Calculation of the convexity adjustment to the forward rate in the Vasicek model for the forward in-arrears contracts on LIBOR rate
Authors:
N. O. Malykh and I. S. Postevoy
Journal:
Theor. Probability and Math. Statist. 99 (2019), 189-198
MSC (2010):
Primary 91G20; Secondary 91-02
DOI:
https://doi.org/10.1090/tpms/1089
Published electronically:
February 27, 2020
MathSciNet review:
3908665
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Additional Information
Abstract: We calculate the convexity adjustment to the forward rate in the Vasicek model for the in-arrears forward contracts. With the help of the no-arbitrage market condition it is shown that such an adjustment should be non-negative. Analytical formulas are found for the in-arrears interest rate options.
References
- J. C. Hull, Options, Futures, and Other Derivatives, 8th ed., Pearson Education, 2012, pp. 87–88.
- D. Mcinerney and T. Zastawniak, Stochastic Interest Rates, vol. 1, Cambridge University Press, 2015, pp. 129–132.
- Antoon Pelsser, Mathematical foundation of convexity correction, Selected Proceedings from Quantitative Methods in Finance, 2002 (Cairns/Sydney), 2003, pp. 59–65. MR 1972376, DOI https://doi.org/10.1088/1469-7688/3/1/306
- P. Hagan, Convexity conundrums: Pricing CMS swaps, caps, and floors, Wilmott Magazine (2003), no. 2, 38–44.
- B. Gaminha, R. M. Gaspar, and O. Oliveira, LIBOR Convexity Adjustments for the Vasicek and Cox–Ingersoll–Ross models, https://ssrn.com/abstract=2677712.
- R. M. Gaspar and A. Murgoci Convexity adjustments for affine term structure models, https://papers.ssrn.com/sol3/papers.cfm?abstract_{i}d=1399323.
- O. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics 5 (1977), no. 2, 177–188.
- H. Corb, Interest Rate Swaps and Other Derivatives, Columbia University Press, 2012, pp. 268–272.
- Hélyette Geman, Nicole El Karoui, and Jean-Charles Rochet, Changes of numéraire, changes of probability measure and option pricing, J. Appl. Probab. 32 (1995), no. 2, 443–458. MR 1334898, DOI https://doi.org/10.2307/3215299
- Nicolas Privault, An elementary introduction to stochastic interest rate modeling, 2nd ed., Advanced Series on Statistical Science & Applied Probability, vol. 16, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. MR 2978698
References
- J. C. Hull, Options, Futures, and Other Derivatives, 8th ed., Pearson Education, 2012, pp. 87–88.
- D. Mcinerney and T. Zastawniak, Stochastic Interest Rates, vol. 1, Cambridge University Press, 2015, pp. 129–132.
- A. Pelsser, Mathematical foundation of convexity correction, Quantitative Finance 3 (2003), no. 1, 59–65. MR 1972376
- P. Hagan, Convexity conundrums: Pricing CMS swaps, caps, and floors, Wilmott Magazine (2003), no. 2, 38–44.
- B. Gaminha, R. M. Gaspar, and O. Oliveira, LIBOR Convexity Adjustments for the Vasicek and Cox–Ingersoll–Ross models, https://ssrn.com/abstract=2677712.
- R. M. Gaspar and A. Murgoci Convexity adjustments for affine term structure models, https://papers.ssrn.com/sol3/papers.cfm?abstract_{i}d=1399323.
- O. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics 5 (1977), no. 2, 177–188.
- H. Corb, Interest Rate Swaps and Other Derivatives, Columbia University Press, 2012, pp. 268–272.
- H. Geman, N. El Karoui, and J.-C. Rochet, Changes of numeraire, changes of probability measure and option pricing, Journal of Applied Probability 32 (1995), no. 2, 443–458. MR 1334898
- N. Privault, An Elementary Introduction to Stochastic Interest Rate Modeling, vol. 16, World Scientific Publishing Co. Pte. Ltd., Singapore, 2012. MR 2978698
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Additional Information
N. O. Malykh
Affiliation:
Department of Innovation and High Technology, Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russian Federation
Email:
malykh@phystech.edu
I. S. Postevoy
Affiliation:
Department of Innovation and High Technology, Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russian Federation
Email:
postevoi@phystech.edu
Keywords:
Convexity adjustment,
forward rate agreement,
Vasicek model,
no-arbitrage market,
in-arrears LIBOR,
iFRA
Received by editor(s):
September 10, 2018
Published electronically:
February 27, 2020
Article copyright:
© Copyright 2020
American Mathematical Society
