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Convexity theory for the term structure equation

  • Erik Ekstrom
  • Johan Tysk
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    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.

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    Paper provided by in its series Papers with number math/0702435.

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    Date of creation: Feb 2007
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    Handle: RePEc:arx:papers:math/0702435
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    1. Erik Ekstr\"om & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526,
    2. 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.
    3. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
    4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    5. Jonatan Eriksson, 2006. "Monotonicity In The Volatility Of Single-Barrier Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 987-996.
    6. 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.
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