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Article

Barrier Caps and Floors under the LIBOR Market Model with Double Exponential Jumps

Jui-Jane Chang, Son-Nan Chen, Chun-Chao Wang and Ting-Pin Wu
The Journal of Derivatives Summer 2014, 21 (4) 7-24; DOI: https://doi.org/10.3905/jod.2014.21.4.007
Jui-Jane Chang
is an associate professor of finance, Department of Financial Engineering and Actuarial Mathematics, at Soochow University in Taiwan.
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  • For correspondence: jjane@scu.edu.tw
Son-Nan Chen
is a professor at the Shanghai Advanced Institute of Finance (SAIF) at Shanghai Jiao Tong University in Shanghai.
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  • For correspondence: snchen@saif.sjtu.edu.cn
Chun-Chao Wang
is an associate professor in the Department of Statistics at National Taipei University in Taiwan.
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  • For correspondence: ccw@mail.ntpu.edu.tw
Ting-Pin Wu
is a professor in the Department of Finance at National Central University in Taiwan.
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  • For correspondence: wutingpin@gmail.com
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Abstract

The LIBOR market model (LMM) has become the standard model for many kinds of interest rate derivatives, such as cap contracts. It assumes that the distribution of the one-period interest rate at each future repricing date is lognormal, so that every caplet can be easily priced using the Black model. Volatilities at different dates are tied together by assumptions that restrict the number of parameters to a manageable set. But interest rates are strongly affected by things like monetary policy decisions, which can lead to sharp, nondiffusive jumps when policy changes. The effect may be seen in the leptokurtosis of the empirical distributions of interest rates and in volatility smiles for caplets. The low probability of extreme rate moves in the standard LMM is especially problematical for barrier options. In this article, the authors introduce a new jump-diffusion process for the LLM that can capture the effects of jumps on interest rate barrier contracts. The authors allow exponential jumps, both up and down, so the model is called the LMM with a double-jump process, or LMMDJ. Explicit valuation equations are provided for the four classes of barrier contracts and are shown to be quite accurate in Monte Carlo simulations.

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The Journal of Derivatives: 21 (4)
The Journal of Derivatives
Vol. 21, Issue 4
Summer 2014
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Barrier Caps and Floors under the LIBOR Market Model with Double Exponential Jumps
Jui-Jane Chang, Son-Nan Chen, Chun-Chao Wang, Ting-Pin Wu
The Journal of Derivatives May 2014, 21 (4) 7-24; DOI: 10.3905/jod.2014.21.4.007

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Barrier Caps and Floors under the LIBOR Market Model with Double Exponential Jumps
Jui-Jane Chang, Son-Nan Chen, Chun-Chao Wang, Ting-Pin Wu
The Journal of Derivatives May 2014, 21 (4) 7-24; DOI: 10.3905/jod.2014.21.4.007
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  • Article
    • Abstract
    • THE LMMDJ
    • THE PRICING FORMULAS OF BARRIER CAPS AND FLOORS WITHIN THE LMMDJ
    • NUMERICAL EXAMPLES
    • CONCLUSION
    • APPENDIX A
    • APPENDIX B
    • APPENDIX C
    • ENDNOTES
    • REFERENCES
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