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Pricing and Hedging of Index Derivatives under an Alternative Asset Price Model with Endogenous Stochastic Volatility

In: Recent Developments In Mathematical Finance

Author

Listed:
  • David Heath

    (University of Technology Sydney, School of Finance & Economics and Department of Mathematical Sciences, PO Box 123, Broadway, NSW, 2007, Australia)

  • Eckhard Platen

    (University of Technology Sydney, School of Finance & Economics and Department of Mathematical Sciences, PO Box 123, Broadway, NSW, 2007, Australia)

Abstract

The paper discusses a financial market model that generates stochastic volatility using a minimal number of factors. These factors model the dynamics of different denominations of a benchmark portfolio. Asset prices are specified as transformations of square root processes. Numerical results for the pricing and hedging of standard derivatives on indices for this class of models are documented. This includes cases where the standard risk neutral pricing methodology fails but a form of arbitrage still exists. However, payoffs can be perfectly hedged. In addition, the term structure of implied volatilities is documented.

Suggested Citation

  • David Heath & Eckhard Platen, 2001. "Pricing and Hedging of Index Derivatives under an Alternative Asset Price Model with Endogenous Stochastic Volatility," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 10, pages 117-126, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812799579_0010
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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. David Heath & Eckhard Platen, 2005. "Currency Derivatives Under A Minimal Market Model With Random Scaling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1157-1177.
    3. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    4. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Platen, Eckhard, 2000. "Risk premia and financial modelling without measure transformation," SFB 373 Discussion Papers 2000,92, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. David Heath & Eckhard Platen, 2003. "Pricing of index options under a minimal market model with log-normal scaling," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 442-450.
    7. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 79-105, March.
    8. Platen, Eckhard, 2001. "A benchmark model for financial markets," SFB 373 Discussion Papers 2001,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. David Feldman & Xin Xu, 2018. "Equilibrium-based volatility models of the market portfolio rate of return (peacock tails or stotting gazelles)," Annals of Operations Research, Springer, vol. 262(2), pages 493-518, March.

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