Papers, wiki, Option Blackboard, encyclopedia, and cards.
We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean and standard deviation parameters. Our findings suggest that the OU model captures signals and trends effectively but underperforms the naive model on a risk-return basis, likely due…
We model the quantities appearing in Internal Revenue Service (IRS) tax guidance for calculating the health insurance premium tax credit created by the Patient Protection and Affordable Care Act, also called Obamacare. We ask the question of whether there is a procedure, computable by hand, which can calculate the appropriate premium tax credit for any household with self-employment income. We motivate current IRS ta…
We model the quantities appearing in Internal Revenue Service (IRS) tax guidance for calculating the health insurance premium tax credit created by the Patient Protection and Affordable Care Act, also called Obamacare. We ask the question of whether there is a procedure, computable by hand, which can calculate the appropriate premium tax credit for any household with self-employment income. We give an example showing…
Emerging market hard-currency bonds are an asset class of growing importance, and contain exposure to an EM sovereign and the underlying industry. The authors investigate how to model this as a modification of the well-known first-to-default (FtD) basket, using the structural model, and find the approach feasible.
‘Pairs Trading’ is an investment strategy used by many Hedge Funds. Consider two similar stocks which trade at some spread. If the spread widens short the high stock and buy the low stock. As the spread narrows again to some equilibrium value, a profit results. This paper provides an analytical framework for such an investment strategy. We propose a mean-reverting Gaussian Markov chain model for the spread which is o…
We perform an extensive and robust study of the performance of three different pairs trading strategies—the distance, cointegration and copula methods—on the entire US equity market from 1962 to 2014 with time-varying trading costs. For the cointegration and copula methods, we design a computationally efficient two-step pairs trading strategy. In terms of economic outcomes, the distance, cointegration and copula meth…
Motivated by Kyle (1985) informed order flow and the Meiklejohn et al. (2013) wallet-clustering tradition, we ask whether persistent coordinated wallets causally raise first-hour buyer flow on the Solana pump.fun bonding-curve marketplace. Using 1,578,333 buyer observations from 166,098 launches over 13.4 days (2026-06-11 to 2026-06-25), a two-stage detection pipeline (intra-launch first-buyer-window extraction plus …
The integration of thematic satellite allocations into core-satellite portfolio architectures is commonly approached using factor exposures, discretionary convictions, or backtested performance, with feasibility assessed primarily through liquidity screens or market-impact considerations. While such approaches may be appropriate at institutional scale, they are ill-suited to small portfolios and robustness-oriented a…
The goal of cryptocurrencies is decentralization. In principle, all currencies have equal status. Unlike traditional stock markets, there is no default currency of denomination (fiat), thus the trading pairs can be set freely. However, it is impractical to set up a trading market between every two currencies. In order to control management costs and ensure sufficient liquidity, we must give priority to covering those…
This research aims to demonstrate a dynamic cointegration-based pairs trading strategy, including an optimal look-back window framework in the cryptocurrency market, and evaluate its return and risk by applying three different scenarios. We employ the Engle-Granger methodology, the Kapetanios-Snell-Shin (KSS) test, and the Johansen test as cointegration tests in different scenarios. We calibrate the mean-reversion sp…
Public evidence can become sufficient to settle a prediction-market contract before the venue records its first determination, but the relevant boundary depends on the applicable rule version, exact release object, source hierarchy, correction history, and unfinished contract conditions. This paper defines two Kalshi clocks: first decidability, the earliest contemporaneous singleton in the rule-evidence mapping, and …
We test a Wall Street investment strategy, “pairs trading,” with daily data over 1962–2002. Stocks are matched into pairs with minimum distance between normalized historical prices. A simple trading rule yields average annualized excess returns of up to 11% for self-financing portfolios of pairs. The profits typically exceed conservative transaction-cost estimates. Bootstrap results suggest that the “pairs” effect di…
