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Arbitrage-Based Pricing when Volatility is Stochastic

Author

Listed:
  • Bossaerts, P.
  • Ghysels, E.
  • Gourieroux, C.
Abstract
The paper investigates the pricing of derivative securities with calendar-time maturities.

Suggested Citation

  • Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche 9615, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:9615
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    File URL: http://hdl.handle.net/1866/2051
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    References listed on IDEAS

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    1. Robert Jarrow & Dilip Madan, 1995. "Option Pricing Using The Term Structure Of Interest Rates To Hedge Systematic Discontinuities In Asset Returns1," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 311-336, October.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
    5. Kamara, Avraham & Miller, Thomas W., 1995. "Daily and Intradaily Tests of European Put-Call Parity," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(4), pages 519-539, December.
    6. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: an Application of trading Volume and Leverage Effects," Cahiers de recherche 9403, Universite de Montreal, Departement de sciences economiques.
    7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    8. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    9. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    10. 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.
    11. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    12. Olivier Scaillet & Boris Leblanc, 1998. "Path dependent options on yields in the affine term structure model," Finance and Stochastics, Springer, vol. 2(4), pages 349-367.
    13. 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.
    14. 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.
    15. 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.
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    Citations

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    Cited by:

    1. Barone-Adesi, Giovanni & Fusari, Nicola & Mira, Antonietta & Sala, Carlo, 2020. "Option market trading activity and the estimation of the pricing kernel: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 216(2), pages 430-449.
    2. Bossaerts, Peter & Hillion, Pierre, 2003. "Local parametric analysis of derivatives pricing and hedging," Journal of Financial Markets, Elsevier, vol. 6(4), pages 573-605, August.
    3. German Rodikov & Nino Antulov-Fantulin, 2022. "Can LSTM outperform volatility-econometric models?," Papers 2202.11581, arXiv.org.
    4. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    5. Amigues, Jean-Pierre & Favard, Pascal & Gaudet, Gerard & Moreaux, Michel, 1998. "On the Optimal Order of Natural Resource Use When the Capacity of the Inexhaustible Substitute Is Limited," Journal of Economic Theory, Elsevier, vol. 80(1), pages 153-170, May.
    6. Dias, Fabio S. & Peters, Gareth W., 2021. "Option pricing with polynomial chaos expansion stochastic bridge interpolators and signed path dependence," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    7. Lange, Rutger-Jan, 2024. "Bellman filtering and smoothing for state–space models," Journal of Econometrics, Elsevier, vol. 238(2).
    8. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
    9. Solomon Abayomi Olakojo, 2020. "A Markov‐switching analysis of Nigeria's business cycles: Are election cycles important?," African Development Review, African Development Bank, vol. 32(1), pages 67-79, March.
    10. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    11. Juan Hoyo & Guillermo Llorente & Carlos Rivero, 2020. "A Testing Procedure for Constant Parameters in Stochastic Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 163-186, June.
    12. Michael Weba, 2024. "Investment strategies based on forecasts are (almost) useless," Papers 2408.01772, arXiv.org.
    13. Isaenko, Sergey, 2023. "Trading strategies and the frequency of time-series," The Quarterly Review of Economics and Finance, Elsevier, vol. 90(C), pages 267-283.
    14. Benjamin Poignard & Manabu Asai, 2023. "High‐dimensional sparse multivariate stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 4-22, January.
    15. Izzeldin, Marwan & Muradoğlu, Yaz Gülnur & Pappas, Vasileios & Sivaprasad, Sheeja, 2021. "The impact of Covid-19 on G7 stock markets volatility: Evidence from a ST-HAR model," International Review of Financial Analysis, Elsevier, vol. 74(C).
    16. Ahsan, Md. Nazmul & Dufour, Jean-Marie, 2021. "Simple estimators and inference for higher-order stochastic volatility models," Journal of Econometrics, Elsevier, vol. 224(1), pages 181-197.
    17. Liao, Wen Ju & Sung, Hao-Chang, 2020. "Implied risk aversion and pricing kernel in the FTSE 100 index," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).

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    More about this item

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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