[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cir/cirwor/99s-47.html
   My bibliography  Save this paper

Latent Variable Models for Stochastic Discount Factors

Author

Listed:
  • René Garcia
  • Eric Renault
Abstract
Latent variable models in finance originate both from asset pricing theory and time series analysis. These two strands of literature appeal to two different concepts of latent structures, which are both useful to reduce the dimension of a statistical model specified for a multivariate time series of asset prices. In the CAPM or APT beta pricing models, the dimension reduction is cross-sectional in nature, while in time-series state-space models, dimension is reduced longitudinally by assuming conditional independence between consecutive returns given a small number of state variables. In this chapter, we use the concept of Stochastic Discount Factor (SDF) or pricing kernel as a unifying principle to integrate these two concepts of latent variables. Beta pricing relations amount to characterize the factors as a basis of a vectorial space for the SDF. The coefficients of the SDF with respect to the factors are specified as deterministic functions of some state variables which summarize their dynamics. In beta pricing models, it is often said that only the factorial risk is compensated since the remaining idiosyncratic risk is diversifiable. Implicitly, this argument can be interpreted as a conditional cross-sectional factor structure, that is a conditional independence between contemporaneous returns of a large number of assets given a small number of factors, like in standard Factor Analysis. We provide this unifying analysis in the context of conditional equilibrium beta pricing as well as asset pricing with stochastic volatility, stochastic interest rates and other state variables. We address the general issue of econometric specifications of dynamic asset pricing models, which cover the modern literature on conditionally heteroskedastic factor models as well as equilibrium-based asset pricing models with an intertemporal specification of preferences and market fundamentals. We interpret various instantaneous causality relationships between state variables and market fundamentals as leverage effects and discuss their central role relative to the validity of standard CAPM-like stock pricing and preference-free option pricing. En finance, les modèles à variables latentes apparaissent à la fois dans les théories d'évaluation des actifs financiers et dans l'analyse de séries chronologiques. Ces deux courants de littérature font appel à deux concepts différents de structures latentes qui servent tous deux à réduire la dimension d'un modèle statistique de séries temporelles sur les prix ou les rendements de plusieurs actifs. Dans les modèles CAPM ou APT, où l'évaluation est fonction de coefficients bêtas, la réduction de dimension est de nature transversale, tandis que dans les modèles de séries chronologiques espace-état, la dimension est réduite longitudinalement en supposant l'indépendance conditionnelle entre les rendements consécutifs étant donné un petit nombre de variables d'état. Dans ce chapitre, nous utilisons le concept de facteur d'actualisation stochastique (SDF) ou noyau de valorisation comme principe unificateur en vue d'intégrer ces deux concepts de variables latentes. Les relations de valorisation avec coefficients bêtas reviennent à caractériser les facteurs comme une base d'un espace vectoriel pour le SDF. Les coefficients du SDF par rapport aux facteurs sont spécifiés comme des fonctions déterministes de certaines variables d'état qui résument leur évolution dynamique. Dans ces modèles d'évaluation à coefficients bêtas, on dit souvent que seul le risque factoriel est compensé puisque le risque résiduel idiosyncratique est diversifiable. Implicitement, cet argument peut être interprété comme une structure factorielle transversale conditionnelle, c'est-à-dire une indépendance conditionnelle entre les rendements contemporains d'un grand nombre d'actifs étant donné un petit nombre de facteurs, comme dans l'analyse factorielle standard. Nous établissons cette analyse unificatrice dans le contexte des modèles conditionnels d'équilibre à coefficients bêtas de même que dans des modèles d'évaluation des actifs financiers avec volatilité stochastique, taux d'intérêt stochastiques et autres variables d'état. Nous adressons la question générale de la spécification économétrique des modèles dynamiques d'évaluation des actifs financiers, qui regroupent la littérature moderne des modèles à facteurs conditionnellement hétéroscédastiques ainsi que les modèles d'équilibre d'évaluation des actifs financiers avec une spécification intertemporelle des préférences et des processus fondamentaux du marché. Nous interprétons diverses relations de causalité instantanées entre les variables d'état et les processus fondamentaux du marché comme des effets de levier et discutons le rôle central qu'elles jouent dans la validité des modèles de référence tels que le CAPM pour les actions ou les modèles d'évaluation sans paramètres de préférence pour les options.

