We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset …
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48 results for “Geometric Arbitrage”
Geometric arbitrage theory uses quantum mechanics to model market dynamics and arbitrage opportunities.
problem Modeling and managing arbitrage opportunities in financial markets.
method Quantum mechanical approach to geometric arbitrage theory, solving the Schroedinger equation.
result Results from quantum mechanics align with classical stochastic models, providing consistency.
Reflected geometric Brownian motion models are not arbitrage-free.
problem No-arbitrage condition violation in financial markets.
method Analysis of reflected geometric Brownian motion models.
result Models violate even the weakest no-arbitrage condition.
Established a relation between short-term and long-term arbitrage measures.
problem Non-equilibrium effects in financial markets.
method Geometric Arbitrage Theory and Stochastic Portfolio Theory.
result A connection between short-term and long-term arbitrage measures.
Extends Black-Scholes model to include arbitrage.
problem Formulating finance models without stochastic geometry.
method Geometric Arbitrage Theory applied to Black-Scholes PDE.
result Equivalence between market dynamics and utility maximization.
We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and loss given defaults characterizing the no-free-lunch-with-vanishing-risk condition …
Arbitrage and Geometryq-fin.MF
The article explores arbitrage opportunities in investments using geometric concepts.
problem Finding arbitrage opportunities in investments with random payoff matrices.
method Explains the Arbitrage Theorem, discusses its geometric meaning, and uses Farkas' Lemma equivalence.
result Determines the probability of arbitrage opportunities in random payoff matrices.
Market bubbles identified via spectral theory of geometric bundles.
problem Identifying asset bubbles in markets with arbitrage opportunities.
method Geometric Arbitrage Theory reformulated as a stochastic principal fibre bundle with a connection Laplacian.
result A market satisfies (NFLVR) if and only if 0 is in the discrete spectrum of the connection Laplacian.
The paper finds the shortest time to exploit arbitrage in multi-stock markets.
problem Finding the shortest time to exploit arbitrage in multi-stock markets.
method Characterizes the minimal time horizon for relative arbitrage in markets with 2 to 3 stocks and uses geometric flows for markets with 4 or more stocks.
result Explicit computation of minimal time horizon for 2 and 3 stocks markets, and characterization via geometric flows for markets with 4 or more stocks.
New characterisation of no-arbitrage condition in discrete time with multiple-priors.
problem Characterizing no-arbitrage in a multiple-priors setting.
method Proposed a new characterisation equivalent to existing no-arbitrage conditions.
result The new characterisation is equivalent to several no-arbitrage conditions and allows proof of important results.
Caratheodory's axiom limits arbitrage in resource-limited systems.
problem Non-arbitrage constraints in resource-limited financial systems.
method Preserving Caratheodory's axiom in resource-limited systems.
result Exponential family is the necessary geometric structure for both thermodynamics and finance.
New method finds better arbitrage opportunities in AMMs.
problem Finding optimal arbitrage trades in multi-token AMMs.
method Closed-form solutions using convex optimisation.
result Better arbitrage opportunities than traditional methods.
No-Arbitrage Symmetriesq-fin.MF
The paper defines symmetries in no-arbitrage markets.
problem Characterizing transformations preserving no-arbitrage.
method Geometric formalization in discrete time models.
result Local characterization of no-arbitrage symmetries.
The study examines a financial model with sticky prices and finds no arbitrage when interest rate is zero.
problem Analyzing financial markets with sticky asset prices and proving no arbitrage conditions.
method Introduced a financial market model with a risky asset following a sticky geometric Brownian motion and a riskless asset with a constant interest rate. Proved no arbitrage conditions and derived pricing equations.
result No arbitrage conditions are met only when the interest rate is zero, and all replicable payoffs are derived under this condition.
Sequences of Arbitragesq-fin.TR
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of arbitrages is reformulated in the linear algebra terms. This admits an elegant geometric…
Modeling price dynamics in AMMs with fees using geometric Brownian motion.
problem Understanding price dynamics in AMMs with transaction fees.
method Geometric Brownian motion, local times, excursion theory.
result Derivation of time-changed representation and limiting behavior of AMM prices.
