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Equilibrium State Prices In A Stochastic Volatility Model

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  • Huyěn Pham
  • Nizar Touzi
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    Abstract

    In a stochastic volatility model, the no-free-lunch assumption does not induce a unique arbitrage price because of market incompleteness. In this paper, we consider a contingent claim on the primitive asset, traded in zero net supply. Given a system of Arrow-Debreu state prices, we provide necessary and sufficient conditions for consistency with an intertemporal additive equilibrium model that we fully characterize. We show that the risk premia corresponding to the minimal martingale of Föllmer and Schweizer (1991) are consistent with logarithmic preferences, while the Hull and White model (1987) (volatility risk premium independent of the asset price) is consistent with a class of utility functions including constant relative risk aversion (CRRA) ones. Copyright 1996 Blackwell Publishers.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 6 (1996)
    Issue (Month): 2 ()
    Pages: 215-236

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    Handle: RePEc:bla:mathfi:v:6:y:1996:i:2:p:215-236

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    Cited by:
    1. Lüders, Erik, 2002. "Asset Prices and Alternative Characterizations of the Pricing Kernel," ZEW Discussion Papers 02-10, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    2. Paola Zerilli, 2005. "Option pricing and spikes in volatility: theoretical and empirical analysis," Money Macro and Finance (MMF) Research Group Conference 2005 76, Money Macro and Finance Research Group.
    3. Elyes Jouini & Clotilde Napp, 1999. "Continuous Time Equilibrium Pricing of Nonredundant Assets," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-008, New York University, Leonard N. Stern School of Business-.
    4. Elyès Jouini & Clotilde Napp, 2002. "Arbitrage pricing and equilibrium pricing : compatibility conditions," Post-Print halshs-00176423, HAL.
    5. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    6. Lüders, Erik & Peisl, Bernhard, 2001. "How do investors' expectations drive asset prices?," ZEW Discussion Papers 01-15, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    7. Srdjan Stojanovic, 2006. "Pricing and Hedging of Multi Type Contracts under Multidimensional Risks in Incomplete Markets Modeled by General Itô SDE Systems," Asia-Pacific Financial Markets, Springer, vol. 13(4), pages 345-372, December.
    8. Bertram Düring, 2009. "Asset pricing under information with stochastic volatility," Review of Derivatives Research, Springer, vol. 12(2), pages 141-167, July.
    9. Ang, Andrew & Liu, Jun, 2007. "Risk, return, and dividends," Journal of Financial Economics, Elsevier, vol. 85(1), pages 1-38, July.
    10. Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation," CIRANO Working Papers 96s-26, CIRANO.
    11. Chourdakis, Kyriakos & Dotsis, George, 2011. "Maximum likelihood estimation of non-affine volatility processes," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 533-545, June.

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