Papers, wiki, Option Blackboard, encyclopedia, and cards.
Abstract: SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilitie…
We study whether nuclear and energy-adjacent equity options exhibit a harvestable variance risk premium. Using CRSP and OptionMetrics data for 2000-2024, we construct a systematic cash-secured short-put strategy on a curated universe of nuclear-related firms. The strategy compares at-the-money put implied volatility with GARCH-based realized volatility forecasts, then evaluates unconditional and IV/RV-filtered put-wr…
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset price hits a certain level) is exponentially distributed. We obtain explicit optimal stopping rules in various cases one of which is interestingly complex because of an unexpected disc…
As decentralized finance (DeFi) evolves, distinguishing between user behaviors - liquidity provision versus active trading - has become vital for risk modeling and on-chain reputation. We propose a behavioral scoring framework for Uniswap that assigns two complementary scores: a Liquidity Provision Score that assesses strategic liquidity contributions, and a Swap Behavior Score that reflects trading intent, volatilit…
We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and entanglement. The equilibrium asset pricing solution is a quantum state. We introduce quantum decision-theoretic foundations of ambiguity and model/parameter uncertainty to deal with …
Cross-market portfolio optimization has become increasingly complex with the globalization of financial markets and the growth of high-frequency, multi-dimensional datasets. Traditional artificial neural networks, while effective in certain portfolio management tasks, often incur substantial computational overhead and lack the temporal processing capabilities required for large-scale, multi-market data. This study in…
The present work addresses the challenge of training neural networks for Dynamic Initial Margin (DIM) computation in counterparty credit risk, a task traditionally burdened by the high costs associated with generating training datasets through nested Monte Carlo (MC) simulations. By condensing the initial market state variables into an input vector, determined through an interest rate model and a parsimonious paramet…
Coupled feedback networks are often monitored channel by channel even though cross-channel paths alter both stability margins and transmitted disturbances. We study identification of a structured feedback matrix L_t = Phi diag(gamma_t) in an output-only setting: no commanded, probing, or reference input exists -- only temporally separated outputs and the scheduling gains gamma_t are observed, while the coupling respo…
The computation of Black-Scholes implied volatility is a fundamental task in quantitative finance, underpinning option valuation, model calibration and risk management. Although implied volatility is routinely used in practice, the inversion of the Black-Scholes pricing formula remains a challenging numerical problem, particularly in asymptotic regimes corresponding to extreme option prices, strikes or maturities, wh…
The authors present a rigorous empirical evaluation of three distinct optimization paradigms for institutional factor portfolio construction: an entropy-based photonic quantum annealer (Dirac-3, Quantum Computing Inc.), a commercial mixed-integer programming solver (Gurobi), and a model-free deep reinforcement learning agent (SAC). Evaluating these pipelines on the Jensen-Kelly-Pedersen 13-factor equity library acros…
Financial observations are continuous, heterogeneous, and noisy, whereas decoder-only next-token models are usually built around discrete symbolic inputs. We introduce Vector-Input Autoregressive Inference for Ordinal-Return Modeling (VAIOM), a decoder-only Transformer for probabilistic next-return modeling on one-hour foreign-exchange bars. VAIOM separates input representation from output likelihood: continuous mult…
Financial markets are hard to predict, not because price moves are purely random, but because structure is strategic, capacity-constrained, and computationally difficult. Classical information theory measures uncertainty, dependence, and directed flow through entropy, KL divergence, NMI, and transfer entropy. This paper extends that foundation to ask: how much detected structure can a bounded investor learn and reuse…
Tail-risk management is not only an instrument-selection problem. It is an allocation problem across loss mechanisms: abrupt crash states, volatility repricing, and persistent drawdowns require different forms of protection. This paper develops a continuous-time CVaR framework that places two common protection sleeves -- long out-of-the-money put options and systematic trend-following overlays -- inside one coherent …
In a deep forecasting pipeline for fat-tailed financial returns at short horizons, which matters more - the backbone architecture or the output head? We compare four modern backbones (TimesNet, DLinear, N-BEATS, iTransformer) under three output heads: a point head, a single-Gaussian density head, and a Gaussian mixture density head with K=4 components. On S and P 500 monthly log-returns (1871-2023) under anchored wal…
Put-call parity is risk-neutral at terminal payoff, but its enforcement is path-dependent and capital-using. I test whether the SPX and RUT carry gap is explained by OIS-based funding, volatility, trading-friction, and financial-condition variables, or also by residual outside-option information. Adding IEFA, IGOV, and IAU improves in-sample and leave-one-year-out fit after U.S.-centered controls. Gains survive broad…
Every universal-trading claim pairs a trader with a market---a path, generator, or law. For any total deterministic computable trader, its code yields a fixed computable countermarket with proportional price moves opposing its positions; hence no such trader wins on every computable path. Gold-style learning cannot identify every computable binary market rule from history. Separately, Turing-universal generators make…
This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility exceeds realized volatility, the practical implementation of short-dated volatility-selling strategies remains underdeveloped in the literature. This study evaluates three pos…
Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach, combining quantum computation with machine learning for modeling nonlinear temporal dependencies in high-dimensional time series. As with many data-driven disciplines, quantitative…
An autoencoder learns to reconstruct its input through a bottleneck, producing a compressed latent that can be used for denoising, retrieval, or as a generative seed.
