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Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)


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  • Sven Rady

    (Graduate School of Business, Stanford University, Stanford, CA 94305-5015, USA)


This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries and a quadratic diffusion coefficient. The paper shows in particular how to interpret the option price formula in terms of exercise probabilities which are calculated under the martingale measures associated with two specific numeraire portfolios. An application to the pricing of bond options and certain interest rate derivatives illustrates the main results.

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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 1 (1997)
Issue (Month): 4 ()
Pages: 331-344

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Handle: RePEc:spr:finsto:v:1:y:1997:i:4:p:331-344

Note: received: January 1996; final version received: December 1996
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Keywords: Option pricing; bond options; change-of-numeraire technique; diffusion process; quadratic diffusion terms;

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Cited by:
  1. Peter Carr & Travis Fisher & Johannes Ruf, 2012. "Why are quadratic normal volatility models analytically tractable?," Papers 1202.6187,, revised Mar 2013.
  2. Christian Zuehlsdorff, 1999. "The Pricing of Derivatives on Assets with Quadratic Volatility," Discussion Paper Serie B 451, University of Bonn, Germany.
  3. Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
  5. Christian Zühlsdorff, 2002. "The Pricing of Derivatives on Assets with Quadratic Volatility," Bonn Econ Discussion Papers bgse5_2002, University of Bonn, Germany.
  6. Christian Zuhlsdorff, 2001. "The pricing of derivatives on assets with quadratic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 235-262.
  7. Leif Andersen, 2011. "Option pricing with quadratic volatility: a revisit," Finance and Stochastics, Springer, vol. 15(2), pages 191-219, June.


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