Fair prices under a unified lattice approach for interest rate derivatives
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An open question in interest rates derivative pricing is whether the price of the contracts should be computed by means of a multi-curve approach (different yield curves for discounting and forwarding) or by using a single curve (just one yield curve both for discounting and forwarding). The answer is of primary importance for financial markets as it allows to define a class of fair contracts. This paper calculates and compares the price of a simple swap within both multi-curve and single curve approaches and proposes a generalization of the lattice approach, which is usually used to approximate short interest rate models in the multi-curve framework. As an example, I show how to use the Black et al. (Financ Anal J 46(1):33–39, 1990) interest rate model on binomial lattice in multi-curve framework and calculate the price of the 2–8 period swaption with a single (LIBOR) curve and two-curve (OIS+LIBOR) approaches. Such technique can be used for pricing any interest rate based contract.
KeywordsInterest rates Single curve Multiple curve Derivative pricing Fair contracts
JEL ClassificationC02 C60 C63
- Ametrano, F., & Bianchetti, M. (2009). Bootstrapping the illiquidity. Modelling Interest Rates: Advances for Derivatives Pricing. Risk Books.Google Scholar
- Bianchetti, M. (2008). Two curves, one price: Pricing & hedging interest rate derivatives decoupling forwarding and discounting yield curves. https://doi.org/10.2139/ssrn.1334356.
- Bianchetti, M. (2010). Multiple curves, one price. Paris: Global derivatives.Google Scholar
- Bianchetti, M., & Carlicchi, M. (2011). Interest rates after the credit crunch: Multiple curve vanilla derivatives and SABR. https://doi.org/10.2139/ssrn.1783070.
- Brigo, D. (2008). CDS options through candidate market models and the CDS-calibrated CIR++ stochastic intensity model. Milton Park: Taylor & Francis.Google Scholar
- Brigo, D., & Mercurio, F. (2006). Interest rate models -PAYPAL-ENV theory and practice with smile, inflation and credit (2nd ed.). Berlin: Springer.Google Scholar
- Chibane, M., & Sheldon, G. (2009). Building curves on a good basis, mimeo. Technical report.Google Scholar
- Clewlow, L., & Strickland, C. (1998). Implementing derivative models. London: Wiley & Sons.Google Scholar
- Fujii, M., Shimada, Y., & Takahashi, A. (2010). A note on construction of multiple swap curves with and without collateral. FSA Research Review, 6, 139–157.Google Scholar
- Hull, J. C. (2009). Options, futures and other derivatives. Upper Saddle River: Pearson Prentice Hall.Google Scholar
- Mercurio, F. (2008). Interest rates and the credit crunch: New formulas and market models. Technical report, QFR, Bloomberg.Google Scholar
- Ron, U. (2000). A practical guide to swap curve construction. Technical report, Bank of CanadaGoogle Scholar
- Sochacki, J., & Buetow, G. (2001). Term-structure models using binomial trees. Technical report, The Research Foundation of AIMR.Google Scholar
- Whittal, C. (2010). Clearnet revalues \$218 trillion swap portfolio using ois. Risk Magazine.Google Scholar