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A note on the exact solution of asset pricing models with habit persistence

Collard, F.; Feve, P.; Ghattassi, I.
Fonte: Cambridge Univ Press Publicador: Cambridge Univ Press
Tipo: Artigo de Revista Científica
Publicado em //2006 Português
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This paper provides a closed-form solution to a standard asset pricing model with habit formation when the growth rate of endowment follows a first-order Gaussian autoregressive process. We determine conditions that guarantee the existence of a stationary bounded equilibrium. The findings are useful because they allow to evaluate the accuracy of various approximation methods to nonlinear rational expectation models. Furthermore, they can be used to perform simulation experiments to study the finite sample properties of various estimation methods.; Fabrice Collard, Patrick Fève and Imen Ghattassi

A Dynamic Asset Pricing Model with Time-Varying Factor and Idiosyncratic Risk

Glabadanidis, P.
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica
Publicado em //2009 Português
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This paper uses a multivariate GARCH model to account for time variation in factor loadings and idiosyncratic risk in improving the performance of the CAPM and the three-factor Fama–French model. I show how to incorporate time variation in betas and the second moments of the residuals in a very general way. Both the static and conditional CAPM substantially outperform the three-factor model in pricing industry portfolios. Using a dynamic CAPM model results in a 30% reduction in the average absolute pricing error of size/book-to-market portfolios. Ad hoc analysis shows that the market beta of a value-minus-growth portfolio decreases whenever the default premium increases as well as during economic recessions.; Paskalis Glabadanidis

A multi-period asset pricing model: implication for size and book-to-market effect

Lin, C.T.
Fonte: Academy of International Business and Economics Publicador: Academy of International Business and Economics
Tipo: Artigo de Revista Científica
Publicado em //2008 Português
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In light of the inadequacy of Sharpe's one-period Capital Asset Pricing Model (CAPM) in explaining stock returns, this paper develops a multi-period two-factor model that incorporates growth in earnings as an additional factor besides beta. This suggests that Sharpe's CAPM may be misspecified due to the omission of the earnings growth variable. In addition, it may explain why size and book-to-market effects are significant since earnings growth and the two factors are highly correlated.; http://www.encyclopedia.com/doc/1G1-190463126.html; Chien-Ting Lin

An Information-Based Framework for Asset Pricing: X-Factor Theory and its Applications

Macrina, Andrea
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/07/2008 Português
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A new framework for asset pricing based on modelling the information available to market participants is presented. Each asset is characterised by the cash flows it generates. Each cash flow is expressed as a function of one or more independent random variables called market factors or "X-factors". Each X-factor is associated with a "market information process", the values of which become available to market participants. In addition to true information about the X-factor, the information process contains an independent "noise" term modelled here by a Brownian bridge. The information process thus gives partial information about the X-factor, and the value of the market factor is only revealed at the termination of the process. The market filtration is assumed to be generated by the information processes associated with the X-factors. The price of an asset is given by the risk-neutral expectation of the sum of the discounted cash flows, conditional on the information available from the filtration. The theory is developed in some detail, with a variety of applications to credit risk management, share prices, interest rates, and inflation. A number of new exactly solvable models are obtained for the price processes of various types of assets and derivative securities; and a novel mechanism is proposed to account for the dynamics of stochastic volatility and dynamic correlation. A discrete-time version of the information-based framework is also developed...

A two-Factor Asset Pricing Model and the Fat Tail Distribution of Firm Sizes

Malevergne, Y.; Sornette, D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/02/2007 Português
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In the standard equilibrium and/or arbitrage pricing framework, the value of any asset is uniquely specified from the belief that only the systematic risks need to be remunerated by the market. Here, we show that, even for arbitrary large economies when the distribution of the capitalization of firms is sufficiently heavy-tailed as is the case of real economies, there may exist a new source of significant systematic risk, which has been totally neglected up to now but must be priced by the market. This new source of risk can readily explain several asset pricing anomalies on the sole basis of the internal-consistency of the market model. For this, we derive a theoretical two-factor model for asset pricing which has empirically a similar explanatory power as the Fama-French three-factor model. In addition to the usual market risk, our model accounts for a diversification risk, proxied by the equally-weighted portfolio, and which results from an ``internal consistency factor'' appearing for arbitrary large economies, as a consequence of the concentration of the market portfolio when the distribution of the capitalization of firms is sufficiently heavy-tailed as in real economies. Our model rationalizes the superior performance of the Fama and French three-factor model in explaining the cross section of stock returns: the size factor constitutes an alternative proxy of the diversification factor while the book-to-market effect is related to the increasing sensitivity of value stocks to this factor.; Comment: 38 pages including 7 tables and 3 figures

