- Deep Learning Techniques for Equity Portfolio Construction, Optimization, and Performance Analysis
- Wavelet Based Reinforcement Learning for Pairs Trading Across Multiple Asset Classes
- Adam Smith's 1776 An Inquiry into the Nature and Causes of the Wealth of Nations, often abbreviated as The Wealth of Nations, is considered his magnum opus and the first modern work that treats economics as a comprehensive system and an academic discipline.
- Louis Bachelier is credited with being the first person to model the stochastic process now called Brownian motion, as part of his doctoral thesis The Theory of Speculation (Théorie de la spéculation, defended in 1900).
- Charles Dow published 255 editorials in the Wall Street Journal analyzing American stock market data using technical analysis, forming the foundations of what is now called Dow theory. William Hamilton expanded upon Dow theory in The Stock Market Barometer (1922).
- Richard Schabacker continued the work of Dow and Hamilton in Technical Analysis and Stock Market Profits (1932).
- Benjamin Graham and David Dodd laid out the foundations of fundamental analysis in Security Analysis: Principles and Technique (1934). Graham further developed value investing in The Intelligent Investor (1949).
- The General Theory of Employment, Interest, and Money (1936) by John Maynard Keynes replaced the neoclassical understanding of employment with Keynes' view that demand, and not supply, is the driving factor determining levels of employment.
- Alfred Cowles founded Yale's Cowles Commission for Research in Economics, which advanced the field of econometrics in the 20th century. Two of his notable publications in Econometrica are Stock Market Forecasting (1944) and A Revision of Previous Conclusions Regarding Stock Price Behavior (1960).
- In 1948, Robert Edwards and John Magee published Technical Analysis of Stock Trends which is widely considered to be one of the seminal works of the discipline.
- The Markowitz model of portfolio management was put forward by Harry Markowitz in 1952 in Portfolio Selection: Efficient Diversification of Investments.
- One of Milton Friedman's most popular works, A Theory of the Consumption Function (1957), challenged traditional Keynesian viewpoints about the household. He went on to publish Capitalism and Freedom (1962), in which he argues for economic freedom as a precondition for political freedom.
- William Sharpe was one of the originators of the capital asset pricing model (CAPM) in his Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk (1964), despite it originally being rejected for publication. He developed the Sharpe ratio for evaluating returns on risk in Mutual Fund Performance (1966).
- The science of bond analysis was largely founded by Martin Leibowitz and Sidney Homer's Inside the Yield Book (1972).
- For a modern guide to technical analysis, take a look at John Murphy's Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications (1999).
- For an overview of the current state of macroeconomics, see Brian Snowdon and Howard Vane's Modern Macroeconomics (2005) and Sanjay Chugh's Modern Macroeconomics (2015).
- Some good books on trading include High Probability Trading, Option Volatility and Pricing, Options Trading: The Bible, Get Rich With Options, and Mind over Markets.
- For more historical perspectives on trading, I also enjoyed reading the Market Wizards books, When Genius Failed, and Michael Lewis's writings from the last few decades such as Liar's Poker.
- Also for more general tips, The Money Game, Mastering the Trade, and Trading in the Zone, or memoirs like How I Made $2,000,000 in the Stock Market from Nicolas Darvas and Reminiscences of a Stock Operator about Jesse Livermore.
- Leibowitz of Inside the Yield Book had a PhD in math before going into finance.
- Professor Edward Thorp started one of the first hedge funds based on statistical arbitrage. Check out his autobiography A Man for all Markets, along with Beat the Dealer and Beat the Market.
- Alongside Thorp as one of the first "quants" who applied mathematical and algorithmic principals to Wall Street is Jim Simons, known in math for the Chern-Simons form, and famous publicly for his hedge fund Rennaissance Technology and its Medallion Fund. His life is chronicled in the biography The Man Who Solved the Market.
- Full Courses
- Algorithmic Trading Using Python - 3 hour course. Video here.
- Algorithmic Trading Using Python - 4 hour course. Video here.
- How To Build A Trading Bot In Python - 9 hour course. Video here.
- Demos
- Stock Option Screener in Python - 16 min demo. Video here.
- Introduction to Algorithmic Trading Using Python - 17 min demo. Video here.
- How To Build A Trading Bot In Python - 18 min demo. Video here.
- How to Code a Trading Bot with QuantConnect - 23 min demo. Video here.
- Coding an Options Trading Algorithm with QuantConnect - 26 min demo. Video here.
- Probability Distribution of Stock Returns - 35 min demo. Video here.
- How to Code an AI Trading bot - 35 min demo. Video here.
Options contracts are a type of derivative instrument, because they are derived from an underlying asset (a security specified by a stock symbol), a strike price, and an expiration date. A call option gives you the right to buy 100 shares of a security at the strike price before the expiration date, and a put option gives you the right to sell 100 shares of a security at the strike price before the expiration date. The current value of an options contract is a function of the time remaining until expiration, the current price of the underlying security, and the volatility. The intrinsic value is the amount of money that can be made by exercising the contract at expiration if it were to expire today; if it expires in the money, meaning the stock price is currently above the strike price for calls, or below the strike price for puts, then this is given by the difference between the current price of the stock and the strike price, multiplied by 100. Otherwise, it is out of the money, and the intrinsic value is just $0 (it has no intrinsic value). The extrinsic value (or time value) is the value derived from the uncertainty and volatility when there is still time remaining until expiration. The total value is the sum of these. Since the time value exponentially decays down to $0 by the expiration date (a process called "theta decay" or "time decay"), at expiration the total value of the option is just the intrinsic value, which may also be $0. Holders of options contracts often will try to sell before expiration, to avoid the decaying value. Sellers of options profit from time decay, but may still close before expiration to limit risk. Complex options strategies may have multiple legs, composed of buying and selling calls and puts at various strike prices and expiration dates, but they are still always either net long or net short on the underlying.
- Pretty much all complex options strategies are made by combining different types of spreads. These all require level 3 options trading. For a basic overview of options, start here and here. You may also want to start learning about the Greeks.
- Here is a nice video on long vertical spreads, also called debit spreads, which is probably the most similar to buying calls or puts directly. The difference is you somewhat offset theta decay (though also limiting your maximum possible gain) by simultaneously selling an equal number of options. Here is the video.
- Here is another video, by the same channel, on short vertical spreads, also called credit spreads. This is where you are trying to profit from theta decay and taking on the role of the "option seller." The problem with selling options though, is that your losses can be huge if the options you sold end up in the money, so you can offset those risks by buying an equal number of options that are further out of the money. This limits your total possible losses. Here is the video.
- If you want to go more in depth, there's a guy I used to watch who does pretty long detailed videos. Here's his video on both types of vertical spreads.
- There is also the wheel, which requires owning the underlying stock. Here's a video on it.
- Once you start watching these videos, you'll find a lot of similar channels with different people's explanations and strategies, so I encourage you to explore and discover new channels that work for you!
Futures, like options, are also a type of derivative, whose price is based on an underlying asset, whether it's an index (e.g., for E-mini S&P futures contracts), or commodities like gold, Bitcoin, corn, and oil. While futures have an expiration date, and quite a bit of leverage, their profit and loss settles to the difference with the underlying more linearly, in a way that is more comparable to forex. The margin requirements offset the leverage they provide, and further leverage can be provided by trading options on futures.
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