Menu Expand

Eine exakte und geschlossene Bewertungsformel für geometrische Average-Rate Optionen

Cite JOURNAL ARTICLE

Style

Büchel, H. Eine exakte und geschlossene Bewertungsformel für geometrische Average-Rate Optionen. Credit and Capital Markets – Kredit und Kapital, 24(3), 361-370. https://doi.org/10.3790/ccm.24.3.361
Büchel, Helmut "Eine exakte und geschlossene Bewertungsformel für geometrische Average-Rate Optionen" Credit and Capital Markets – Kredit und Kapital 24.3, 1991, 361-370. https://doi.org/10.3790/ccm.24.3.361
Büchel, Helmut (1991): Eine exakte und geschlossene Bewertungsformel für geometrische Average-Rate Optionen, in: Credit and Capital Markets – Kredit und Kapital, vol. 24, iss. 3, 361-370, [online] https://doi.org/10.3790/ccm.24.3.361

Format

Eine exakte und geschlossene Bewertungsformel für geometrische Average-Rate Optionen

Büchel, Helmut

Credit and Capital Markets – Kredit und Kapital, Vol. 24 (1991), Iss. 3 : pp. 361–370

Additional Information

Article Details

Author Details

Helmut Büchel, Berlin

References

  1. Aitchison, J. und Brown, J. A. C.: The Lognormal Distribution; Cambridge University Press, 1976.  Google Scholar
  2. Black, F. und Scholes, M.: The Pricing of Options and Corporate Liabilities; Journal of Political Economy, Vol. 81, May - June 1973, p. 637 - 659.  Google Scholar
  3. Büchel, H.: Bewertung von Optionen mit aktienkursabhängigem Basispreis; ZfbF, Okt. 1988, p. 884 - 895.  Google Scholar
  4. Fischer, S.: Call Option Pricing when the Exercise Price is Uncertain and the Valuation of Index Bonds; Journal of Finance, 33, 1978, p. 169 - 176.  Google Scholar
  5. Garman, M.B. und Kohlhagen, S. W.: Foreign Currency Option Values; Journal of International Money and Finance, 1983, 2, p. 231 - 237.  Google Scholar
  6. Kemna, A.G.Z. und Vorst, A.C.F.: A Pricing Method for Options Based on Average Asset Values; Journal of Banking and Finance, 14, 1990, p. 113 - 129.  Google Scholar
  7. Krzyzak, K.: Average-Rate Options - Asean Elegance; Risk, Vol. 3, No. 1, Dec. 1989 - Jan. 1990, p. 30 - 49.  Google Scholar
  8. Margrabe, W.: The Value of an Option to Exchange One Asset for Another; Journal of Finance, 33, 1978, p. 177 - 186.  Google Scholar
  9. Osborne, M. F. M.: Brownian Motion in the Stock Market; Operations Research, 1959, p. 145 - 173.  Google Scholar
  10. Ruttiens, A.: Average-Rate Options - Classical Replica; Risk, Vol. 3, No. 2, Febr. 1990, p. 33 - 36.  Google Scholar
  11. Smith, C. W. Jr.: Option Pricing: A Review; Journal of Financial Economics, Vol. 3, 1976, P. 3 - 51.  Google Scholar
  12. Stulz, R.: Options on the Minimum or Maximum of two Risky Assets, Analysis and Applications; Journal of Financial Economics 10, 1982, p. 161 - 185.  Google Scholar
  13. Welcker, J. und Schindler, K.: Währungsoptionsscheine und Rückerstattungswährungsoptionsscheine (RWOS - money back currency warrant) der Nordiska Investerringsbanken (NIB); Kredit und Kapital, 22. Jg., Heft 2, 1989, p. 239 - 266.  Google Scholar
  14. Welcker, J. und Nerge, C.: Erfolgsrezepte der Experten; Börsen-Journal, Nr. 18, 8.9.1989, p. 41 - 43.  Google Scholar
  15. Aitchison, J. und Brown, J. A. C.: The Lognormal Distribution; Cambridge University Press, 1976.  Google Scholar
  16. Black, F. und Scholes, M.: The Pricing of Options and Corporate Liabilities; Journal of Political Economy, Vol. 81, May – June 1973, p. 637 – 659.  Google Scholar
  17. Büchel, H.: Bewertung von Optionen mit aktienkursabhängigem Basispreis; ZfbF, Okt. 1988, p. 884 – 895.  Google Scholar
  18. Fischer, S.: Call Option Pricing when the Exercise Price is Uncertain and the Valuation of Index Bonds; Journal of Finance, 33, 1978, p. 169 – 176.  Google Scholar
  19. Garman, M.B. und Kohlhagen, S. W.: Foreign Currency Option Values; Journal of International Money and Finance, 1983, 2, p. 231 – 237.  Google Scholar
  20. Kemna, A.G.Z. und Vorst, A.C.F.: A Pricing Method for Options Based on Average Asset Values; Journal of Banking and Finance, 14, 1990, p. 113 – 129.  Google Scholar
  21. Krzyzak, K.: Average-Rate Options – Asean Elegance; Risk, Vol. 3, No. 1, Dec. 1989 – Jan. 1990, p. 30 – 49.  Google Scholar
  22. Margrabe, W.: The Value of an Option to Exchange One Asset for Another; Journal of Finance, 33, 1978, p. 177 – 186.  Google Scholar
  23. Osborne, M. F. M.: Brownian Motion in the Stock Market; Operations Research, 1959, p. 145 – 173.  Google Scholar
  24. Ruttiens, A.: Average-Rate Options – Classical Replica; Risk, Vol. 3, No. 2, Febr. 1990, p. 33 – 36.  Google Scholar
  25. Smith, C. W. Jr.: Option Pricing: A Review; Journal of Financial Economics, Vol. 3, 1976, P. 3 – 51.  Google Scholar
  26. Stulz, R.: Options on the Minimum or Maximum of two Risky Assets, Analysis and Applications; Journal of Financial Economics 10, 1982, p. 161 – 185.  Google Scholar
  27. Welcker, J. und Schindler, K.: Währungsoptionsscheine und Rückerstattungswährungsoptionsscheine (RWOS – money back currency warrant) der Nordiska Investerringsbanken (NIB); Kredit und Kapital, 22. Jg., Heft 2, 1989, p. 239 – 266.  Google Scholar
  28. Welcker, J. und Nerge, C.: Erfolgsrezepte der Experten; Börsen-Journal, Nr. 18, 8.9.1989, p. 41 – 43.  Google Scholar

Abstract

Geometric Average-Rate Options An Exact Closed-End Evaluation Formula

This contribution seeks to evaluate geometric average-rate options. It develops a closed-end evaluation formula, easy to programme, which differs significantly from the formula published by Kemna and Vorst in 1990. It turns out, among other things, that the variance of the geometric average rate is a quadratic function of the residual lifetime of the option, when a constant rate of variance is assumed for the rate of the underlyings. If the period at the base of the geometric average is reduced to one day, the resultant special cases represent the classic formulae for European options.