Backpropagation computes gradients of a scalar loss with respect to every weight by applying the chain rule backwards through the computational graph.
Batch normalization re-centers and re-scales layer inputs using mini-batch statistics, then learns a scale and shift, reducing internal covariate shift and allowing higher learning rates.
A CNN shares a local kernel across spatial (or temporal) positions, building translation-equivariant features. It is the inductive bias that cracked modern computer vision.
An embedding is a learned dense vector for an object (token, sentence, image, user) such that geometry supports retrieval, clustering, or as input to a downstream model.
FlashAttention computes exact attention with tiling that keeps softmax stats in SRAM, cutting HBM traffic and unlocking longer contexts at the same FLOP count.
Knowledge distillation trains a smaller student to match a teacher’s output distribution (soft labels), transferring behavior without copying every weight.
LSTM is a gated RNN whose cell state can carry information across many steps, with input, forget, and output gates trained by gradient descent.
A neural network is a layered function approximator: units compute a weighted sum, apply a nonlinearity, and pass the result forward so the whole stack can learn a mapping from inputs to outputs.
Scaling laws are empirical power laws relating language-model loss to parameter count, data, and compute, used to plan pretraining rather than guess.
Seq2seq maps an input sequence to an output sequence of possibly different length via an encoder–decoder, originally with RNNs and later with Transformers.
A VAE is a probabilistic autoencoder: the encoder outputs a distribution q(z|x), the decoder p(x|z), and training maximizes an ELBO with a KL term that keeps the latent well-behaved.
A word embedding is a dense vector for a token such that geometry (distance, direction) reflects distributional meaning. It is the input layer of almost every neural NLP model.
Crisis alpha is return earned from persistent trends that form after a market crisis starts — not a prediction of the crash day, and not a put that pays on a two-day dip.
A collar is long stock, long a put, and short a call — a banded payoff, often structured to be zero-debit.
A protective put is long the asset and long a put — a floor under the position for a premium that bleeds.
A put option is the right to sell the underlying at a strike — convex downside, or a hedge that costs carry.
Put-call parity is the no-arbitrage link C − P = F − K (discounted) — a European call and put with the same K and T are one instrument plus cash.
Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.
A straddle is a call and a put at the same strike — a bet on a large move, long or short, without picking direction.
A strangle is an OTM call plus an OTM put — cheaper than a straddle, needs a bigger move, same vol-vs-realized logic.
A gamma squeeze is a price spiral where dealer hedging of short call (or put) gamma forces them to buy rallies and sell dips, amplifying the move that created the gamma.
Hysteresis is path dependence: a temporary shock permanently scars the level of output, employment, or inflation expectations instead of washing out.
The Keynesian multiplier is how much equilibrium output changes for a one-unit change in autonomous spending, set by the marginal propensity to consume and leakages (tax, imports).
The Taylor rule is a simple policy reaction: set the policy rate to a neutral real rate plus inflation, then add weights on the inflation gap and the output gap.