Path Integral and Asset Pricing

Kakushadze, Zura
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White model, we can apply the same techniques to "less-tractable" models such as the Black-Karasinski model. We give explicit formulas for computing the bond pricing function in such models in the analog of quantum mechanical "semiclassical" approximation. We also outline how to apply perturbative quantum mechanical techniques beyond the "semiclassical" approximation, which are facilitated by Feynman diagrams.; Comment: 30 pages; a minor misprint corrected; to appear in Quantitative Finance

Asset Pricing in an Imperfect World

Cassese, Gianluca
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/10/2014 Português
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In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non empty, i.e. if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. Eventually we show that under very weak conditions the coherent pricing of options allows for a very clear representation which allows, as in Breeden and Litzenberger, to extract the implied probability.; Comment: arXiv admin note: substantial text overlap with arXiv:1406.0412

Heat Kernel Framework for Asset Pricing in Finite Time

Macrina, Andrea
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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A heat kernel approach is proposed for the development of a general, flexible, and mathematically tractable asset pricing framework in finite time. The pricing kernel, giving rise to the price system in an incomplete market, is modelled by weighted heat kernels which are driven by multivariate Markov processes and which provide enough degrees of freedom in order to calibrate to relevant data, e.g. to the term structure of bond prices. It is shown how, for a class of models, the prices of bonds, caplets, and swaptions can be computed in closed form. The dynamical equations for the price processes are derived, and explicit formulae are obtained for the short rate of interest, the risk premium, and for the stochastic volatility of prices. Several of the closed-form asset price models presented in this paper are driven by combinations of Markovian jump processes with different probability laws. Such models provide a rich basis for consistent applications in several sectors of a financial market including equity, fixed-income, commodities, and insurance. The flexible, multidimensional and multivariate structure, on which the asset price models are constructed, lends itself well to the transparent modelling of dependence across asset classes. As an illustration...

Housing risk and return: Evidence from a housing asset-pricing model

Case, Karl; Cotter, John; Gabriel, Stuart
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/03/2011 Português
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This paper investigates the risk-return relationship in determination of housing asset pricing. In so doing, the paper evaluates behavioral hypotheses advanced by Case and Shiller (1988, 2002, 2009) in studies of boom and post-boom housing markets. The paper specifies and tests a multi-factor housing asset pricing model. In that model, we evaluate whether the market factor as well as other measures of risk, including idiosyncratic risk, momentum, and MSA size effects, have explanatory power for metropolitan-specific housing returns. Further, we test the robustness of the asset pricing results to inclusion of controls for socioeconomic variables commonly represented in the house price literature, including changes in employment, affordability, and foreclosure incidence. We find a sizable and statistically significant influence of the market factor on MSA house price returns. Moreover we show that market betas have varied substantially over time. Also, results are largely robust to the inclusion of other explanatory variables, including standard measures of risk and other housing market fundamentals. Additional tests of model validity using the Fama-MacBeth framework offer further strong support of a positive risk and return relationship in housing. Our findings are supportive of the application of a housing investment risk-return framework in explanation of variation in metro-area cross-section and time-series US house price returns. Further...

Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty

Bayraktar, Erhan; Zhang, Yuchong
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated. Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfies \emph{efficient friction}, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems.; Comment: Final version. To appear in Mathematics of Operations Research

Entropy-Based Financial Asset Pricing

Ormos, Mihaly; Zibriczky, David
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/01/2015 Português
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We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return - entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behaviour of the beta along with entropy.; Comment: 21 pages, 6 figures, 3 tables and 4 supporting files

The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions

Pulido, Sergio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a well-known result of Ansel and Stricker. In the second part we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims.; Comment: Published in at http://dx.doi.org/10.1214/12-AAP914 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

A note on arbitrage, approximate arbitrage and the fundamental theorem of asset pricing

Fontana, Claudio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/11/2013 Português
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We provide a critical analysis of the proof of the fundamental theorem of asset pricing given in the paper "Arbitrage and approximate arbitrage: the fundamental theorem of asset pricing" by B. Wong and C.C. Heyde (Stochastics, 2010) in the context of incomplete It\^o-process models. We show that their approach can only work in the known case of a complete financial market model and give an explicit counterexample.; Comment: 10 pages

