Skip to main content
SpringerLink
Log in

Valuation of exotic options using moments

  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

In this paper we discuss the problem of recovering a density from its moments. For theoretical reasons, we propose the use of fractional moments combined with the Maximum Entropy density. We then discuss the application to the pricing of exotic options.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abate, J. and Whitt, W. (1992). The Fourier-series method for inverting transforms of probability distributions, Queueing Systems Theory Appl. vol. 10, 5–88.

    Article  Google Scholar 

  • Akhiezer, N.I. (1965). The Classical Moment Problem and some Related Questions in Analysis. Oliver & Boyd, London.

    Google Scholar 

  • Avellaneda, M. (1998). Minimum Entropy Calibration of Asset Pricing Models. Journal of Theoretical and Applied Finance vol. 1(4), 447–472.

    Article  Google Scholar 

  • Buchen, P.W. and Kelly, M. (1996). The Maximum Entropy Distribution of an Asset Inferred from Option Prices, Journal of Financial and Quantitative Analysis vol. 31(1), 143–159.

    Article  Google Scholar 

  • Cressie, N. (1986). The Moment Generating Function has its Moments. Journal of Statistical Planning and Inference vol. 13, 337–344.

    Article  Google Scholar 

  • Dufresne, D. (1989). Weak Convergence of Random Growth Processes with Applications to Insurance. Insurance: Math. Econonom. vol. 8, 187–201.

    Article  Google Scholar 

  • Dufresne, D. (2000). Laguerre Series for Asian and Other Options. Mathematical Finance vol. 10(4), 407–428.

    Article  Google Scholar 

  • Fusai, G. (2001). Applications of the Laplace Transform for Evaluating Occupation Time Options and other Derivatives. PhD. Thesis, University of Warwick.

  • Fusai, G. and Tagliani, A. (2002). An Accurate Valuation of Asian Options Using Moments, International Journal of Theoretical and Applied Finance vol. 5(2), 147–169

    Article  Google Scholar 

  • Geman, H. and Yor, M. (1992). Quelques Relations Entre Processus de Bessel, Options Asiatique et Fonctions Confluentes Hypergéométriques. C.R. Acad. Sci. Paris vol. 314(1), 471–474.

    Google Scholar 

  • Geman, H. and Yor, M. (1993). Bessel Processes, Asian Options and Perpetuities. Mathematical Finance vol. 3(4), 349–375.

    Article  Google Scholar 

  • Golan, A., Judge, G. and Miller, D. (1996). Maximum Entropy Econometrics: Robust Estimation with Limited Data, John Wiley & Sons.

  • Jaynes, E.T. (1978). Where Do we Stand on Maximum Entropy, in The Maximum Entropy Formalism, (R.D. Levine and M. Tribus, eds.). MIT Press Cambridge MA, 15–118.

    Google Scholar 

  • Kesavan, H.K. and Kapur, J.N. (1992). Entropy Optimization Principles with Applications. Academic Press.

  • Kullback, S. (1967). A lower bound for discrimination information in terms of variation. IEEE Trans, on Information Theory IT-13, 126–127.

    Google Scholar 

  • Levy, E. (1992). Pricing European Average Rate Currency Options. Journal of International Money and Finance vol. 11, 474–491.

    Article  Google Scholar 

  • Lin, G.D. (1992). Characterizations of Distributions via Moments. Sankhja: The Indian Journal of Statistics vol. 54, Series A, 128–132.

    Google Scholar 

  • Lindsay, B.G. and Basak, P. (1995). Moments Determine the Tail of a Distribution (But not Much Else). Technical report 95-7, Center for likelihood Studies, Dept. of Statistics, The Pennsylvania State University, University Park, PA.

    Google Scholar 

  • Lindsay, B.G. and Roeder, K. (1997). Moment-based Oscillation Properties of Mixture Models. Ann. Statist, vol. 25, 378–386.

    Article  Google Scholar 

  • Shohat, J.A. and Tamarkin, J.D. (1943). The Problem of Moments. AMS Mathematical Survey, 1, Providence RI.

  • Stoyanov, J. (1997). Counterexamples in Probability (2nd edition). Wiley Series in Probability and Statistics.

  • Tagliani, A. (2001). Recovering a Probability Density Function from its Mellin Transform, Applied Mathematics and Computation vol. 118, 151–159.

    Article  Google Scholar 

  • Thompson, G.W.P. (1999). Topics in Mathematical Finance. PhD. Thesis, Queens’ College, January.

  • Turnbull, S. and Wakeman, L. (1991). A Quick Algorithm for Pricing European Average Options. Journal of Financial and Quantitative Analysis vol. 26, 377- 89.

    Article  Google Scholar 

  • Wilmott, P., Dewynne, J.N. and Howison, S. (1993). Option Pricing: Mathematical Models and Computation. Oxford Financial Press.

Download references

Author information

Authors and Affiliations

  1. IMQ, Università L. Bocconi, Viale Isonzo 25, Milano, Italia

    Mauro D’Amico

  2. Facoltà di Economia, SEMEQ, Università del Piemonte Orientale, Via Perrone 18, Novara, Italia

    Gianluca Fusai

  3. Disa, Università di Trento, Via Inama 1, 38100, Trento, Italia

    Aldo Tagliani

Authors
  1. Mauro D’Amico
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gianluca Fusai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aldo Tagliani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Mauro D’Amico or Aldo Tagliani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

D’Amico, M., Fusai, G. & Tagliani, A. Valuation of exotic options using moments. Oper Res Int J 2, 157–186 (2002). https://doi.org/10.1007/BF02936326

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02936326

Keywords

Search

Navigation