Valoración de opciones asiáticas con MATHEMATICA

  1. Cruz Báez, Domingo Israel
  2. González Rodríguez, José Manuel
Revista:
Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA

ISSN: 1575-605X

Año de publicación: 2007

Volumen: 8

Número: 1

Páginas: 139-150

Tipo: Artículo

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Otras publicaciones en: Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA

Resumen

En este trabajo, utilizando el programa Mathematica, proponemos una implementación del valor de una opción asiática aritmética, que tiene una gran precisión computacional. Para ilustrar este hecho, realizamos una comparativa con otros métodos bien conocidos en la literatura financiera.

Referencias bibliográficas

  • [AlziiaryDecampsKoehl] B. Alziiary, J. Decamps, and P. Koehl. A P.D.E. approach to Asian options: analytical and numerical evidence. Journal of Banking & Finance, 21, 613-640, 1997.
  • [BarraquandPrudet] J. Barraquand and T. Prudet. Pricing of American path-dependent contingent Claims. Mathematical Finance, 6, 17-51, 1996.
  • [BlackScholes] Black, F. and Scholes, M. The pricing of options and corporate liabilities. Journal of Political Economy, 81 (1973), 637-654.
  • [Craddocketal] Craddock, M.; Heath, D.; Platen, E. Numerical inversion of Laplace transforms: A survey of techniques with applications to derivatives pricing. J. Computational Finance 4(1) 57--81, 2000.
  • [CruzBaez] Cruz-Báez, D.I.; González-Rodríguez, J.M. Valoración de opciones Asiáticas aritméticas por medio de la transformación de Laplace y Mathematica. XX Congreso Asepelt - España, Tenerife, 2006.
  • [CruzBaez06] Cruz-Báez, D.I. and González-Rodríguez, A different approach for pricing Asian options, Appl. Math. Lett. (2007), doi:10.1016/j.aml.2007.03.016.
  • [DewynneWilmott] J. N. Dewynne and P. Wilmott, A note on average rate options with discrete sampling. SIAM Journal of Applied Mathematics, 55 (1), 267-276, 1995.
  • [DewynneWilmott2] J. N. Dewynne and P. Wilmott. Asian options as linear complementarity problems. Advances in Futures and Options Research, 8, 145-173, 1995.
  • [Dufresne] Dufresne, D. Laguerre series for Asian and other options, Math. Finance, 10 (2000), pp. 407-428.
  • [Dufresne01] D. Dufresne.The integral of geometric Brownian motion. Adv. Appl. Probab. 33 (2001), 223--241.
  • [Erdelyietal] Erdélyi, A.; Magnus, W.; Oberhettinger, F. and Tricomi. F. G.: Tables of Integral Transforms. Vol. I. McGraw-Hill, New Yor, 1954.
  • [EydelandGeman] Eydeland, A.; Geman, H. Domino effect, Risk 8, 65--67, 1995.
  • [Fuetal] Fu, M.C.; Madan, D.B., Wang, T. Pricing continuous Asian options: a comparison of Monte Carlo and Laplace inversion methods, J. Comp. Fin. 2 (1998), 49-74.
  • [GemanYor] Geman, H. and Yor, M. Bessel processes, Asian options, and perpetuities, Math. Finance, 3 (1993), pp. 349--375.
  • [Hull] Hull, J. C.: Options, Futures and Other Derivatives 6th Edition. Prentice Hall, 2006.
  • [KemmaVorst] Kemna, A. and Vorst, A. A pricing method for options based on average asset Values. Journal of Banking and Finance, 14,113-129, 1990.
  • [Lebedev] Lebedev, N. N. Special Functions and their Applications. Dover, New Yor, 1972.
  • [Levy] E. Levy. Pricing European average rate currency options, Journal of International Money and Finance, 11, 474-491, 1992.
  • [LevyTurnbull] E. Levy and S. Turnbull. Average intelligence, RISK, 5, ( February), 53-59, (1992).
  • [Linetsky] Linetsky, V. Spectral Expansions for Asian (Average Price) Options, Operations Research Vol. 52, No. 6, 2004, pp. 856--867.
  • [Merton] Merton, R. C.: Theory of rational option pricing, Bell J. Econom. Management Sci. 4 (1973), 141-183.
  • [RogersShi] L. Rogers and Z. Shi. The value of an Asian option. Journal of Applied Probability, 32, 1077-108, 1995.
  • [Shaw] Shaw, W. Modelling Financial Derivatives with Mathematica, Cambridge University Press, 1998.
  • [Thompson] Thompson, G. W. P. Fast narrow bounds on the value of Asian options. Working Paper, Centre for Financial Research, Judge Institute of Management Science, University of Cambridge, 2000.
  • [TurnbullWakeman] S. M. Turnbull and L. Wakeman. A quick algorithm for pricing European average options, Journal of Financial and Quantitative Analysis, 26 (3), 377-389, 1991.
  • [Vecer] J. Vecer. A new PDE approach for pricing arithmetic average Asian options. J. Computational Finance 4(4) 105--113, 2001.
  • [Vorst] Vorst, T. Averaging options, in I. Nelken, editor, The Handbook of Exotic Options, Irwin, Homewood, IL, 175-199, 1996.
  • [Wilmott] Wilmott, P. Paul Wilmott on Quantitative Finance, John Wiley & Sons, 2000.
  • [Yor] M. Yor, On some exponential functionals of Brownian motion, Adv. Appl. Probab., 24 (1992), pp. 509--531.
  • [Zhang] Zhang, J. E. A semi-analytical method for pricing and hedging continuously sampled arithmetic average rate options. Journal of Computational Finance, 5, 59-- 79, 2001.
  • [ZvanForsyth] Zvan, R.; Forsyth, P. and Vetzal, K. Robust numerical methods for PDE models of Asian options. Journal of Computational Finance, 1(2), 39-78, 1998.
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