Finitely additive probabilities and the Fundamental Theorem of Asset Pricing

Kardaras, Constantinos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/11/2009 Português
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This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that absence of arbitrages of the first kind in the market is equivalent to the existence of a finitely additive probability, weakly equivalent to the original and only locally countably additive, under which the discounted wealth processes become "local martingales". The aforementioned result is then used to obtain an independent proof of the FTAP of Delbaen and Schachermayer. Finally, an elementary and short treatment of the previous discussion is presented for the case of continuous-path semimartingale asset-price processes.; Comment: 14 pages. Dedicated to Prof. Eckhard Platen, on the occasion of his 60th birthday. This is the 2nd part of what comprised the older arxiv submission arXiv:0904.1798

Generalized asset pricing: Expected Downside Risk-Based Equilibrium Modelling

Ormos, Mihaly; Timotity, Dusan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/12/2015 Português
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We introduce an equilibrium asset pricing model, which we build on the relationship between a novel risk measure, the Expected Downside Risk (EDR) and the expected return. On the one hand, our proposed risk measure uses a nonparametric approach that allows us to get rid of any assumption on the distribution of returns. On the other hand, our asset pricing model is based on loss-averse investors of Prospect Theory, through which we implement the risk-seeking behaviour of investors in a dynamic setting. By including EDR in our proposed model unrealistic assumptions of commonly used equilibrium models - such as the exclusion of risk-seeking or price-maker investors and the assumption of unlimited leverage opportunity for a unique interest rate - can be omitted. Therefore, we argue that based on more realistic assumptions our model is able to describe equilibrium expected returns with higher accuracy, which we support by empirical evidence as well.; Comment: 55 pages, 15 figures, 1 table, 3 appandices, Econ. Model. (2015)

Implicit transaction costs and the fundamental theorems of asset pricing

Allaj, Erindi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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 three terms, one is able to capture the implicit transaction costs, the second the price impact and the last the bid-ask spread 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 c?adl?ag (right-continuous with left limits) and c?agl?ad (left-continuous with right limits) paths of bounded quadratic variation and of ?finitely many jumps. That is, c?adl?ag and c?agl?ad predictable trading strategies of infinite variation, with?finitely many jumps and of ?finite quadratic variation are allowed in our setting. Restricting ourselves to c?agl?ad 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...

Ambiguous volatility and asset pricing in continuous time

Epstein, Larry G.; Ji, Shaolin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/01/2013 Português
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This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described.

Asset pricing with random information flow

Brody, Dorje C.; Law, Yan Tai
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/09/2010 Português
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In the information-based approach to asset pricing the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market then determines the overall magnitude of asset volatility. By letting this information flow rate random, we obtain an elementary stochastic volatility model within the information-based approach. Such an extension is economically justified on account of the fact that in real markets information flow rates are rarely measurable. Effects of having a random information flow rate is investigated in detail in the context of a simple model setup. Specifically, the price process of the asset is derived, and its characteristic behaviours are revealed via simulation studies. The price of a European-style option is worked out, showing that the model has a sufficient flexibility to fit volatility surface. As an extension of the random information flow model, price manipulation is considered. A simple model is used to show how the skewness of the manipulated and unmanipulated price processes take opposite signature.; Comment: 19 pages, 8 figures

A simplified Capital Asset Pricing Model

Vovk, Vladimir
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/11/2011 Português
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We consider a Black-Scholes market in which a number of stocks and an index are traded. The simplified Capital Asset Pricing Model is the conjunction of the usual Capital Asset Pricing Model, or CAPM, and the statement that the appreciation rate of the index is equal to its squared volatility plus the interest rate. (The mathematical statement of the conjunction is simpler than that of the usual CAPM.) Our main result is that either we can outperform the index or the simplified CAPM holds.; Comment: 6 pages

Martingale selection problem and asset pricing in finite discrete time

Rokhlin, Dmitry B.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $\xi_t\in V_t$, admitting an equivalent martingale measure. The aim of this note is to underline the connection between this problem and the problems of asset pricing in general discrete-time market models with portfolio constraints and transaction costs. For the case of relatively open convex sets $V_t(\omega)$ we present effective necessary and sufficient conditions for the solvability of a suitably generalized martingale selection problem. We show that this result allows to obtain computationally feasible formulas for the price bounds of contingent claims. For the case of currency markets we also give a comment on the first fundamental theorem of asset pricing.; Comment: 6 pages