Numeraire-invariant option pricing and american, bermudan, trigger stream rollover (v1.6)

Farshid Jamshidian

Finance from EconWPA

Abstract: Part 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.

Keywords: Option; Snell envelope; stooping time; martingale; Doob-Meyer Decomposition; price process (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2004-07-20
Note: Type of Document - pdf; pages: 41
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0407015

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