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The Small and Large Time Implied Volatilities in the Minimal Market Model

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  • Zhi Guo
  • Eckhard Platen

Abstract

This paper derives explicit formulas for both the small and large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run even though they are negligible in the short time limit.

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File URL: http://arxiv.org/pdf/1109.6154
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1109.6154.

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Date of creation: Sep 2011
Date of revision: Oct 2011
Handle: RePEc:arx:papers:1109.6154

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Web page: http://arxiv.org/

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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. Martin Forde & Antoine Jacquier, 2011. "The large-maturity smile for the Heston model," Finance and Stochastics, Springer, vol. 15(4), pages 755-780, December.
  3. Michael Roper & Marek Rutkowski, 2009. "On The Relationship Between The Call Price Surface And The Implied Volatility Surface Close To Expiry," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 427-441.
  4. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Leunglung Chan & Eckhard Platen, 2010. "Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model," Papers 1007.2968, arXiv.org, revised Jan 2011.
  6. L. Rogers & M. Tehranchi, 2010. "Can the implied volatility surface move by parallel shifts?," Finance and Stochastics, Springer, vol. 14(2), pages 235-248, April.
  7. Carr, Peter P & Jarrow, Robert A, 1990. "The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value," Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 469-92.
  8. Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
  9. Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Martin Forde & Antoine Jacquier, 2009. "Small-Time Asymptotics For Implied Volatility Under The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 861-876.
  11. repec:wop:humbsf:2000-91 is not listed on IDEAS
  12. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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