Absence Of Arbitrage Opportunities Research Articles

Applying Theorem of Ross to Transition Probability Matrix in Energy Options Pricing after Political Tensions and Russia-Ukraine Conflict

Probability Matrix, it is necessary to obtain energy options pricing. The paper found the true probabilities of transition from the current state of the market to other states. The energy options pricing including effects of Political tensions is proposed. The methods are based on true probabilities of transition to the next state of the energy market. It can be used to predict the movement of the underlying asset of energy options (oil and gas derivatives pricing). For example, one strategy might be to compare the energy sources at the beginning 2022 (before 24.02.2024) with the current state of the market. The results show that this matrix can be implemented in energy options pricing, which represents the true probabilities of transition from the current state of the market to modern state. Practical implementation is an investment strategy in oil and gas futures that should include the median of a given distribution with the current state of the market after beginning of Russia-Ukraine conflict. The absence of arbitrage opportunities is a fundamental principle underlying modern financial pricing theory. This concept is peculiar to the statement of the fundamental theorem of asset pricing. The results prove idea that at a fixed point in time is the information about some market quotations of American Call options can be determined. The results have a set of quotes that are available in both directions: both for strikes and for periods to maturity.

Put–Call Parities, absence of arbitrage opportunities, and nonlinear pricing rules

AbstractWhen prices of assets traded in a financial market are determined by nonlinear pricing rules, different parities between call and put options have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity‐sensitive (Choquet and/or Šipoš) pricing rules, that is, pricing rules that can be represented via discounted expectations with respect to non‐additive probability measures. We analyze how nonadditivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Šipoš pricing rules to be arbitrage free. Finally, we identify violations of the Call‐Put Parity with the presence of bid–ask spreads.

Revisiting Semidefinite Programming Approaches to Options Pricing: Complexity and Computational Perspectives

In this paper, we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics but only the absence of arbitrage opportunities. We formulate this as a generalized moment problem and utilize the well-known moment-sum-of-squares hierarchy of Lasserre to obtain bounds on the range of the possible prices. A complementary approach (also from Lasserre) is employed for comparison. We present several numerical examples to demonstrate the viability of our approach. The framework we consider makes it possible to incorporate different kinds of observable data, such as moment information, as well as observable prices of options on the assets of interest. History: Accepted by Antonio Frangioni, area editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [Grant 813211 (POEMA)]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1220 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.6602361 ].

A REVIEW OF THE METHODS OF ECONOMIC AND MATHEMATICAL MODELING BASED ON THE PRINCIPLES OF ECONOPHYSICS. PART 2

A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of information systems and mathematical methods in economics is given. The first part gives the concept of a financial bubble and methods for finding them. At the beginning of the article, the development of econophysics is given. Therefore, using the research of physicists as a model, econophysics should begin its research not from the upper floors of an economic building (in the form of financial markets, distribution of returns on financial assets, etc.), but from its fundamental foundations or, in the words of physicists, from elementary economic objects and forms of their movement (labor, its productivity, etc.). Only in this way can econophysics find its subject of study and become a "new form of economic theory". Further, the main prerequisites of financial bubble models in the market are considered: the principle of the absence of arbitrage opportunities, the existence of rational agents, a risk-driven model, and a price-driven model. A well-known nonlinear LPPL model (log periodic power law model) was proposed. In the works of V.O. Arbuzov, it was proposed to use procedures for selecting models. Namely, basic selection, "stationarity" filtering, and spectral analysis were introduced. The results of the model were presented in the works of D. Sornette and his students. The second part gives the concept of percolation and its application in Economics. We will consider a mathematical model proposed by J.P. Bouchaud, D. Stauffer, and D. Sornette that recreates the behavior of an agent in the market and their interaction, geometrically describing a phase transition of the second kind. In this model, the price of an asset in a single time interval changes in proportion to the difference between supply and demand in this market. The results are published in the works of A.A. Byachkova, B.I. Myznikova and A.A. Simonov. There are two types of phase transition: the first and second kind. During the phase transition of the first kind, the most important, primary extensive parameters change abruptly: the specific volume, the amount of stored internal energy, the concentration of components, and other indicators. It should be noted that this refers to an abrupt change in these values with changes in temperature, pressure, and not a sudden change in time. The most common examples of phase transitions of the first kind are: melting and crystallization, evaporation and condensation. During the second kind of phase transition, the density and internal energy do not change. The jump is experienced by their temperature and pressure derivatives: heat capacity, coefficient of thermal expansion, or various susceptibilities. Phase transitions of the second kind occur when the symmetry of the structure of a substance changes: it can completely disappear or decrease. For quantitative characterization of symmetry in a second-order phase transition, an order parameter is introduced that runs through non-zero values in a phase with greater symmetry, and is identically equal to zero in an unordered phase. Thus, we can consider percolation as a phase transition of the second kind, by analogy with the transition of paramagnets to the state of ferromagnets. The percolation threshold or critical concentration separates two phases of the percolation grid: in one phase there are finite clusters, in the other phase there is one infinite cluster. The key situation to study is the moment of formation of an infinite cluster on the percolation grid, since this means the collapse of the market, when the overwhelming part of agents for this market has a similar opinion about their actions to buy or sell an asset. The main characteristics of the process are the threshold probability of market collapse, as well as the empirical distribution function of price changes in this market. Keywords: econophysics, behavior of agents in the market, market crash, second-order phase transition, percolation theory, model calibration, agent model calibration, percolation gratings, gradient percolation model, percolation threshold, clusters, fractal dimensions, phase transitions of the first and second kind.

