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Opciones, cobertura y procesos de difusión con saltos: Una aplicación a los títulos de Gcarso

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  • Francisco Venegas Martínez

    (Oxford University)

Abstract

We present two models for hedging European options on an underlying asset driven by a mixed diffusion-jump process. The first model, values the option as the average of option prices hedging sequential jumps. In the second model, the option price is determined by minimizing the variance of the portfolio value. In particular, we develop hedging strategies for the case of GCARSO shares

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  • Francisco Venegas Martínez, 2001. "Opciones, cobertura y procesos de difusión con saltos: Una aplicación a los títulos de Gcarso," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 16(2), pages 203-226.
    • Handle: RePEc:emx:esteco:v:16:y:2001:i:2:p:203-226
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    File URL: https://estudioseconomicos.colmex.mx/index.php/economicos/article/view/204/206
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    1. Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages 87-99.
    2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Svensson, Lars E. O., 1992. "The foreign exchange risk premium in a target zone with devaluation risk," Journal of International Economics, Elsevier, vol. 33(1-2), pages 21-40, August.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Jarrow, Robert A & Rosenfeld, Eric R, 1984. "Jump Risks and the Intertemporal Capital Asset Pricing Model," The Journal of Business, University of Chicago Press, vol. 57(3), pages 337-351, July.
    7. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    8. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    9. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    10. 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.
    11. Penati, Alessandro & Pennacchi, George, 1989. "Optimal portfolio choice and the collapse of a fixed-exchange rate regime," Journal of International Economics, Elsevier, vol. 27(1-2), pages 1-24, August.
    12. Ahn, Chang Mo & Thompson, Howard E, 1988. " Jump-Diffusion Processes and the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 43(1), pages 155-174, March.
    13. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    14. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 377-389, September.
    15. 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.
    16. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    17. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
    18. Venegas-Martinez, Francisco, 2001. "Temporary stabilization: A stochastic analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1429-1449, September.
    19. Rendleman, Richard J. & Bartter, Brit J., 1980. "The Pricing of Options on Debt Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(1), pages 11-24, March.
    20. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
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    1. Carbajal-De-Nova, Carolina & Venegas-Martínez, Francisco, 2019. "On the paradigm shift of asset pricing models, before and after the global financial crisis: a literature review," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 15(29), pages 7-38, Primer se.

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