In this work, we identify the most general measure of arbitrage for any market model governed by Itô processes. We show that our arbitrage measure is invariant under changes of numéraire and equivalent probability. Moreover, such measure has a geometrical interpretation as a gauge connection. The connection has zero cu…
Geometric Mean Market Makers super-hedge impermanent loss without models.
problem Super-hedging impermanent loss in Geometric Mean Market Makers.
method Model-free rebalancing strategy.
result Loss-versus-rebalancing vanishes due to finite variation exchange rate.
Novel approach to financial derivatives pricing using rough path theory.
problem No-arbitrage conditions in financial markets necessitating precise integration methods.
method Developed a polynomial-based approximation class for rough path functionals, extending to non-geometric rough paths.
result Motivated a hypothesis for payoff functionals in financial markets, facilitating analysis.
Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of ours, we prove the existence of investment opportunities producing an exponentiall…
Study growth of LP wealth in G3Ms affected by trading fees and arbitrage.
problem Analyzing profitability of LPs in G3Ms under trading fees and arbitrage.
method Stochastic reflected diffusion processes to model G3M dynamics.
result Long-term expected logarithmic growth of LP wealth calculated.
We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brownian motion recently introduced by Peng (20…
Conditional Davis Pricingq-fin.MF
Study shows non-replicable endowments can lead to unique price intervals.
problem Non-replicable endowments and their impact on price intervals.
method Formulas and examples for calculating marginal utility-based prices.
result Non-replicable endowments can lead to unique price intervals, unlike replicable endowments.
AMMs enforce target-weighted portfolios, outperforming traditional funds in returns and tracking error.
problem Enforcing target-weighted portfolios in decentralized exchanges.
method Introducing a multi-asset fee structure to enforce a geometric mean market maker invariant, allowing compliance with the mandate to be verified directly from pool holdings.
result G3M portfolios outperform traditional funds in annualized returns and tracking error for certain fee ranges.
Optimal fees for G3Ms align LP value with market accuracy.
problem Optimal fees for G3Ms to attract liquidity without sacrificing accuracy.
method Developed a framework for determining LP value with fees for G3Ms under diffusion.
result LPs prefer G3Ms over other strategies as fees approach zero.
New framework uses cohomology to analyze probabilistic distortions and arbitrage.
problem Analyzing probabilistic distortions and arbitrage in categorical filtrations.
method Transport cohomological framework, simplicial structure, loop effects, holonomy.
result Nontrivial probabilistic distortions and obstructions generated by loops.
We create consistent option surfaces without arbitrage.
problem Constructing consistent option surfaces free of arbitrage across different maturities.
method Combining PCA-Smolyak approximation with chain-consistent diffusion and c-EMOT bridge.
result Computable certificates for strong convexity, solver correctness, and Dupire/Greeks stability.
New algorithm finds more arbitrage opportunities in DEXs.
problem Detecting arbitrage loops and non-loops in decentralized exchanges.
method Combining line graph and modified Moore-Bellman-Ford algorithm.
result Found more arbitrage loops and non-loops compared to existing methods.
This paper introduces strategies to maximize arbitrage profits in decentralized exchanges.
problem Maximizing profits from arbitrage loops in decentralized exchanges.
method Three strategies: MaxPrice, MaxMax, and Convex Optimization.
result The Convex Optimization strategy yields the highest monetized arbitrage profit in theory and practice.
Study upper hedging prices for contingent claims in models with various types of arbitrage.
problem Valuation of contingent claims in market models with different types of arbitrage.
method Analysis of market models with increasing profit, strong arbitrage, and arbitrage of the first kind.
result Option prices are reduced when increasing profit is present, and corporate stock price processes can be derived from issuance and repurchase plans.
Paper explores arbitrage and CAPM in continuous time.
problem Understanding arbitrage and CAPM in continuous time.
method Analyzes instantaneous arbitrage and its relation to CAPM.
result Arbitrage and CAPM arguments differ in assumptions about the market portfolio.
Local no-arbitrage under capital gains taxes is weaker than in frictionless markets.
problem How local in time is the no-arbitrage property under capital gains taxes?
method Introducing robust local no-arbitrage (RLNA) and proving it under a sharp dichotomy condition.
result No-arbitrage alone does not imply the existence of an equivalent separating measure.