Preface. Acknowledgments. PART ONE: BACKGROUND MATERIAL. Chapter 1. Introduction. The CAPM Model. Market Neutral Strategy. Pairs Trading. Outline. Audience. Chapter 2. Time Series. Overview. Autocorrelation. Time Series Models. Forecasting. Goodness of Fit versus Bias. Model Choice. Modeling Stock Prices. Chapter 3. Factor Models. Introduction. Arbitrage Pricing Theory. The Covariance Matrix. Application: Calculating…
Abstract This survey reviews the growing literature on pairs trading frameworks, i.e., relative‐value arbitrage strategies involving two or more securities. Research is categorized into five groups: The distance approach uses nonparametric distance metrics to identify pairs trading opportunities. The cointegration approach relies on formal cointegration testing to unveil stationary spread time series. The time‐series…
Abstract We examine the impact of trading costs on pairs trading profitability in the U.S. equity market, 1963 to 2009. After controlling for commissions, market impact, and short selling fees, pairs trading remains profitable, albeit at much more modest levels. Specifically, we document a risk‐adjusted return of about 30 basis points per month among portfolios of well‐matched pairs that are formed within refined ind…
We propose the VIX-derived volatility (VDV) model, a VIX-first framework for joint SPXVIX modeling. In the model, we define explicit dynamics for the VIX process to price VIX futures and options, yielding a VIX-side calibration that is independent of the SPX dynamics. Using the rolling-window definition of the VIX, we then derive a coupling function to obtain the SPX volatility process as a latent process consistent …
This paper proposes the certainty-equivalent first-order learning (CEFOL) algorithm, a deep learning algorithm for solving discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is challenging because nonlinear certainty equivalent appears in the Bellman equation and the first-order optimality conditions but is difficult to evaluate. By introducing a separate neu…
Systematic Investment Plans (SIPs) are a primary vehicle for retail equity participation in India, yet the impact of their intra-month timing remains underexplored. This study offers a 22-year (2003--2024) comparative analysis of SIP performance in the Nifty 50 index, contrasting the conventional first-trading-day (FTD-SIP) strategy with an alternative aligned to monthly Futures and Options expiry days (EXP-SIP). Usi…
Adam is an adaptive first-order optimizer that keeps exponential moving averages of the gradient and its square, giving per-parameter step sizes.
BPE grows a vocabulary by repeatedly merging the most frequent adjacent pairs, starting from characters or bytes, until a target vocab size is reached.
CLIP jointly trains an image encoder and a text encoder so matched image–caption pairs are close in a shared space, enabling zero-shot visual classification by text prompts.
Contrastive learning pulls representations of related pairs together and pushes unrelated pairs apart. It is the pretraining idea behind SimCLR, CLIP, and many embedding models.
PPO is a policy-gradient algorithm that clips the probability ratio so each update stays close to the previous policy, giving much of TRPO’s stability with first-order SGD.
RAG retrieves relevant documents first, then conditions a language model on that evidence so answers can be grounded, cited, and updated without retraining.
Which expiry you hold and when you roll is a first-class P&L — not an operations footnote — especially in commodities and VIX.
Trade the VIX curve as a first-class market — trend on VIX, carry on contango, and a respect for inversion — not just an equity hedge overlay.
Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.
Moneyness is where spot sits versus strike — in, at, or out of the money — the first map of option value and of Greek shape.
Bidless means there is no meaningful posted or workable bid — you can sell only by walking the stairs or waiting, which is how fire sales become prices.
An IPO is a private firm’s first sale of stock to public investors — a liquidity and valuation event, not a proof of quality.
Cyprus 2013 combined a Greek-PSI hole in bank assets with a huge banking system versus GDP and ended in bail-in, capital controls, and a depositor haircut above insurance — a euro-area first.
The Panic of 1792 was the first US securities-market crash, after a leveraged attempt to corner federal debt, and the first Treasury-led lender-of-last-resort operation under Hamilton.
