Numeraire-invariant option pricing and american, bermudan, trigger stream rollover (v1.6)
AbstractPart I proposes a numeraire-invariant option pricing framework. It defines an option, its price process, and such notions as option indistinguishability and equivalence, domination, payoff process, trigger option, and semipositive option. It develops some of their basic properties, including price transitivity law, indistinguishability results, convergence results, and, in relation to nonnegative arbitrage, characterizations of semipositivity and consequences thereof. These are applied in Part II to study the Snell envelop and american options. The measurability and right-continuity of the former is established in general. The american option is then defined, and its pricing formula (for all times) is presented. Applying a concept of a domineering numeraire for superclaims derived from (the additive) Doob-Meyer decomposition, minimax duality formulae are given which resemble though differ from those in [R] and [H-K]. Multiplicative Doob-Meyer decomposition is discussed last. A part III is also envisaged.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0407015.
Length: 41 pages
Date of creation: 20 Jul 2004
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Note: Type of Document - pdf; pages: 41
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Option; Snell envelope; stooping time; martingale; Doob-Meyer Decomposition; price process;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-07-26 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
- Mark Joshi & Jochen Theis, 2002. "Bounding Bermudan swaptions in a swap-rate market model," Quantitative Finance, Taylor and Francis Journals, vol. 2(5), pages 370-377.
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