Moment matching approximation of Asian basket option prices

  • Authors:

  • Griselda Deelstra;Ibrahima Diallo;Michèle Vanmaele

  • Affiliations:

  • Department of Mathematics, Université Libre de Bruxelles (U.L.B.), CP 210, 1050 Brussels, Belgium and ECARES, Solvay Business School, Université Libre de Bruxelles (U.L.B.), CP 210, 1050 ...;Department of Mathematics, Université Libre de Bruxelles (U.L.B.), CP 210, 1050 Brussels, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, Building S9, 9000 Gent, Belgium

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

In this paper we propose some moment matching pricing methods for European-style discrete arithmetic Asian basket options in a Black & Scholes framework. We generalize the approach of [M. Curran, Valuing Asian and portfolio by conditioning on the geometric mean price, Management Science 40 (1994) 1705-1711] and of [G. Deelstra, J. Liinev, M. Vanmaele, Pricing of arithmetic basket options by conditioning, Insurance: Mathematics & Economics 34 (2004) 55-57] in several ways. We create a framework that allows for a whole class of conditioning random variables which are normally distributed. We moment match not only with a lognormal random variable but also with a log-extended-skew-normal random variable. We also improve the bounds of [G. Deelstra, I. Diallo, M. Vanmaele, Bounds for Asian basket options, Journal of Computational and Applied Mathematics 218 (2008) 215-228]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity.