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Discontinuous Interest Rate Processes: An Equilibrium Model for Bond Option Prices

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  • Attari, Mukarram

Abstract

This paper obtains equilibrium interest rate option prices for discontinuous short-term interest rate processes. The prices are first obtained for a general distribution of jump sizes using a process with a number of fixed size jumps. The pricing formulas are then used to obtain option prices when the jump distribution is known to be one of the continuous distributions. The commonly used jump-diffusion, stochastic volatility jump-diffusion, and Gamma process option prices can be obtained as limiting cases. The methodology is also applied to obtain the prices of options on stocks. Finally, the paper shows how portfolios to hedge derivative securities can be built.

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  • Attari, Mukarram, 1999. "Discontinuous Interest Rate Processes: An Equilibrium Model for Bond Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(3), pages 293-322, September.
    • Handle: RePEc:cup:jfinqa:v:34:y:1999:i:03:p:293-322_00
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    Cited by:

    1. Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
    2. Frances Shaw & Finbarr Murphy & Fergal G. O’Brien, 2016. "Jumps in Euribor and the effect of ECB monetary policy announcements," Environment Systems and Decisions, Springer, vol. 36(2), pages 142-157, June.
    3. Odusami, Babatunde O., 2021. "Volatility jumps and their determinants in REIT returns," Journal of Economics and Business, Elsevier, vol. 113(C).
    4. Brito, R. & Flores, R., 2001. "A Jump Difusion Yield Factor Model of Interest Rate," Finance Lab Working Papers flwp_37, Finance Lab, Insper Instituto de Ensino e Pesquisa.

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