Pricing and hedging vulnerable option with funding costs and collateral

We explore the valuation and hedging strategies of a European vulnerable option with funding costs and collateralization for local volatility models. It is found that, in the absence of arbitrage opportunities, the option price must lie within a no-arbitrage band. The boundaries of no-arbitrage band are computed as solutions to backward stochastic differential equations (BSDEs in short) of replicating strategy and offsetting strategy. Under some conditions, we obtain the closed-form representations of the no-arbitrage band for local volatility models. In particular, the fully explicit expressions of the no-arbitrage band for Black–Scholes model and the constant elasticity of variance (CEV) model with time-dependent parameters are derived. Furthermore, we provide a strategy for the option holder by using the risky bond issued by the option writer to hedge the remaining potential losses. By virtue of numerical simulation, the impact of the default risk, funding costs and collateral can be observed visually.

External balances, trade and financial conditions

I present a new model for the U.S. external position that accounts for the accumulation of international debt over the past 60years. The model is based on the present value restriction that links a country's external position to future trade flows and financial conditions in the absence of arbitrage opportunities and Ponzi schemes. It features the role played by the stochastic discount factor, the trade and valuation adjustment channels and provides a decomposition of the U.S. external position into secular and cyclical components. The model shows that shocks operating via the valuation channel are the dominant drivers of cyclical dynamics, accounting for approximately 80% of the variance over the 60-year sample. This channel works primarily via capital gains and losses on U.S. foreign assets and is closely tied to the international value of the U.S. dollar. In contrast, there is no evidence that valuation channel adjustments contribute to the secular dynamics, but differences between the average returns on foreign assets and liabilities raise the steady-state debt-to-GDP ratio from approximately 12 to 15%. The long-term deterioration in the U.S. position represents a move towards the steady-state before the early 1990s and a move away from the steady-state thereafter. I quantify the expected improvement in future U.S. trade balances needed to justify this as a sustainable path and show that they are very different from its actual behavior during the last 60years. I also study the behavior of the U.S. position during the 2007–2008 financial crisis.

IMPLICIT TRANSACTION COSTS AND THE FUNDAMENTAL THEOREMS OF ASSET PRICING

This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Implicit transaction costs are composed of two terms, one is able to capture the bid-ask spread, and the second the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having cádlág (right-continuous with left limits) and cáglád (left-continuous with right limits) paths of bounded quadratic variation and of finitely many jumps. That is, cádlág and cáglád predictable trading strategies of infinite variation, with finitely many jumps and of finite quadratic variation are allowed in our setting. Restricting ourselves to cáglád predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with implicit transaction costs. To better understand how to apply the theory proposed we provide an example of an implicit transaction cost economy that is linear and nonlinear in the order size.

Detecting capital market convergence clubs

AbstractIn this study, we propose a new method to find convergence clubs that combine pairwise method of testing convergence with maximal clique algorithm. Unlike many of those already developed in the literature, this new method aims to find convergence clubs endogenously without depending on priori classifications. We use our method to study convergence among different capital markets as captured by their respective indices. Stock market convergence would indicate the absence of arbitrage opportunities in moving between the different markets as they would all present investors with similar risks. Furthermore, stock market convergence would be a precursor to GDP convergence as these economies would be bound by similar (possibly unobservable) common factors that affect long run macroeconomic performance.

