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Local Scale Invariance And Contingent Claim Pricing Ii: Path-Dependent Contingent Claims

Author

Listed:
  • J. K. HOOGLAND

    (Centrum voor Wiskunde en Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands)

  • C. D. D. NEUMANN

    (Centrum voor Wiskunde en Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands)

Abstract

This article is the second one in a series on the use of local scale invariance in finance. In the first [6], we introduced a new formalism for the pricing of derivative securities, which focuses 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 exponentially 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.

Suggested Citation

  • J. K. Hoogland & C. D. D. Neumann, 2001. "Local Scale Invariance And Contingent Claim Pricing Ii: Path-Dependent Contingent Claims," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 23-43.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:01:n:s0219024901000869
    DOI: 10.1142/S0219024901000869
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    Cited by:

    1. Rei[ss], Oliver & Schoenmakers, John & Schweizer, Martin, 2007. "From structural assumptions to a link between assets and interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 593-612, February.
    2. Andrew Ming-Long Wang & Yu-Hong Liu & Yi-Long Hsiao, 2009. "Barrier option pricing: a hybrid method approach," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 341-352.
    3. Chih-Chen Hsu & Chung-Gee Lin & Tsung-Jung Kuo, 2020. "Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading," Mathematics, MDPI, vol. 8(12), pages 1-16, December.

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