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A class of complete benchmark models with intensity-based jumps

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Abstract

This paper proposes a class of complete financial market models, the benchmark models, with security price processes that exhibit intensity-based jumps. The benchmark or reference unit is chosen to be the growth-optimal portfolio. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. In the proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real-world probability measure. This concept of fair pricing generalizes the classical risk-neutral approach and the actuarial present-value pricing methodology.

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  • Eckhard Platen, 2004. "A class of complete benchmark models with intensity-based jumps," Published Paper Series 2004-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:2004-5
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    File URL: https://www.cambridge.org/core/journals/journal-of-applied-probability/article/class-of-complete-benchmark-models-with-intensitybased-jumps/A3B91A0F91C5F54DEF10CDD7523D168E
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    Citations

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    Cited by:

    1. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
    2. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Eckhard Platen & Renata Rendek, 2009. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 264, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    5. I. Venkat Appal Raju & N. Selvaraju, 2012. "Growth Optimal Portfolio for unobservable Markov-modulated markets," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(1), pages 31-40.
    6. Ashkan Nikeghbali & Eckhard Platen, 2008. "On honest times in financial modeling," Papers 0808.2892, arXiv.org.
    7. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009, January-A.

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