GDP is the market value of final goods and services produced in an economy over a period — the size of the flow, not the wealth stock.
Industrial Production — Physical output trends that confirm or contradict financial market cyclical narratives.
Labor Force Participation — Supply-side labor availability affecting wage pressure and potential output estimates.
Output Gap — Estimated distance of GDP from potential output, informing policy reaction functions.
Unit Labor Costs — Compensation per unit of output — a core driver of services inflation persistence.
A blue chip is a large, established, usually profitable listed company — a reputation, not a risk-free claim.
The Great Depression was a multi-year collapse of output, prices, and banks after the 1929 crash, amplified by the gold standard, Fed errors, and a wave of bank failures — the defining 20th-century crisis.
The South Sea Bubble was a 1720 London equity-and-debt-conversion mania around the South Sea Company that imploded the same year, taking a layer of insider finance and political reputations with it.
Yield to worst is the lowest yield among the plausible call, put, and maturity paths — the conservative quote on an embedded-option bond.
The efficient frontier is the set of mean-variance-optimal portfolios — maximum expected return for each volatility, given the inputs.
Long high-ESG-score names and short low-ESG names — a levels sort whose premium is disputed and vendor-dependent.
An autoencoder learns to reconstruct its input through a bottleneck, producing a compressed latent that can be used for denoising, retrieval, or as a generative seed.
Backpropagation computes gradients of a scalar loss with respect to every weight by applying the chain rule backwards through the computational graph.
Batch normalization re-centers and re-scales layer inputs using mini-batch statistics, then learns a scale and shift, reducing internal covariate shift and allowing higher learning rates.
A blue chip is a large, established, usually profitable listed company — a reputation, not a risk-free claim.
A collar is long stock, long a put, and short a call — a banded payoff, often structured to be zero-debit.
A CNN shares a local kernel across spatial (or temporal) positions, building translation-equivariant features. It is the inductive bias that cracked modern computer vision.
Crisis alpha is return earned from persistent trends that form after a market crisis starts — not a prediction of the crash day, and not a put that pays on a two-day dip.
The efficient frontier is the set of mean-variance-optimal portfolios — maximum expected return for each volatility, given the inputs.
An embedding is a learned dense vector for an object (token, sentence, image, user) such that geometry supports retrieval, clustering, or as input to a downstream model.
Long high-ESG-score names and short low-ESG names — a levels sort whose premium is disputed and vendor-dependent.
FlashAttention computes exact attention with tiling that keeps softmax stats in SRAM, cutting HBM traffic and unlocking longer contexts at the same FLOP count.
A gamma squeeze is a price spiral where dealer hedging of short call (or put) gamma forces them to buy rallies and sell dips, amplifying the move that created the gamma.
The Great Depression was a multi-year collapse of output, prices, and banks after the 1929 crash, amplified by the gold standard, Fed errors, and a wave of bank failures — the defining 20th-century crisis.
Hysteresis is path dependence: a temporary shock permanently scars the level of output, employment, or inflation expectations instead of washing out.
Industrial Production — Physical output trends that confirm or contradict financial market cyclical narratives.
The Keynesian multiplier is how much equilibrium output changes for a one-unit change in autonomous spending, set by the marginal propensity to consume and leakages (tax, imports).
Knowledge distillation trains a smaller student to match a teacher’s output distribution (soft labels), transferring behavior without copying every weight.
Labor Force Participation — Supply-side labor availability affecting wage pressure and potential output estimates.
LSTM is a gated RNN whose cell state can carry information across many steps, with input, forget, and output gates trained by gradient descent.
A neural network is a layered function approximator: units compute a weighted sum, apply a nonlinearity, and pass the result forward so the whole stack can learn a mapping from inputs to outputs.
Output Gap — Estimated distance of GDP from potential output, informing policy reaction functions.
A protective put is long the asset and long a put — a floor under the position for a premium that bleeds.
A put option is the right to sell the underlying at a strike — convex downside, or a hedge that costs carry.
Put-call parity is the no-arbitrage link C − P = F − K (discounted) — a European call and put with the same K and T are one instrument plus cash.