Scale invariance and contingent claim pricing II: Path-dependent contingent claims
This article is the second one in a series on the use of scaling invariance in finance. In the first paper, we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects only, and which completely avoids the use of martingale techniques. In this article we show the use of the formalism in the context of path-dependent options. We derive compact and intuitive formulae for the prices of a whole range of well known options such as arithmetic and geometric average options, barriers, rebates and lookback options. Some of these have not appeared in the literature before. For example, we find rather elegant formulae for double barrier options with moving barriers, continuous dividends and all possible configurations of the barriers. The strength of the formalism reveals itself in the ease with which these prices can be derived. This allowed us to pinpoint some mistakes regarding geometric mean options, which frequently appear in the literature. Furthermore, symmetries such as put-call transformations appear in a natural way within the framework.
|Date of creation:||16 Jul 1999|
|Date of revision:|
|Note:||Type of Document - PDF; prepared on NT/Latex; to print on PDF printer; pages: 20 . See also http://www.cwi.nl/~jiri for postscript version|
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- Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing," Finance 9907002, EconWPA.
- Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
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