On Valuing Constant Maturity Swap Spread Derivatives
Author(s)
Leonard Tchuindjo
ABSTRACT
Motivated by statistical tests on historical data that confirm the normal distribution assumption on the spreads between major constant maturity swap (CMS) indexes, we propose an easy-to-implement two-factor model for valuing CMS spread link instruments, in which each forward CMS spread rate is modeled as a Gaussian process under its relevant measure, and is related to the lognormal martingale process of a corresponding maturity forward LIBOR rate through a Brownian motion. An illustrating example is provided. Closed-form solutions for CMS spread options are derived.
Motivated by statistical tests on historical data that confirm the normal distribution assumption on the spreads between major constant maturity swap (CMS) indexes, we propose an easy-to-implement two-factor model for valuing CMS spread link instruments, in which each forward CMS spread rate is modeled as a Gaussian process under its relevant measure, and is related to the lognormal martingale process of a corresponding maturity forward LIBOR rate through a Brownian motion. An illustrating example is provided. Closed-form solutions for CMS spread options are derived.
Cite this paper
L. Tchuindjo, "On Valuing Constant Maturity Swap Spread Derivatives," Journal of Mathematical Finance, Vol. 2 No. 2, 2012, pp. 189-194. doi: 10.4236/jmf.2012.22020.
L. Tchuindjo, "On Valuing Constant Maturity Swap Spread Derivatives," Journal of Mathematical Finance, Vol. 2 No. 2, 2012, pp. 189-194. doi: 10.4236/jmf.2012.22020.
References
[1] Fannie Mae, “Fannie Mae Universal Debt Facility,” Fed- eral Home Loan Association, Washington DC, 2008. http://www.fanniemae.com/markets/debt/pdf/CUSIP_PS31398ANE8.pdf [2] R. Carmona and V. Durrleman, “Pricing and Hedging of Spread Options,” SIAM Review, Vol. 45, No. 4, 2003, pp. 627-685. doi:10.1137/S0036144503424798 [3] D. Belomestny, A. Kolodko and J. Schoenmakers, “Pricing Spreads in the Libor Market Model,” Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 2008. [4] M. Lutz and R. Kiesel, “Efficient Pricing of CMS Spread Options in a Stochastic Volatility LMM,” Institute of Mathematical Finance, Ulm University, Ulm, 2010. [5] W. Margrabe, “The Value of an Option to Exchange One Asset for the Another,” Journal of Finance, Vol. 33, No. 1, 1978, pp. 177-186. doi:10.2307/2326358 [6] H. Geman, N. Karoui and J. C. Rochet, “Change of Numeraire, Change of Probability Measure and Option Pricing,” Journal of Applied Probability, Vol. 32, No. 2, 1995, pp. 443-458. doi:10.2307/3215299 [7] F. Jamshidian, “Bond and Option Evaluation in the Gaussian Interest Rate Model,” Research in Finance, Vol. 9, 1991, pp. 131-170. [8] A. V. Antonov and M. Arneguy, “Analytical Formulas for Pricing CMS Products in the Libor Market Model with Stochastic Volatility,” Numerix Software Ltd., London, 2009. [9] A. Pelsser, “Efficient Methods for Valuing Interest Rate Derivative,” Springer-Verlag, New York, 2000.
[1] Fannie Mae, “Fannie Mae Universal Debt Facility,” Fed- eral Home Loan Association, Washington DC, 2008. http://www.fanniemae.com/markets/debt/pdf/CUSIP_PS31398ANE8.pdf [2] R. Carmona and V. Durrleman, “Pricing and Hedging of Spread Options,” SIAM Review, Vol. 45, No. 4, 2003, pp. 627-685. doi:10.1137/S0036144503424798 [3] D. Belomestny, A. Kolodko and J. Schoenmakers, “Pricing Spreads in the Libor Market Model,” Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 2008. [4] M. Lutz and R. Kiesel, “Efficient Pricing of CMS Spread Options in a Stochastic Volatility LMM,” Institute of Mathematical Finance, Ulm University, Ulm, 2010. [5] W. Margrabe, “The Value of an Option to Exchange One Asset for the Another,” Journal of Finance, Vol. 33, No. 1, 1978, pp. 177-186. doi:10.2307/2326358 [6] H. Geman, N. Karoui and J. C. Rochet, “Change of Numeraire, Change of Probability Measure and Option Pricing,” Journal of Applied Probability, Vol. 32, No. 2, 1995, pp. 443-458. doi:10.2307/3215299 [7] F. Jamshidian, “Bond and Option Evaluation in the Gaussian Interest Rate Model,” Research in Finance, Vol. 9, 1991, pp. 131-170. [8] A. V. Antonov and M. Arneguy, “Analytical Formulas for Pricing CMS Products in the Libor Market Model with Stochastic Volatility,” Numerix Software Ltd., London, 2009. [9] A. Pelsser, “Efficient Methods for Valuing Interest Rate Derivative,” Springer-Verlag, New York, 2000.