Fundamental Theorem Of Asset Pricing 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.

Sustainability-valued discrete option pricing in complete markets

ABSTRACT We consider option pricing using recombining binomial trees, with a two-fold purpose. The first is to introduce environmental, social and governance (ESG) sustainability valuation into option pricing. We explore this in a number of scenarios, including enhancement of yield due to trader information and the impact of the past history of a market driver. The second is to emphasize the use of discrete dynamic pricing, rather than continuum models, as the natural model that governs actual market practice. Furthermore, use of continuous, rather than discrete, compounding (e.g. of the risk-free rate) in discrete option pricing models violates conditions of the fundamental theorem of asset pricing and no-arbitrage. By considering models based upon both compounding methods, we show explicitly where this violation occurs and demonstrate computational differences that arise as a result.

Fundamental Theorem of Asset Pricing under fixed and proportional costs in multi-asset setting and finite probability space

The Fundamental Theorem of Asset Pricing is extended to a market model over a finite probability space with many assets that can be exchanged into one another under combined fixed and proportional transaction costs. The absence of arbitrage in this setting is shown to be equivalent to the existence of a family of absolutely continuous single-step probability measures and a multi-dimensional martingale with respect to such a family.

A conditional Version of the second fundamental theorem of asset pricing in discrete time

A conditional Version of the second fundamental theorem of asset pricing in discrete time

Arbitrage theory in a market of stochastic dimension

AbstractThis paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements: (i) there exists a supermartingale numéraire portfolio; (ii) each dissected market, which is of a fixed dimension between dimensional jumps, has locally finite growth; (iii) there is no arbitrage of the first kind; (iv) there exists a local martingale deflator; (v) the market is viable. We also present the optional decomposition theorem, which characterizes a given nonnegative process as the wealth process of some investment‐consumption strategy. Furthermore, similar results still hold in an open market embedded in the entire market of stochastic dimension, where investors can only invest in a fixed number of large capitalization stocks. These results are developed in an equity market model where the price process is given by a piecewise continuous semimartingale of stochastic dimension. Without the continuity assumption on the price process, we present similar results but without explicit characterization of the numéraire portfolio.

Hedging quantitative easing

Arguably the greatest concern surrounding quantitative easing is its potential for expanding the money supply at a rate which outstrips the rate of growth in national output. This will almost surely lead to greater uncertainty in inflationary expectations and this, in turn, can have adverse consequences for stock prices. Our analysis employs the hedging procedures which underscore the Fundamental Theorem of Asset Pricing in conjunction with stochastic processes for stock prices and the money supply to design hedging strategies against potential downside movements in stock prices caused by the uncertainty in inflationary expectations associated with rapid monetary growth.

Insurance–finance arbitrage

AbstractMost insurance contracts are inherently linked to financial markets, be it via interest rates, or—as hybrid products like equity‐linked life insurance and variable annuities—directly to stocks or indices. However, insurance contracts are not for trade except sometimes as surrender to the selling office. This excludes the situation of arbitrage by buying and selling insurance contracts at different prices. Furthermore, the insurer uses private information on top of the publicly available one about financial markets. This paper provides a study of the consistency of insurance contracts in connection with trades in the financial market with explicit mention of the information involved.By defining strategies on an insurance portfolio and combining them with financial trading strategies, we arrive at the notion of insurance–finance arbitrage (IFA). In analogy to the classical fundamental theorem of asset pricing, we give a fundamental theorem on the absence of IFA, leading to the existence of an insurance–finance‐consistent probability. In addition, we study when this probability gives the expected discounted cash‐flows required by the EIOPA best estimate.The generality of our approach allows to incorporate many important aspects, like mortality risk or general levels of dependence between mortality and stock markets. Utilizing the theory of enlargements of filtrations, we construct a tractable framework for insurance–finance consistent valuation.

Fundamental theorem of asset pricing with acceptable risk in markets with frictions

We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given market. Trading is subject to nonproportional transaction costs and portfolio constraints, and full replication by way of market instruments is not always possible. Rationality is defined in terms of consistency with market prices and acceptable risk thresholds. We obtain a direct and a dual description of market-consistent prices with acceptable risk. The dual characterisation requires an appropriate extension of the classical fundamental theorem of asset pricing where the role of arbitrage opportunities is played by good deals, i.e., costless investment opportunities with acceptable risk–reward tradeoff. In particular, we highlight the importance of scalable good deals, i.e., investment opportunities that are good deals regardless of their volume.

Excess profit relative to the benchmark asset under the $ \alpha $-confidence level

<abstract><p>We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ \alpha $-confidence level, $ \alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ \alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ \alpha $-REP.</p></abstract>

Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation

We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices for other single- and multi-asset derivatives and even allow for the presence of bid–ask spread in these prices. We provide a fundamental theorem of asset pricing for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probability measures into a more tractable minimization problem over vectors, subject to certain constraints. Then, we recast this problem into a linear semi-infinite optimization problem and provide two algorithms for its solution. These algorithms provide upper and lower bounds for the prices that are ε-optimal, as well as a characterization of the optimal pricing measures. These algorithms are efficient and allow the computation of bounds in high-dimensional scenarios (e.g., when d = 60). Moreover, these algorithms can be used to detect arbitrage opportunities and identify the corresponding arbitrage strategies. Numerical experiments using both synthetic and real market data showcase the efficiency of these algorithms, and they also allow understanding of the reduction of model risk by including additional information in the form of known derivative prices. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported by the Nanyang Technological University [NAP Grant] and the Hellenic Foundation for Research and Innovation [Grant HFRI-FM17-2152]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2022.4456 .

