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 Theory”
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.
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.
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 …
Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geom…
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.
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.
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…
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…
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…
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…
De Finetti's 1931 work laid the groundwork for modern arbitrage theory.
problem The lack of recognition of de Finetti's contributions to arbitrage theory.
method Examining de Finetti's 1931 work and its relation to recent developments in Robust Finance.
result De Finetti's work is considered the precursor of Asset Pricing Theory.
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.
Arbitrage and Geometryq-fin.MF
This article introduces the notion of arbitrage for a situation involving a collection of investments and a payoff matrix describing the return to an investor of each investment under each of a set of possible scenarios. We explain the Arbitrage Theorem, discuss its geometric meaning, and show its equivalence to Farkas…
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.
We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators reaction on it. The model accounts for both violation of the no-arbit…
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.
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…
Study arbitrage theory without numéraire, generalizing NUPBR.
problem Arbitrage theory in markets without numéraire.
method Disintegration of probability space into crash times.
result Generalization of NUPBR to no unbounded profits with bounded risk.
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.
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.
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
problem Analyzing arbitrage bubbles in financial markets.
method Developed a generalized Black-Scholes equation with stochastic arbitrage bubbles.
result The Black-Scholes model is a low-energy limit of a stochastic model.
In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly…
New formulation tackles arbitrage in volatile markets using eigenvalue bounds.
problem Arbitrage opportunities in volatile markets beyond a certain time horizon.
method Formulated as a stochastic optimal control problem, solved via PDE.
result Characterized arbitrage time horizon through PDE solution.
Convex Order and Arbitrageq-fin.MF
Paper finds optimal transport measures for arbitrage strategies.
problem Link between convex order and arbitrage strategies.
method Develops algorithms and models for finding optimal transport measures.
result Constructs a model-independent arbitrage strategy.
Aggregation of financial marketsq-fin.MF
We formalize how markets aggregate via arbitrage and quantify liquidity loss.
problem How financial markets aggregate and the loss of liquidity.
method Characterize markets via utility functions, use thermodynamics analogy, derive limit order book representation, compute aggregation loss.
result Arbitrage-mediated aggregation leads to market-dynamical entropy quantifying liquidity loss.
Volatility smile and stochastic arbitrage returnscond-mat.other
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that…
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.
Study arbitrage in financial markets with trading restrictions.
problem Arbitrage in financial markets with trading constraints.
method Portfolio optimization problems and discrete-time setup.
result Solvability of portfolio optimization problems equivalent to absence of first kind arbitrage.
Risk-neutral pricing for APTecon.GN
We price financial models using optimization and probability theory.
problem Financial model pricing under risk-averse investors.
method Infinite dimensional optimization, probabilistic and functional analytic tools.
result Existence of optimal strategies and convergence of reservation prices.
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.
Paper establishes robust no-arbitrage conditions under projective determinacy.
problem Understanding financial models under Knightian uncertainty.
method Adopting a projective framework, treating all model components uniformly in terms of measurability.
result Establishes characterizations of robust no-arbitrage condition under PD.
Revisits behavioral finance option pricing model to align with rational asset pricing theory.
problem Inconsistency between behavioral finance and rational asset pricing models in option pricing.
method Introduces arbitrage transaction costs to modify the behavioral finance option pricing formula.
result Modifies behavioral finance option pricing formula to be consistent with rational asset pricing theory.
Paper solves PDEs for optimal investment strategies in volatile markets.
problem Finding optimal investment strategies in volatile markets.
method Numerical methods using time-changed Bessel bridges.
result Solves PDEs for relative arbitrage opportunities in volatility-stabilized markets.
Conditional Davis Pricingq-fin.MF
We study the set of marginal utility-based prices of a financial derivative in the case where the investor has a non-replicable random endowment. We provide an example showing that even in the simplest of settings - such as Samuelson's geometric Brownian motion model - the interval of marginal utility-based prices can …
Price Impact on Term Structureq-fin.TR
Theory of price impact on bond term structure.
problem Understanding price impact in interest rate markets.
method Formulated instantaneous and transient price impact on bonds with different maturities, connecting to no-arbitrage theory.
result Price impact can be embedded in the pricing measure and no-arbitrage preserved.
We derive behavioral finance option pricing formulas consistent with the rational dynamic asset pricing theory. In the existing behavioral finance option pricing formulas, the price process of the representative agent is not a semimartingale, which leads to arbitrage opportunities for the option seller. In the literatu…
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…
Absence-of-Arbitrage (AoA) is the basic assumption underpinning derivatives pricing theory. As part of the OTC derivatives market, the CDS market not only provides a vehicle for participants to hedge and speculate on the default risks of corporate and sovereign entities, it also reveals important market-implied default…
New method finds profitable investment opportunities by considering additional financial variables.
problem Finding trading strategies that outperform the market with high probability.
method Generalizing functionally generated portfolios to include continuous-path semimartingales.
result Inclusion of additional processes can reduce time horizons for profitable arbitrage opportunities.
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fe…