Abstract
In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one of the main goals being also that of exhibiting an “adjustment factor” when passing from the one-curve to the two-curve setting. The model itself corresponds to short rate modeling where the short rate and a short rate spread are driven by affine factors; this allows for correlation between short rate and short rate spread as well as to exploit the convenient affine structure methodology. We briefly comment also on the calibration of the model parameters, including the correlation factor.
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References
Bianchetti, M. (2012). Two curves, one price: pricing and hedging interest rate derivatives, decoupling forwarding and discounting yield curves. arXiv:0905.2770v4
Brigo, D., Morini, M., & Pallavicini, A. (2013). Counterparty credit risk, collateral and funding with pricing cases for all asset classes. New York: Wiley, Forthcoming.
Chiarella, C., Nikitopoulos Sklibosios, C., & Schloegl, E. (2007). A Markovian defaultable term structure model with state dependent volatilities. International Journal of Theoretical and Applied Finance, 10, 155–202.
Chiarella, C., Maina, S. C., Nikitopoulos & Sklibosios, C. (2010). Markovian defaultable HJM term structure models with unspanned stochastic volatility. Quantitative Finance Research Centre Research Paper no. 283, Sydney: University of Technology.
Corcuera, J. M., Farkas, G., Schoutens, W., & Valkeila, E. (2013). A short rate model using ambit processes. In Malliavin calculus and stochastic analysis: A festschrift in honor of David Nualart. Springer proceedings in mathematics and statistics (Vol. 34, pp. 525–553). New York: Springer Science+Business Media.
Crépey, S., Gerboud, R., Grbac, Z., & Ngor, N. (2013a). Counterparty risk and funding: The four wings of the TVA. International Journal of Theoretical and Applied Finance, 16(2), 1350006.
Crépey, S., Grbac, Z., & Nguyen, H.-N. (2012). A multiple-curve HJM model of interbank risk. Mathematics and Financial Economics, 6, 155–190.
Crépey, S., Grbac, Z., Ngor, N., & Skovmand, D. (2013b). A Levy HJM multiple-curve model with application to CVA computation. (Preprint)
Douady, R., & Jeanblanc, M. (2002). A rating-based model for credit derivatives. European Investment Review, 1, 17–29.
Filipović, D. (2009). In Term structure models a graduate course. Berlin: Springer Verlag.
Filipović, D., & Trolle, A. B. (2013). The term structure of interbank risk. Journal of Financial Econometrics, 109, 707–733.
Fontana, C., & Montes, J. M. (2014). A unified approach to pricing and risk management of equity and credit risk. Journal of Computational and Applied Mathematics, 259(B), 350–361.
Fuji, M., Shimada, Y., & Takahashi, A. (2009). A note on the construction of multiple swap curves with and without collateral. CARF Working Paper Series F-154.
Fuji, M., Shimada, Y., & Takahashi, A. (2011). A market model of interest rates with dynamic basis spreads in the presence of collateral and multiple currencies. Wilmott Magazine, 54, 61–73.
Grbac, Z., Papapantoleon, A., Schoenmakers, J., & Skovmand, D. (2014). Affine LIBOR models with multiple curves: Theory, examples and calibration. (Preprint)
Keller-Ressel, M., Papapantoleon, A., & Teichmann, J. (2013). The Affine Libor Models. Mathematical Finance, 23, 627–658.
Kenyon, C. (2010). Short-Rate Pricing After the Liquidity and Credit Shocks: Including the Basis. Retrieved August 18, 2010, from SSRN: http://ssrn.com/abstract=1558429 or http://dx.doi.org/10.2139/ssrn.1558429
Kijima, M., Tanaka, K., & Wong, T. (2009). A multi-quality model of interest rates. Quantitative Finance, 9, 133–145.
Mercurio, F. (2010). Interest Rates and The Credit Crunch: New Formulas and Market Models. Bloomberg Portfolio Research Paper (2010–01).
Mercurio, F. (2010). LIBOR Market Models with Stochastic Basis. Bloomberg Education and Quantitative Research Paper (2010–05).
Pallavicini, A., & Brigo, D. (2013). Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs. arXiv:1304.1397v1.
Piterbarg, V. (2010). Funding beyond discounting: collateral agreements and derivatives pricing. Risk Magazine, 24, 97–102.
Acknowledgments
We are grateful to Giulio Miglietta as well as to Claudio Fontana and Zorana Grbac for very constructive comments.
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Morino, L., Runggaldier, W.J. (2014). On Multicurve Models for the Term Structure. In: Dieci, R., He, XZ., Hommes, C. (eds) Nonlinear Economic Dynamics and Financial Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-07470-2_16
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DOI: https://doi.org/10.1007/978-3-319-07470-2_16
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