Analysis and Forecast of Tracking Performance of Hong Kong Exchange-Traded Funds: Evidence from Tracker Fund and X iShares A50

This study examines the tracking performance of two Hong Kong exchange-traded funds (ETFs): Tracker Fund and X iShares A50. The turnover of these two ETFs was more than half the total turnover of the 141 ETFs in the Hong Kong market during 2005–2013. Tracking performance is assessed using pricing deviation, which is found to be nonzero and predictable. This indicates that the premium paid by investors is of considerable economic interest. The significant differences in the tracking performance of physical ETFs and synthetic ETFs highlight the relative inability of synthetic ETF to track the market. Additionally, we document the existence of co-integration between the ETF prices and stock market prices. An econometric model is estimated to forecast the pricing deviation, which shows different price dynamics between the two ETFs, but an absence of arbitrage opportunities. The time series regression model of pricing deviation is significantly influenced by market value, dividend yield, trading volume, bid-ask spread, and market risk. The size of the regression coefficients indicates that synthetic ETFs have relatively poor ability to track the market during market fluctuations.

Elements of Quantum Finance Models

Both academic research and practical application of mathematical finance have been extremely fruitful since the seminal work of Black-Scholes-Merton in the early 1970s. In this framework, the prices of financial assets are modeled as stochastic processes in probability spaces inside which the machinery of stochastic calculus is a powerful tool. The fundamental asset pricing theorem states that the absence of arbitrage opportunities in a market is equivalent to the existence of a probability measure, equivalent to the objective probability, under which the discounted prices of the assets become local martingales. This linkage between finance on the one hand and probability theory on the other is the key to the success of mathematical finance. In this note, we show that it is possible to extend a classical probability model to a quantum probability model. Classical stochastic calculus is replaced by its quantum counterpart on a Boson Fock space. In particular, we show that the fundamental asset pricing theorem remains valid in this non-commutative setting. By its very nature of coping with non-commutative random variables however, many essential elements of classic mathematical finance but in quantum form have not been recovered in this note. A couple that have been established are not in their full generality. For instance, existence of non-trivial self-financing portfolios and preserving of self-financing property under change of numeraire can only be reclaimed subject to technical conditions. This writing puts together a few helpful results for the purpose of future studies of this potentially new research subject.

Robust No Arbitrage of the Second Kind with a Continuum of Assets and Proportional Transaction Costs

Motivated by bond markets with a continuum of possible maturities, we study a robust version of the absence of arbitrage opportunity of the second kind introduced by Rasonyi in a continuous-time and infinite-dimensional financial market model with proportional transaction costs.

Skewed Generalized Error Distribution of Financial Assets and Option Pricing

This article provides a mathematical and empirical investigation of the reasons for the presence of skewness and kurtosis in financial data. The results indicate that this phenomenon is triggered by higher-order moment dependencies in the data, such as asymmetric and conditional volatility. Moreover, the article develops and tests successfully a skewed extension of the generalized error distribution (SGED), which is then used to model European call option prices. Under the standard assumptions of risk neutrality, normality of log-returns, and absence of arbitrage opportunities, the SGED model yields as special cases several well-known models for pricing options on stocks, stock indices, currencies, and currency futures.

General financial market model defined by a liquidation value process

Financial market models defined by a liquidation value process generalize the conic models of Schachermayer and Kabanov where the transaction costs are proportional to the exchanged volumes of traded assets. The solvency set of all portfolio positions that can be liquidated without any debt is not necessary convex, e.g. in presence of proportional transaction costs and fixed costs. Therefore, the classical duality principle based on the Hahn–Banach separation theorem is not appropriate to characterize the prices super hedging a contingent claim. Using an alternative method based on the concepts of essential supremum and maximum, we provide a characterization of European and American contingent claim prices under the absence of arbitrage opportunity of the second kind.

An Alternative Proof of the Froot and Stein Theorem on Optimal Corporate Hedging Policy

The requirement for additional conditions to accompany the original derivation of the Froot and Stein Theorem was demonstrated by Hogh et al. (2006). Guillen et al. (2008) proved the result without these qualifications, using an arbitrage-free pricing approach. Below an alternative proof of the theorem is given, sustaining the Froot and Stein pricing model assumption for traded risks as far as consistent with absence of arbitrage opportunities.

