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Equilibrium Valuation of Options on the Market Portfolio with Stochastic Volatility and Return Predictability


  • Melanie Cao


This paper uses an extension of the equilibrium model of Lucas (1978) to study the valuation of options on the market portfolio with return predictability, endogenous stochastic volatility and interest rates. Equilibrium conditions imply that the mean-reverting of the rate of dividend growth induces the predictable feature of the market portfolio. Although the actual drift of the price for the market portfolio does not explicitly enter into the option price formula when the equivalent martingale pricing principle is used, parameters underlying the predictable feature affect option prices through their influence on endogenized volatility and interest rates. Equilibrium conditions also review that there is strong interdependence between the equilibrium price process for the market portfolio and its volatility process, both of which are induced by the process for aggregate dividend. Closed-form pricing formulas for options on the market portfolio incorporate both stochastic volatility and stochastic interest rates. With realistic parameter values, numerical examples show that stochastic volatility and stochastic interest rates are both necessary for correcting the pricing biases generated by the Black-Scholes model. In addition, Closed-form solutions for European bond option prices are obtained, which encompass the Vasicek (1977) model and the Cox-Ingersoll-Ross (1985) model. In this sense, the current model provides a consistent way to price options written on the market portfolio and the bonds.

Suggested Citation

  • Melanie Cao, 1997. "Equilibrium Valuation of Options on the Market Portfolio with Stochastic Volatility and Return Predictability," Working Papers 961, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:961

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    References listed on IDEAS

    1. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    2. Obstfeld, Maurice, 1996. "Models of currency crises with self-fulfilling features," European Economic Review, Elsevier, vol. 40(3-5), pages 1037-1047, April.
    3. Maurice Obstfeld & Kenneth S. Rogoff, 1996. "Foundations of International Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262150476, January.
    4. Carmen M. Reinhart & Graciela L. Kaminsky, 1999. "The Twin Crises: The Causes of Banking and Balance-of-Payments Problems," American Economic Review, American Economic Association, vol. 89(3), pages 473-500, June.
    5. Stockman, Alan C., 1988. "Real exchange-rate variability under pegged and floating nominal exchange-rate systems: An equilibrium theory," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 29(1), pages 259-294, January.
    6. Francesco Giavazzi & Marco Pagano, 1991. "The Advantage of Tying One's Hands: EMS Discipline and Central Bank Credibility," NBER Chapters,in: International Volatility and Economic Growth: The First Ten Years of The International Seminar on Macroeconomics, pages 303-330 National Bureau of Economic Research, Inc.
    7. Krugman, Paul, 1979. "A Model of Balance-of-Payments Crises," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 11(3), pages 311-325, August.
    8. Obstfeld, Maurice & Taylor, Alan M., 1997. "Nonlinear Aspects of Goods-Market Arbitrage and Adjustment: Heckscher's Commodity Points Revisited," Journal of the Japanese and International Economies, Elsevier, vol. 11(4), pages 441-479, December.
    9. Rotemberg, Julio J., 1985. "Money and the terms of trade," Journal of International Economics, Elsevier, vol. 19(1-2), pages 141-160, August.
    10. Charles Engel & John H. Rogers, 1995. "Regional Patterns in the Law of One Price: The Roles of Geography vs. Currencies," NBER Working Papers 5395, National Bureau of Economic Research, Inc.
    11. Alvarez, Fernando & Atkeson, Andrew, 1997. "Money and exchange rates in the Grossman-Weiss-Rotemberg model," Journal of Monetary Economics, Elsevier, vol. 40(3), pages 619-640, December.
    12. Lucas, Robert Jr., 1982. "Interest rates and currency prices in a two-country world," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 335-359.
    13. Kollman, R., 1996. "The Exchange Rate in a Dynamic-Optimizing Current Account Model with Nominal Rigidities: A Quantitative Investigation," Cahiers de recherche 9614, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    14. Grilli, Vittorio & Roubini, Nouriel, 1992. "Liquidity and exchange rates," Journal of International Economics, Elsevier, vol. 32(3-4), pages 339-352, May.
    15. Rodriguez Mendizabal, Hugo, 2002. "Monetary Union and the Transaction Cost Savings of a Single Currency," Review of International Economics, Wiley Blackwell, vol. 10(2), pages 263-277, May.
    16. Helpman, Elhanan & Razin, Assaf, 1982. "A Comparison of Exchange Rate Regimes in the Presence of Imperfect Capital Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 365-388, June.
    17. Dowd, Kevin & Greenaway, David, 1993. "Currency Competition, Network Externalities and Switching Costs: Towards an Alternative View of Optimum Currency Areas," Economic Journal, Royal Economic Society, vol. 103(420), pages 1180-1189, September.
    18. Kimball, Miles S, 1995. "The Quantitative Analytics of the Basic Neomonetarist Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 1241-1277, November.
    19. Schlagenhauf, Don E. & Wrase, Jeffrey M., 1995. "Liquidity and real activity in a simple open economy model," Journal of Monetary Economics, Elsevier, vol. 35(3), pages 431-461, June.
    20. Mussa, Michael, 1982. "A Model of Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 90(1), pages 74-104, February.
    21. Lucas, Robert Jr., 1990. "Liquidity and interest rates," Journal of Economic Theory, Elsevier, vol. 50(2), pages 237-264, April.
    22. Romer, David, 1987. "The monetary transmission mechanism in a general equilibrium version of the baumol-tobin model," Journal of Monetary Economics, Elsevier, vol. 20(1), pages 105-122, July.
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    More about this item


    Stochastic volatility; Return predictability; Stochastic interest rate; Options; Equilibrium;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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