Fundamental theorem of asset pricing: a strengthened version and а martingale measures search area

In the article a strengthened version of the ’Fundamental Theorem of Asset Pricing’ for a one-period market model is proven. The principal role in this result is played by total and nonanihilating cones.

Model risk quantification based on relative entropy

Model risk can be broadly defined as the possibility of suffering losses due to errors either in the development or use of models. Financial pricing and risk measurement are subject to model risk, and its quantification is a hot topic in both academia and the financial industry. This paper presents a technique for challenging derivative pricing models that will also help to quantify model risk. The proposed approach is based on the fundamental theorems of asset pricing, which allow a model to be interpreted as a pricing measure, and on the use of the minimum relative entropy technique as a way of changing between measures. This paper makes three contributions to the literature. First, it overcomes many of the limitations of previous approaches that identified models and probability measures. Second, a statistical divergence is defined for both quantifying the divergence between measures, and therefore between models, and determining the set of optimal market instruments in the calibration of models. Third, the proposed methodology is able to assess the model risk of a target portfolio. Further, it is theoretically possible to determine a model without model risk for such a portfolio. This last framework has been explicitly designed to be easily applied by financial industry practitioners.

LARGE PLATONIC MARKETS WITH DELAYS

The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large Platonic markets, which allow infinitely many assets and incorporate a restricted information setting. The discussion is divided into information delays and order execution delays. The former enables modeling of markets, where the observed information is delayed, while the latter provides the opportunity to defer the indexed time of a received asset price. Both delays may be designed randomly and inhomogeneously over time. We show that delayed markets are equipped with a fundamental theorem of asset pricing and our main result is inheritance of the no asymptotic Lp-free lunch condition under both delay types. Eventually, we suggest an approach to verify absence of Lp-free lunch on markets with multiple brokers endowed with deviating trading speeds.

COHERENT RISK MEASURE ON L0: NA CONDITION, PRICING AND DUAL REPRESENTATION

The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on [Formula: see text] is fixed to characterize the family of acceptable wealths that play the role of nonnegative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce a dual characterization of the super-hedging prices (called risk-hedging prices) of a European option. Moreover, we show that the set of all risk-hedging prices is closed under NA. At last, we provide a dual representation of the risk-measure on [Formula: see text] under some conditions.

No-arbitrage concepts in topological vector lattices

We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA_1 and NA_1 may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.

A unified framework for robust modelling of financial markets in discrete time

We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in finite discrete time. In particular, we prove a fundamental theorem of asset pricing and a superhedging theorem which encompass the formulations of Bouchard and Nutz [12] and Burzoni et al. [13]. In bringing the two streams of literature together, we examine and compare their many different notions of arbitrage. We also clarify the relation between robust and classical ℙ-specific results. Furthermore, we prove when a superhedging property with respect to the set of martingale measures supported on a set Omega of paths may be extended to a pathwise superhedging on Omega without changing the superhedging price.

Perturbation analysis of sub/super hedging problems

AbstractWe investigate the links between various no‐arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. No‐arbitrage conditions, either in this abstract setting or in the case of a market consisting of European Call options, give rise to duality properties of infinite‐dimensional sub‐ and super‐hedging problems. With a view towards applications, we show how duality is preserved when reducing these problems over finite‐dimensional bases. We also introduce a rigorous perturbation analysis of these linear programing problems, and highlight numerically the influence of smile extrapolation on the bounds of exotic options.

Risk‐neutral pricing techniques and examples

AbstractTractability and flexibility are among the two most attractive features of models in mathematical finance. For the pricing of derivative products, to avoid arbitrage opportunities, the fundamental theorem of asset pricing requires the existence of an equivalent martingale measure under which the discounted price process is a (local) martingale. In the semimartingale setting, the traditional approach of risk‐neutral valuation uses a change of measure invoking Girsanov's theorem. This approach often destroys the tractability of the process which is undesirable for quantitative finance applications. To overcome these limitations, we employ a transformation based on the concept of intertwining relationships that allows us to convert Markovian semigroups into a pricing semigroup while keeping its tractability. In order to illustrate the usefulness of this approach, we apply it to exponential Lévy, positive self‐similar, and generalized CIR processes that all fall within the class of polynomial processes introduced by Cuchiero et al. (2012). Furthermore, for the jump CIR class, relying on recent work of Patie and Savov (2019), we provide an eigenvalues expansion of the pricing semigroup and carry out some numerical experiments.

Viability and Arbitrage Under Knightian Uncertainty

We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order. We derive the fundamental equivalence of economic viability of asset prices and absence of arbitrage. We also obtain a modified version of the fundamental theorem of asset pricing using the notion of sublinear pricing measures. Different versions of the efficient market hypothesis are related to the assumptions one is willing to impose on the common order.

Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics

We present a numerically efficient approach for machine-learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be used to implement a stochastic implied volatility model in the following two steps: 1) Train a market simulator for option prices, for example as discussed in our recent work here; 2) Find a risk-neutral density, specifically in our approach the minimal entropy martingale measure. The resulting model can be used for risk-neutral pricing, or for Deep Hedging in the case of transaction costs or trading constraints. To motivate the proposed approach, we also show that market dynamics are free from in the absence of transaction costs if and only if they follow a risk-neutral measure. We additionally provide a more general characterization in the presence of convex transaction costs and trading constraints. These results can be seen as an analogue of the fundamental theorem of asset pricing for statistical arbitrage under trading frictions and are of independent interest.