Currency Derivatives under a Minimal Market Model with Random Scaling
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.
|Date of creation:||01 Mar 2005|
|Date of revision:|
|Publication status:||Published as: Heath, D. and Platen, E., 2005, "Currency Derivatives under a Minimal Market Model with Random Scaling", International Journal of Theoretical and Applied Finance, 8(8), 1157-1177.|
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- Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
- 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.
- 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.
- Eckhard Platen, 2006.
"A Benchmark Approach To Finance,"
Wiley Blackwell, vol. 16(1), pages 131-151.
- 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.
- 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.
- Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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