March 2023’s US regional-bank crisis (SVB, Signature, First Republic) was a social-media deposit run on duration-mismatched, uninsured-deposit franchises — 1980s S&L math plus a Twitter fuse.
Mexico’s 1994–95 tequila crisis was a devaluation-and-tesobono run after political shocks and a crawling peg that had become incredible — the first big 1990s EM capital-account crisis.
Modified duration is the percent price change for a 1% (100bp) parallel yield move — the first-order hedge ratio from the yield function.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
A pip is the conventional smallest FX increment — usually 0.0001 for most pairs and 0.01 for JPY pairs.
Cointegration Pairs Trading — Mean-reversion on stationary spreads between related instruments.
An interest-rate swap exchanges fixed coupons for floating (or the reverse) on a notional — the vanilla rates derivative.
Time global equity exposure with calendar rules (Halloween, first-half vs second-half year) rather than a fundamental forecast.
Mean-revert spreads between country (or regional) ETFs that usually travel together — pairs at the index layer.
Trade a spread between two historically linked stocks when it is statistically wide, and unwind when it mean-reverts.
Adam is an adaptive first-order optimizer that keeps exponential moving averages of the gradient and its square, giving per-parameter step sizes.
Bidless means there is no meaningful posted or workable bid — you can sell only by walking the stairs or waiting, which is how fire sales become prices.
BPE grows a vocabulary by repeatedly merging the most frequent adjacent pairs, starting from characters or bytes, until a target vocab size is reached.
CLIP jointly trains an image encoder and a text encoder so matched image–caption pairs are close in a shared space, enabling zero-shot visual classification by text prompts.
Cointegration Pairs Trading — Mean-reversion on stationary spreads between related instruments.
Contrastive learning pulls representations of related pairs together and pushes unrelated pairs apart. It is the pretraining idea behind SimCLR, CLIP, and many embedding models.
Which expiry you hold and when you roll is a first-class P&L — not an operations footnote — especially in commodities and VIX.
Cyprus 2013 combined a Greek-PSI hole in bank assets with a huge banking system versus GDP and ended in bail-in, capital controls, and a depositor haircut above insurance — a euro-area first.
Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
An IPO is a private firm’s first sale of stock to public investors — a liquidity and valuation event, not a proof of quality.
Time global equity exposure with calendar rules (Halloween, first-half vs second-half year) rather than a fundamental forecast.
Modified duration is the percent price change for a 1% (100bp) parallel yield move — the first-order hedge ratio from the yield function.
Moneyness is where spot sits versus strike — in, at, or out of the money — the first map of option value and of Greek shape.
Mean-revert spreads between country (or regional) ETFs that usually travel together — pairs at the index layer.
Trade a spread between two historically linked stocks when it is statistically wide, and unwind when it mean-reverts.
The Panic of 1792 was the first US securities-market crash, after a leveraged attempt to corner federal debt, and the first Treasury-led lender-of-last-resort operation under Hamilton.
A pip is the conventional smallest FX increment — usually 0.0001 for most pairs and 0.01 for JPY pairs.
PPO is a policy-gradient algorithm that clips the probability ratio so each update stays close to the previous policy, giving much of TRPO’s stability with first-order SGD.
RAG retrieves relevant documents first, then conditions a language model on that evidence so answers can be grounded, cited, and updated without retraining.
March 2023’s US regional-bank crisis (SVB, Signature, First Republic) was a social-media deposit run on duration-mismatched, uninsured-deposit franchises — 1980s S&L math plus a Twitter fuse.
Mexico’s 1994–95 tequila crisis was a devaluation-and-tesobono run after political shocks and a crawling peg that had become incredible — the first big 1990s EM capital-account crisis.
Trade the VIX curve as a first-class market — trend on VIX, carry on contango, and a respect for inversion — not just an equity hedge overlay.