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Convexity theory for the term structure equation

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  • Erik Ekstrom
  • Johan Tysk

Abstract

We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these conditions the price is decreasing in the drift and increasing in the volatility of the short rate. We also study convexity properties of the logarithm of the price.

Suggested Citation

  • Erik Ekstrom & Johan Tysk, 2007. "Convexity theory for the term structure equation," Papers math/0702435, arXiv.org.
    • Handle: RePEc:arx:papers:math/0702435
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    References listed on IDEAS

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    1. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. "General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    2. Alvarez, Luis H. R., 2001. "On the form and risk-sensitivity of zero coupon bonds for a class of interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 83-90, February.
    3. Erik Ekstrom & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526, arXiv.org.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
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