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

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  • Farshid Jamshidian

    (NIB Capital Bank, University of Twente)

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.

Suggested Citation

  • Farshid Jamshidian, 2004. "Numeraire-invariant option pricing and american, bermudan, trigger stream rollover (v1.6)," Finance 0407015, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0407015
    Note: Type of Document - pdf; pages: 41
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    References listed on IDEAS

    as
    1. 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.
    2. Mark Joshi & Jochen Theis, 2002. "Bounding Bermudan swaptions in a swap-rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 370-377.
    3. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    4. 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.
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    Cited by:

    1. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks," Papers 2302.12439, arXiv.org, revised Nov 2024.
    2. Joshi, Mark & Tang, Robert, 2014. "Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 25-45.
    3. L. C. G. Rogers, 2015. "Bermudan options by simulation," Papers 1508.06117, arXiv.org, revised Jan 2016.
    4. Nicholas Andrew Yap Swee Guan, 2015. "Regression and Convex Switching System Methods for Stochastic Control Problems with Applications to Multiple-Exercise Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 26, July-Dece.

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    More about this item

    Keywords

    Option; Snell envelope; stooping time; martingale; Doob-Meyer Decomposition; price process;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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