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A CLOSED-FORM SOLUTION FOR LOOKBACK OPTIONS USING MELLIN TRANSFORM APPROACH

윤지훈|전준기
영남수학회 (Youngnam Mathematical Society)|2016.05|East Asian Mathematical Journal|제32권 제3호|pp. 301-310|DOI http://dx.doi.org/10.7858/eamj.2016.022

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참고문헌

키워드

Mellin transformFloating lookback optionMethod of images
주제분류수학

초록

Lookback options, in the terminology of nance, are a typeof exotic option with path dependency whose the payo depends on theoptimal (maximum or minimum) underlying asset's price occurring overthe life of the option. In this paper, we exploit Mellin transform techniquesto nd a closed-form solution for European lookback options in Black-Scholes model.

Abstract

Lookback options, in the terminology of nance, are a typeof exotic option with path dependency whose the payo depends on theoptimal (maximum or minimum) underlying asset's price occurring overthe life of the option. In this paper, we exploit Mellin transform techniquesto nd a closed-form solution for European lookback options in Black-Scholes model.

참고문헌 (12)

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  3. M. Dai, "Quanto lookback options", Math. Finance, 14, pp.445~467 (2004)
  4. Z.-A. Elshegmani, "Analytical Solution for an Arithmetic Asian Option using Mellin Transforms", Int. Journal of Math. Analysis, 5, pp.1259~1265 (2011)
  5. R. Frontczak, "Pricing Options in Jump Diffusion Models using Mellin Transforms", Jour-nal of Mathematical Finance, 3, pp.366~373 (2013)
  6. M. B. Goldman, "Path dependent options: buy at the low, sell at the high", J. Finance, 34, pp.1111~1127 (1979)
  7. H. He, "Double lookbacks", Math. Finance, 8, pp.201~228 (1998)
  8. B. Oksendal, "Stochastic Differential Equations" (2003), Springer
  9. R. Panini, "Option pricing with Mellin transforms", Mathematical and Computer Modelling, 40, pp.43~56 (2004)
  10. R. Panini, "Pricing perpetual options using Mellin transforms", Appl. Math. Lett., 18, pp.471~474 (2005)
  11. J.-H. Yoon, "Mellin transform method for European option pricing with Hull-White sto-chastic interest rate", Journal of Applied Mathematics, 2014, pp.7~ (2014)
  12. J.-H. Yoon, "The pricing of vulnerable options with double Mellin trans-forms", J. Math. Anal. Appl., 422, pp.838~857 (2015)

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