Suggested Citation

  • René Garcia & Eric Renault, 1999. "Latent Variable Models for Stochastic Discount Factors," CIRANO Working Papers 99s-47, CIRANO.
    • Handle: RePEc:cir:cirwor:99s-47
    as

    Download full text from publisher

    File URL: https://cirano.qc.ca/files/publications/99s-47.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fiorentini, Gabriele & Sentana, Enrique, 1998. "Conditional Means of Time Series Processes and Time Series Processes for Conditional Means," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1101-1118, November.
    2. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
    6. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    7. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    8. Meddahi, N & Renault, E., 1996. "Aggregations and Marginalization of Garch and Stochastic Volatility Models," Papers 96.433, Toulouse - GREMAQ.
    9. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    10. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237, October.
    11. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    12. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    13. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    14. Florens, J P & Mouchart, M, 1982. "A Note on Noncausality," Econometrica, Econometric Society, vol. 50(3), pages 583-591, May.
    15. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    16. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    17. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    18. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
    19. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
    20. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    21. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-799, September.
    22. Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH‐type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26, January.
    23. Amin, Kaushik I & Ng, Victor K, 1993. "Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
    24. Turnbull, Stuart M & Milne, Frank, 1991. "A Simple Approach to Interest-Rate Option Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 87-120.
    25. Ferson, Wayne E & Korajczyk, Robert A, 1995. "Do Arbitrage Pricing Models Explain the Predictability of Stock Returns?," The Journal of Business, University of Chicago Press, vol. 68(3), pages 309-349, July.
    26. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    27. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    28. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    29. Harvey, Campbell R, 1991. "The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-157, March.
    30. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    31. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
    32. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    33. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    2. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    3. Paul Gilbert & Lise Pichette, 2003. "Dynamic Factor Analysis for Measuring Money," Staff Working Papers 03-21, Bank of Canada.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    2. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    3. GARCIA, René & RENAULT, Éric, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Universite de Montreal, Departement de sciences economiques.
    4. Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
    5. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.
    6. René Garcia & Richard Luger & Eric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : Nouvelle version Février 2002)," CIRANO Working Papers 2001s-02, CIRANO.
    7. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    8. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    9. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    10. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    11. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. repec:adr:anecst:y:1991:i:24:p:01 is not listed on IDEAS
    13. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
    14. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    15. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    16. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    17. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    18. F. Fornari & A. Mele, 1998. "ARCH Models and Option Pricing : The Continuous Time Connection," THEMA Working Papers 98-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    19. Bakshi, Gurdip S. & Zhiwu, Chen, 1997. "An alternative valuation model for contingent claims," Journal of Financial Economics, Elsevier, vol. 44(1), pages 123-165, April.
    20. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    21. Antonis Demos & Sofia Parissi, 1998. "Testing Asset Pricing Models: The Case of Athens Stock Exchange," Multinational Finance Journal, Multinational Finance Journal, vol. 2(3), pages 189-223, September.

    More about this item

    Keywords

    Stochastic discount factors; latent variables; conditional beta pricing; conditional factor models; equilibrium asset pricing; models with latent variables; Facteurs d'actualisation stochastiques; variables latentes; évaluation des actifs financiers avec bêtas conditionnels; modèles à facteurs conditionnels; modèles d'équilibre d'évaluation des actifs financiers; modèles à variables latentes;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G1 - Financial Economics - - General Financial Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:99s-47. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Webmaster (email available below). General contact details of provider: https://edirc.repec.org/data/ciranca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.