stochastic-processes-and-financial-applications

A major 2026 academic study (292 million trades, 327,000 binary contracts across Kalshi and Polymarket) reveals that prediction market calibration is not uniform — it is a structured, multidimensional phenomenon. Understanding these biases gives sophisticated Polymarket trading bots a massive, repeatable edge. Key Calibration Findings The paper decomposes calibration variance into four components…

When making a high-frequency or mid-frequency prediction on an assets return, what are the advantages and disadvantages of making a continuous prediction vs a prediction that only fires on a particular event? For example my model might have a number of features: order imbalance, trade imbalance etc Do I want to make a continuous prediction of where the asset price is going? Or do I want to make p…

A smart contract does not need an overflow, reentrancy bug, or broken access-control check to lose money. Sometimes, the exploit is hidden inside an ordinary division: uint256 result = amount * rate / SCALE; The expression looks harmless. It may even produce the expected answer in every unit test. But financial smart contracts operate with integer arithmetic. Fractions are discarded, rounding dir…

I build algorithmic trading bots as a side project. Nothing fancy — just small strategies that trade US equity options automatically. The problem I kept running into wasn't the strategy logic. It was the data. Every time I wanted to pull real-time options chains, Greeks, or IV, I had two options: Pay $99+/mo to a data provider Scrape something I probably shouldn't be scraping Neither felt right f…

"AI picked these stocks" is one of the most repeated claims on FinTwit right now. Almost none of it is reproducible. Screenshot of a ChatGPT chat. No data source. No filters. No way to check if the tickers even exist. If you're: building AI agents that touch market data, evaluating whether LLMs can actually reason over financial datasets, or just tired of "AI stock picker" threads with zero code …

I'm curious about an exercise found in Optimization Methods in Finance . Exercise 8.2 (pg 143) explores a variant of the more commonly used form of MVO. When I refer to the more common variant I'm talking about: $$ \begin{aligned} \operatorname{max}_x \mu^Tx - \frac{\delta}{2}x^T\Sigma x & \\ Ax &= b \\ Cx &\ge d \end{aligned} $$ The variant that directly uses standard deviation by taking the squ…

I'm implementing the solution with drift from "Dealing with the inventory risk" from Gueant, Lehalle and Tapia. I'm using the link https://arxiv.org/pdf/1105.3115.pdf as reference. I can reproduce the standard solution with no issues, and then reproduce the surfaces in the paper. I'm trying now to implement the solution with drift, which is very similar to the standard solution, with a new compon…

The Quest Begins (The "Why") Honestly, I was tired of staring at charts at 2 a.m., trying to catch that perfect entry while my coffee went cold. I’d set a manual alert, jump onto the exchange, click “buy”, and then second‑guess myself as the price slipped away. It felt like I was playing a never‑ending game of Whac‑A‑Mole, and I kept losing the mole. One night, after yet another missed opportunit…

Let's say you decide to buy a 2Y10Y ATM swaption straddle (i.e. buy 10 million ATM payer swaption and buy 10 million ATM receiver swaption). In order to delta hedge, I believe you would short the 2Y10Y forward swap. My questions are: How exactly does this delta hedging work? When do you profit from it (is it when there is a big move in realized volatility in the underlying forward swap)? What nee…

A comprehensive theoretical and computational analysis of the early exercise decision for rational investors. Explores Black's approximation, Monte Carlo simulation, and the Longstaff-Schwartz method for determining optimal exercise strategies. 📊 Deep Research • 📈 Options Strategy Topics: quantitative finance, investment analysis, financial education, options trading, derivatives

The Quest Begins (The "Why") Picture this: I’m sitting at my desk, coffee gone cold, staring at a spreadsheet that looks like something out of Indiana Jones and the Last Crusade – a maze of dates, prices, and a gut feeling that I’ve cracked the code to beat the market. I had a shiny new idea: buy when the 50‑day moving average crosses above the 200‑day (the classic “golden cross”) and sell when i…

This study investigates short-term price reversals—temporary retracements following adverse daily returns—and develops a systematic trading framework to capture this effect across multiple asset classes. Using daily data from six liquid ETFs spanning equities, fixed income, currencies, gold, and commodities over the period 2006–2025, the strategy applies a long-term trend filter based on a 200-da…

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Negative Risk (NegRisk) is one of the most powerful innovations on Polymarket for builders of sophisticated Polymarket trading bots . It dramatically improves capital efficiency in multi-outcome “winner-take-all” events by mathematically linking all related conditional tokens. Why Negative Risk Matters In standard multi-outcome markets, positions are completely independent. Betting against one ca…

I have a payoff structure but I do not know the price of the bond. The bond is municipal. What discount rates should I take for each period in order to calculate its fair price?

The purpose of this paper is to obtain a duality between the game put and call options assuming three component penalties – proportion of the usual option payoff, shares of the underlying asset, and a fixed amount. We examine separately the cases of finite and infinite maturities. For the perpetual options, we need to derive a polynomial-style equations for the optimal boundaries. We prove the ex…

We present recent results on probabilistic well-posedness of the two dimensional NLS, posed on the sphere. These results deal with low regularity solutions. The construction of such solutions is beyond the scope of applicability of the deterministic methods of Burq-Gérard-Tzvetkov developed between 2000 and 2004.