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Liquidity Providers on Automated Market Makers generate millions of USD in transaction fees daily. However, the net value of a Liquidity Position is vulnerable to price changes in the underlying assets in the pool. The dominant measure of loss in a Liquidity Position is Impermanent Loss. Impermanent Loss for Constant Function Market Makers has been widely studied. We propose a new metric to measure Liquidity Position…
We consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset. We consider the perspective of small investors whose trades do not induce market impact and who possess different levels of information about the liqui…
Bilateral CVA as currently implement has the counterintuitive effect of profiting from one's own widening CDS spreads, i.e. increased risk of default, in practice. The unified picture of CVA and liquidity introduced by Morini & Prampolini 2010 has contributed to understanding this. However, there are two significant omissions for practical implementation that come from the same source, i.e. positions not booked in us…
The Empirical Mode Decomposition (EMD) provides a tool to characterize time series in terms of its implicit components oscillating at different time-scales. We apply this decomposition to intraday time series of the following three financial indices: the S\&P 500 (USA), the IPC (Mexico) and the VIX (volatility index USA), obtaining time-varying multidimensional cross-correlations at different time-scales. The correla…
This paper studies Relief-Gated Relative Rotation (RGRR), a two-ETF rule that allocates between QQQ and DIA by mapping screened relative and macro states into a continuous QQQ weight. RGRR is economic rather than mechanical: it rotates between a growth-heavy sleeve and a Dow/value-heavy sleeve only when QQQ-DIA relative states are confirmed by rate, volatility, credit, or broad-market relief conditions. Candidate mai…
We establish four structural results for signature volatility models. First, we prove global existence and uniqueness of strong solutions to the signature SDE $dS_t = S_t \langle \ell, \widehat{W}_t \rangle \, dB_t$ on the weighted tensor algebra $T_w$, identifying the admissibility class through a summability condition H1 and an exponential-integrability condition H3 for the square-integrable stochastic-exponential …
Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately …
Granger causality can uncover the cause and effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into a rotational and gradient component which reveals the hierarchy of Granger causality flow. Using Kenneth French's business sector return time series, it is revealed that during the Covid crisis, pr…
Compositional data are contemporarily defined as positive vectors, the ratios among whose elements are of interest to the researcher. Financial statement analysis by means of accounting ratios a.k.a. financial ratios fulfils this definition to the letter. Compositional data analysis solves the major problems in statistical analysis of standard financial ratios at industry level, such as skewness, non-normality, non-l…
Central banks manage about \$12 trillion in foreign exchange reserves, influencing global exchange rates and asset prices. However, some of the largest holders of reserves report minimal information about their currency composition, hindering empirical analysis. I describe a Hidden Markov Model to estimate the composition of a central bank's reserves by relating the fluctuation in the portfolio's valuation to the exc…
This paper surveys the evolution of industrial concentration of the Brazilian automotive market as well as its positioning in the worldmarket. Data available by OICA (International Organization of Motor Vehicle Manufacturers) were used to better understand the characteristics of the Brazilian market on the world stage. A cluster analysis algorithm (by the k-means technique) ranks Brazil with a concentration profile i…
Implied volatilities form a well-known structure of smile or surface which accommodates the Bachelier model and observed market prices of interest rate options. For the swaptions that we study, three parameters are taken into account for indexing the implied volatilities and form a "volatility cube": strike (or moneyness), time to maturity of the option contract, duration of the underlying swap contract. It should be…
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into $k$ classes using the $k$-shell decomposition method. We investigate the influences of trading behaviors on the price impact by comparing a closed …
Income tax systems with pass-through entities transfer a firm's incomes to the shareholders, which are taxed individually. In 2014, a Chilean tax reform introduced this type of entity and changed to an accrual basis that distributes incomes (but not losses) to shareholders. A crucial step for the Chilean taxation authority is to compute the final income of each individual, given the complex network of corporations an…
The guaranteed minimum withdrawal benefit (GMWB) rider, as an add on to a variable annuity (VA), guarantees the return of premiums in the form of peri- odic withdrawals while allowing policyholders to participate fully in any market gains. GMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We consider fair pricing of the GMWB rider …
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European options, up-and-out options, double-barrier knock-out options, and options which pay a rebate upon hitt…
We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows, in particular, to solve the American optimal stopping problem without having to compute the option…
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form op…
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.
Positional encodings inject order into a permutation-invariant attention mixer so the model knows that token i is not token j.
