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Probabilistic Greeks

Author

Listed:
  • Andrés D. Fundia

    (Tecnológico de Monterrey, Campus Ciudad de México)

  • Francisco Venegas-Martínez

    (Tecnológico de Monterrey, Campus Ciudad de México)

Abstract

En la fórmula de valuación de opciones Black-Scholes-Merton, los coeficientes que multiplican a las principales variables (el precio del subyacente y el precio de ejercicio) son iguales a algunas "Griegas" (derivadas parciales del precio con respecto a las principales variables). En este trabajo probamos que esta propiedad no es sólo verdadera para una distribución log-normal, sino también se satisface para cualquier distribución que cumpla con algunas condiciones naturales y para algunas opciones exóticas. Estas identidades son derivadas a partir de una nueva representación integral de las Griegas. Esta representación permite determinar las Griegas en una forma sencilla y sistemática simplificando las complejidades computacionales y matemáticas tradicionalmente relacionadas en estos cálculos. Cuando calculamos las griegas, estos resultados pueden ser aplicados para simplificar la derivación de expresiones cerradas, acelerar los métodos numéricos y obtener mejores ajustes.

Suggested Citation

  • Andrés D. Fundia & Francisco Venegas-Martínez, 2004. "Probabilistic Greeks," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 3(3), pages 303-311, Septiembr.
    • Handle: RePEc:imx:journl:v:3:y:2004:i:3:p:303-311
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    References listed on IDEAS

    as
    1. 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..
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Estimation; Asset Pricing;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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