The paper explores arbitrage in financial markets under uncertainty using Wasserstein distance.
problem Investigating arbitrage in financial markets with distributional uncertainty.
method Using Wasserstein distance, the paper considers weak and strong forms of arbitrage conditions and introduces a relaxation called statistical arbitrage.
result The paper derives dual formulations of robust arbitrage conditions and conducts computational experiments to answer questions about ambiguity and statistical arbitrage.
The paper investigates cyclic arbitrage opportunities in decentralized exchanges.
problem Price discrepancies in decentralized exchanges lead to arbitrage opportunities.
method Theoretical framework and analysis of transaction-level data.
result Traders have executed over 292,606 cyclic arbitrages over eleven months, exploiting more than 138 million USD in revenue.
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to superreplicate a constant c>1. The optimal arbitrage strategy is the strategy for…
This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a numéraire asset. Fundamental theorems of asset pricing are stated and proven in this context. The distinction between the notions of investment-consumption arbitrage and pure-investment arbitrage provide…
Virtual Arbitrage Pricing Theorycond-mat.stat-mech
We generalize the Arbitrage Pricing Theory (APT) to include the contribution of virtual arbitrage opportunities. We model the arbitrage return by a stochastic process. The latter is incorporated in the APT framework to calculate the correction to the APT due to the virtual arbitrage opportunities. The resulting relatio…
No-arbitrage constraints on implied variance slope are weak, leading to almost guaranteed arbitrage in many cases.
problem Weak constraints on implied variance slope in the Black-Scholes model lead to arbitrage opportunities.
method Analysis of constraints on implied variance slope and their implications for arbitrage.
result Arbitrage is almost always guaranteed in a wide range of slope values where constraints are enforced.
We refute Taleb's claim that election forecasts are arbitrage-violating.
problem The validity of probabilistic election forecasts using no-arbitrage pricing techniques.
method We use mild assumptions to show all forecasts are arbitrage-free.
result Taleb's heuristic for evaluating forecasts is incorrect.
Short-term arbitrage found in markets with bounded growth rates.
problem Short-term relative arbitrage in markets with bounded growth rates.
method Time-homogeneity hypothesis applied to show short-term arbitrage.
result Short-term relative arbitrage exists in markets with bounded growth rates.
Study a financial market with singular drift and no arbitrage, considering jumps and delays.
problem Model a financial market with singular drift and no arbitrage, considering jumps and delays.
method Use geometric Itô-Lévy process with singular drift term, incorporate jumps and delays, and apply white noise calculus.
result No arbitrage in the market when delay θ > 0, maximal value finite.
Physics of Financehep-th
We give a brief introduction to the Gauge Theory of Arbitrage. Treating a calculation of Net Present Values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. Thi…
We explore the role that random arbitrage opportunities play in hedging financial derivatives. We extend the asymptotic pricing theory presented by Fedotov and Panayides [Stochastic arbitrage return and its implication for option pricing, Physica A 345 (2005), 207-217] for the case of hedging a derivative when arbitrag…
Deep learning models reconstruct volatility surfaces from noisy data under no-arbitrage constraints.
problem Reconstructing implied volatility surfaces from sparse and noisy option quotes.
method Compared multiple neural architectures including Transformers, U-Nets, and variational autoencoders.
result Transformer and U-Net architectures achieve strong reconstruction accuracy, especially under sparse observation regimes.
Investors pay for learning inside information that allows arbitrage.
problem How much is an investor willing to pay for inside information that leads to arbitrage opportunities?
method Indifference valuation approach, studying optimal investment-consumption problems with inside information.
result Characterization of when the value of informational arbitrage is universal.
We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional diffusion setting and examine how these notions of no-arbitrage relate to each other.
Paper presents online learning for statistical arbitrage without stationarity assumptions.
problem Statistical arbitrage strategies often rely on assumptions that may not hold for non-stationary processes.
method Online learning algorithms for mean reversion models without stationarity assumptions.
result Strong learning guarantees for online learning in non-stationary processes.
Diversity and no arbitrageq-fin.PM
A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy to construct diffusion models which are both diverse and free of arbitrage. Can o…