Self-attention is attention where queries, keys, and values all come from the same sequence, so each position can mix information from every other position in one layer.
Size each new futures position so that 1 ATR move equals a fixed fraction of equity — the Turtle risk unit, still the cleanest per-trade language.
How much money a program can run before it is the market — position limits, ADV caps, and the point where adding AUM only buys slippage.
Gross is the sum of |positions|; net is the signed residual — in a CTA both move with signal agreement, unlike a 130/30 that is always ~100 net.
When too many trend books own the same contract the same way, entries get worse, exits gap, and ‘the CTA unwind’ becomes a flow event.
Positions that do not intend to sit overnight — session trends, opening-range breaks, or inventory mean reversion inside the day.
A price-based engine with a fundamental veto or tilt — inventories, COT, positioning, or nowcasts that can cut or flip a trend.
A CTA that trades futures on economic data, not only price — growth, inflation, positioning, and nowcasts as the signal set.
Dealer gamma positioning describes whether option dealers are structurally long or short gamma, shaping how hedging flows amplify or dampen market moves.
Options Open Interest — Outstanding contracts revealing crowd positioning and potential gamma walls.
A protective put is long the asset and long a put — a floor under the position for a premium that bleeds.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
Don’t fight the Fed is the rule of thumb that a determined policy impulse (easing or tightening) will eventually dominate discretionary macro views.
DV01 is the dollar value of one basis point: how much the position’s mark changes if the yield (or the curve point you risk on) moves by 0.01%.
Short covering is buying to close a short — a rally driven by the short base shrinking, not by new longs arriving with a fundamental bid.
Margin is collateral posted against a leveraged position — the cash or securities that keep the broker or CCP whole.
Money market fund assets track the amount of cash parked in short-term low-risk vehicles, providing insight into liquidity preference, deposit substitution, and defensive positioning.
SVD factors any matrix A = U Σ V' into orthogonal rotations and a diagonal of singular values — the workhorse behind PCA, low-rank approximation, and many recommenders.
Short Interest Ratio — Crowded short positioning that can fuel squeezes or confirm bearish consensus.
Short selling is selling a borrowed security, hoping to buy it back cheaper — a negative inventory financed by the borrow.
The disposition effect is the habit of selling winners and keeping losers — realizing gains, papering losses, versus a mark-to-market rule.
Portfolio Construction Engine — Optimization layer translating forecasts into positions under constraints.
Size each new futures position so that 1 ATR move equals a fixed fraction of equity — the Turtle risk unit, still the cleanest per-trade language.
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.
How much money a program can run before it is the market — position limits, ADV caps, and the point where adding AUM only buys slippage.
Gross is the sum of |positions|; net is the signed residual — in a CTA both move with signal agreement, unlike a 130/30 that is always ~100 net.
Dealer gamma positioning describes whether option dealers are structurally long or short gamma, shaping how hedging flows amplify or dampen market moves.
The disposition effect is the habit of selling winners and keeping losers — realizing gains, papering losses, versus a mark-to-market rule.
DV01 is the dollar value of one basis point: how much the position’s mark changes if the yield (or the curve point you risk on) moves by 0.01%.
Positions that do not intend to sit overnight — session trends, opening-range breaks, or inventory mean reversion inside the day.
Margin is collateral posted against a leveraged position — the cash or securities that keep the broker or CCP whole.
Money market fund assets track the amount of cash parked in short-term low-risk vehicles, providing insight into liquidity preference, deposit substitution, and defensive positioning.
Options Open Interest — Outstanding contracts revealing crowd positioning and potential gamma walls.
Portfolio Construction Engine — Optimization layer translating forecasts into positions under constraints.
Positional encodings inject order into a permutation-invariant attention mixer so the model knows that token i is not token j.
A protective put is long the asset and long a put — a floor under the position for a premium that bleeds.
A price-based engine with a fundamental veto or tilt — inventories, COT, positioning, or nowcasts that can cut or flip a trend.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
Self-attention is attention where queries, keys, and values all come from the same sequence, so each position can mix information from every other position in one layer.
Short Interest Ratio — Crowded short positioning that can fuel squeezes or confirm bearish consensus.
SVD factors any matrix A = U Σ V' into orthogonal rotations and a diagonal of singular values — the workhorse behind PCA, low-rank approximation, and many recommenders.
A CTA that trades futures on economic data, not only price — growth, inflation, positioning, and nowcasts as the signal set.