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 “arbitrage theory”
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…
In this work a relation between a measure of short-term arbitrage in the market and the excess growth of portfolios as a notion of long-term arbitrage is established. The former originates from "Geometric Arbitrage Theory" and the latter from "Stochastic Portfolio Theory". Both aim to describe non-equilibrium effects i…
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.
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…
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 …
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…
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…
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 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.
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.
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geomet…
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.
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…
We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. A…
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…
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…
The paper analyzes arbitrage theory in a fluctuating market of stochastic dimension.
problem Arbitrage opportunities in a market with time-varying asset numbers.
method Develops the fundamental theorem of asset pricing and optional decomposition theorem in a stochastic dimension market.
result Equivalence of conditions for no arbitrage and viability in a stochastic dimension market.
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…
Abstract framework for no-arbitrage concepts in topological vector lattices.
problem Generalization of no-arbitrage concepts in topological vector lattices.
method Imposing a structural condition on trading strategies and deriving abstract FTAP.
result NUPBR, NAA, and NA may not be equivalent in general setting.
Develops SPT with price impact, deriving formulas for wealth and arbitrage conditions.
problem Tackles price impact in high-dimensional markets.
method Incorporates nonlinear price impact and impact decay models.
result Derives master formula for trading strategies and wealth dynamics.
The paper applies thermodynamics to financial markets to prove no-arbitrage constraints.
problem No arbitrage in financial markets under price impact.
method Stochastic thermodynamics applied to financial trading cycles.
result Proves any round-trip trading strategy yields non-positive expected profit.
Monotonicity of normalized implied-volatility coordinates under no-arbitrage
problem Monotonicity of normalized implied-volatility coordinates under no-arbitrage
method Elementary discrete no-arbitrage proof
result Monotonicity principle extended to Bachelier implied volatility
Golden age of mathematical finance in the late 20th century.
problem Foundations of mathematical finance during the late 20th century.
method Collaboration between economists and probabilists.
result Established two fundamental theorems of arbitrage theory and close formulas for options.
The study uses reproducing kernels to model bond discount curves.
problem Estimating bond discount curves under no-arbitrage conditions.
method Introduced reproducing kernels as a regression basis for estimating bond discount curves.
result Reproducing kernels provide a tractable solution for calibrating models to market data.
The paper develops a new model for high-dimensional spatial arbitrage pricing.
problem Estimating spatial interactions in high-dimensional asset pricing.
method Integrates spatial interactions with multi-factor analysis using generalized shrinkage Yule-Walker (SYW) estimation.
result Established asymptotic properties for high-dimensional spatial arbitrage pricing models.
We discuss the finding that cross-sectional characteristic based models have yielded portfolios with higher excess monthly returns but lower risk than their arbitrage pricing theory counterparts in an analysis of equity returns of stocks listed on the JSE. Under the assumption of general no-arbitrage conditions, we arg…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We giv…
We analyze the martingale selection problem of Rokhlin (2006) in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in examples spanning frictionless mar…
Perishable Goods versus Re-tradable Assets: A Theoretical Reappraisal of a Fundamental Dichotomyq-fin.GN
New theory shows perishable goods markets are more stable and efficient.
problem Lower stability and efficiency of markets for re-tradable assets compared to perishable goods.
method Reformulation of no-trade and no-arbitrage theorems in neoclassical finance.
result Perishable goods markets exhibit higher stability and efficiency.
This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the literature as the first kind of non-arbitrage. For this non-arbitrage notion, we ob…
Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expe…
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…
Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidenceq-fin.PM
The study extends SPT to account for real-world transaction costs, improving portfolio performance.
problem Real-world transaction costs affect portfolio performance, especially during market stress.
method Developed a continuous-time model with stochastic transaction costs and derived lower bounds for cost-adjusted wealth.
result Functionally generated portfolios can still achieve relative arbitrage after accounting for transaction costs.
The paper develops no arbitrage results for trajectory based models by imposing general constraints on the trading portfolios. The main condition imposed, in order to avoid arbitrage opportunities, is a local continuity requirement on the final portfolio value considered as a functional on the trajectory space. The pap…
Generalizes optimal portfolio theory to include capital gains taxes.
problem Investment optimization in markets with capital gains taxes.
method Mathematical analysis of a specific market model with realistic tax rules.
result Closedness of attainable terminal wealth set under no unbounded non-substitutable investment condition.