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Currency Derivatives under a Minimal Market Model with Random Scaling

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Abstract

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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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp154.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 154.

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Length: 21
Date of creation: 01 Mar 2005
Date of revision:
Handle: RePEc:uts:rpaper:154

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Keywords: currency derivatives; stochastic volatility; random scaling; minimal market model;

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  1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  2. 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.
  3. 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.
  4. David Heath & Eckhard Platen, 2004. "Understanding the Implied Volatility Surface for Options on a Diversified Index," Research Paper Series 128, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  6. 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.
  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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Cited by:
  1. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.
  2. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126, arXiv.org.
  3. Alvise De Col & Alessandro Gnoatto & Martino Grasselli, 2012. "Smiles all around: FX joint calibration in a multi-Heston model," Papers 1201.1782, arXiv.org, revised Jun 2013.
  4. Platen, Eckhard, 2006. "Portfolio selection and asset pricing under a benchmark approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 23-29.

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