Cost-efficient contingent claims with market frictions

In complete frictionless securities markets under uncertainty, it is well-known that in the absence of arbitrage opportunities, there exists a unique linear positive pricing rule, which induces a state-price density (e.g., Harrison and Kreps (1979)). Dybvig (1988) showed that the cheapest way to acquire a certain distribution of a consumption bundle (or security) is when this bundle is anti-comonotonic with the state-price density, i.e., arranged in reverse order of the state-price density. In this paper, we look at extending Dybvig's ideas to complete markets with imperfections represented by a nonlinear pricing rule (e.g., due to bid-ask spreads). We consider an investor in a securities market where the pricing rule is "law-invariant" with respect to a capacity (e.g., Choquet pricing as in Araujo et al. (2011), Chateauneuf et al. (1996), Chateauneuf and Cornet (2015), or Cerreia-Vioglio et al. (2015)). The investor holds a security with a random payoff X and his problem is that of buying the cheapest contingent claim Y on X, subject to some constraints on the performance of the contingent claim and on its level of risk exposure. The cheapest such claim is called "cost-efficient". If the capacity satisfies standard continuity and a property called "strong diffuseness" introduced in Ghossoub (2015), we show the existence and monotonicity of cost-efficient claims, in the sense that a cost-efficient claim is anti-comonotonic with the underlying security's payoff X. Strong diffuseness is satisfied by a large collection of capacities, including all distortions of diffuse probability measures. As an illustration, we consider the case of a Choquet pricing functional with respect to a capacity and the case of a Choquet pricing functional with respect to a distorted probability measure. Finally, we consider a simple example in which we derive an explicit analytical form for a cost-efficient claim.

A Quantum Finance Model

Both academic research and practical application of mathematical finance have been extremely fruitful since the seminal work of Black-Scholes-Merton in the early 1970s. In this framework, the prices of financial assets are modeled as stochastic processes in probability spaces inside which the machinery of stochastic calculus is a powerful tool. The fundamental asset pricing theorem states that the absence of arbitrage opportunities in a market is equivalent to the existence of a probability measure, equivalent to the objective probability, under which the discounted prices of the assets become local martingales. This linkage between finance on the one hand and the probability theory on the other is the key to the success of mathematical finance. In this note, we show that it is possible to extend the classical probability model to a quantum probability model. The classical stochastic calculus is replaced by its quantum counterpart on the Boson Fock space. In particular, we show that the fundamental asset pricing theorem remains valid in this non-commutative setting. As an application, prices of quantum European options are obtained.

Banking and back-loading emission permits

In this article we focus on the so-called back-loading policy adopted by the European Commission to increase the carbon market price. This environmental measure consists of removing a share of the allowances allocated for a given period in order to reallocate some or all of them later on. To analyze the impact of the permits back-loading, we determine the CO2 price equilibrium with and without the policy measure, considering not only the market for permits but also the output market of regulated sectors. We propose a two-period model, where the market for permits is perfectly competitive, and the output market can be either competitive or oligopolistic. First, we define the condition under which banking from one period to another is optimal. This condition, that is the absence of arbitrage opportunities (AOA), depends not only from the period initial allocation but also on production market fundamentals. When this condition is satisfied, the market for emission is shown intertemporally efficient. Second, we point out that the back-loading measure may create inefficiencies or leave unaffected the permits price, if it alters the AOA.

General Financial Market Model Defined by a Liquidation Value Process

We present a general financial market model defined by a liquidation value process. This approach generalizes the conic models of Schachermayer and Kabanov where the transaction costs are proportional to the exchanged volumes of traded assets. This allows to consider financial market models where proportional transaction costs and fixed costs coexist. In this case, the solvency set of all portfolio positions that can be liquidated without any debt is not necessary convex. Therefore, the usual duality principle based on the Hahn-Banach separation theorem is not appropriate to characterize the prices super hedging a contingent claim. We propose an alternative method to price European or American contingent claims under absence of arbitrage opportunity of the second kind.

Shortfall Risk Minimization in Discrete Time Financial Market Models

In this paper, we study theoretical and computational aspects of risk minimization in financial market models operating in discrete time. To define the risk, we consider a class of convex risk measures defined on $L^{p}(\mathbb{P})$ in terms of shortfall risk. Under mild assumptions, namely, the absence of arbitrage opportunity and the nondegeneracy of the price process, we prove the existence of an optimal strategy by performing a dynamic programming argument in a non-Markovian framework. In a Markovian framework, the shortfall risk and optimal dynamic strategies are estimated using three main tools: Newton--Raphson Monte Carlo--based procedure, stochastic approximation algorithm, and Markovian quantization scheme. Finally, we illustrate our approach by considering several shortfall risk measures and portfolios inspired by energy and financial markets.

Arbitrage Pricing Theory Under Transaction Costs and Application to the Tobin Tax

This paper studies arbitrage pricing theory in financial markets with transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Transaction costs are composed of two terms, one is able to capture the implicit transaction costs, and the second the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having caglad (right-continuous with left limits) and caglad (left-continuous with right limits) paths of bounded quadratic variation and of finitely many jumps. That is, caglad and caglad predictable trading strategies of infinite variation, with finitely many jumps and of finite quadratic variation are allowed in our setting. Restricting ourselves to caglad predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with transaction costs. To better understand how to apply the theory proposed we provide an example with linear and non-linear transaction costs.