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Article

Modifying the LMM to Price Constant Maturity Swaps

Ting-Pin Wu and Son-Nan Chen
The Journal of Derivatives Winter 2010, 18 (2) 20-32; DOI: https://doi.org/10.3905/jod.2010.18.2.020
Ting-Pin Wu
is an associate professor in the Department of Finance at the National Central University in Taoyuan, Taiwan.
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  • For correspondence: tpwu@mail.ntpu.edu.tw
Son-Nan Chen
is a professor of finance at the Shanghai Advanced Institute of Finance (SAIF) at Shanghai Jiao Tong University in Shanghai, China.
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  • For correspondence: slchen@nccu.edu.tw
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Abstract

An interest rate swap involves an exchange of cash payments calculated by applying two different interest rates to the same notional principal. In a constant maturity swap (CMS), one rate is the rate on the fixed-rate leg of the swap of a specified maturity and the other is a money market rate, such as LIBOR. For example, a CMS swap might call for exchanging the current 10-year swap rate against 90-day LIBOR. The problem in valuing the contract is that a CMS swap is normally priced under the forward measure (where forward short rates are assumed to be lognormal), while a 10-year swap would be priced under the forward swap measure (in which the swap rates are lognormal). The two measures are incompatible because neither one allows both rates to be lognormal. Wu and Chen develop a lognormal “approximation” to the swap rate within the LIBOR market model, allowing the pricing of CMS swaps of several types to be done more easily and accurately than with the convexity-adjustment alternative.

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The Journal of Derivatives: 18 (2)
The Journal of Derivatives
Vol. 18, Issue 2
Winter 2010
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Modifying the LMM to Price Constant Maturity Swaps
Ting-Pin Wu, Son-Nan Chen
The Journal of Derivatives Nov 2010, 18 (2) 20-32; DOI: 10.3905/jod.2010.18.2.020

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Modifying the LMM to Price Constant Maturity Swaps
Ting-Pin Wu, Son-Nan Chen
The Journal of Derivatives Nov 2010, 18 (2) 20-32; DOI: 10.3905/jod.2010.18.2.020
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  • Article
    • Abstract
    • REVIEW OF THE LMM AND AN APPROXIMATE DISTRIBUTION OF A SWAP RATE IN THE LMM
    • PRICING CONSTANT MATURITY SWAPS
    • NUMERICAL STUDIES
    • CONCLUSION
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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