Numeraire-invariant option pricing and american, bermudan, trigger stream rollover

F. Jamshidian

    Research output: Contribution to conferencePaperAcademic

    33 Downloads (Pure)

    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.
    Original languageEnglish
    Number of pages41
    Publication statusPublished - 2004
    Event4th Winter School on Financial Mathematics - Lunteren, the Netherlands
    Duration: 24 Jan 200526 Jan 2005

    Other

    Other4th Winter School on Financial Mathematics
    Period24/01/0526/01/05
    OtherJanuary 24-26, 2005

    Keywords

    • IR-59730
    • martingale
    • stooping time
    • price process
    • Doob-Meyer Decomposition
    • Option
    • Snell envelope

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