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Currency Derivatives Under A Minimal Market Model With Random Scaling

  • 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)

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 08 (2005)
Issue (Month): 08 ()
Pages: 1157-1177

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Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:08:p:1157-1177
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  1. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
  3. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. David Heath & Eckhard Platen, 2004. "Understanding the Implied Volatility Surface for Options on a Diversified Index," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 55-77, March.
  5. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  7. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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