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Primary Article

Pricing American Interest Rate Options under the Jump-Extended Vasicek Model

Natalia A. Beliaeva, Sanjay K. Nawalkha and Gloria M. Soto
The Journal of Derivatives Fall 2008, 16 (1) 29-43; DOI: https://doi.org/10.3905/jod.2008.710896
Natalia A. Beliaeva
An assistant professor of finance in the Sawyer Business School at Suffolk University in Boston, MA.
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  • For correspondence: natalia_beliaeva@yahoo.com
Sanjay K. Nawalkha
An associate professor of finance in the Isenberg School of Management at the University of Massachusetts in Amherst, MA.
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  • For correspondence: nawalkha@som.umass.edu
Gloria M. Soto
A tenured professor of applied economics and finance at the University of Murcia in Murcia, Spain.
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  • For correspondence: gsoto@um.es
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Abstract

By introducing Brownian motion to finance, Black, Scholes, and Merton caused a quantum jump in sophistication and realism in the returns processes assumed in asset pricing models. Diffusion processes have taken us a long way, but for many markets there is considerable evidence that diffusions aren't enough to represent real world returns accurately. We need the possibility of occasional discrete jumps, as well. Short-term interest rates are especially prone to jumps because they are strongly influenced by administered rates, such as the Fed funds rate, that are changed in discrete increments. In this article, the authors develop a model of the short rate in the spirit of the Vasicek model, but with exponential up-jump and down-jump processes appended. The pricing equations for European options on zero coupon bonds and interest rate swaps can be obtain by cumulant or Fourier transform techniques, but for American exercise the authors also present a lattice model suitable for computing theoretical values and hedging parameters. The key to capturing the jump effects within a lattice framework is to allow multiple branching from each node, such that large jump moves can occur. Convergence properties of both techniques seem quite good.

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The Journal of Derivatives
Vol. 16, Issue 1
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Pricing American Interest Rate Options under the Jump-Extended Vasicek Model
Natalia A. Beliaeva, Sanjay K. Nawalkha, Gloria M. Soto
The Journal of Derivatives Aug 2008, 16 (1) 29-43; DOI: 10.3905/jod.2008.710896

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Pricing American Interest Rate Options under the Jump-Extended Vasicek Model
Natalia A. Beliaeva, Sanjay K. Nawalkha, Gloria M. Soto
The Journal of Derivatives Aug 2008, 16 (1) 29-43; DOI: 10.3905/jod.2008.710896
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