Tim, Xiao (2011): An efficient lattice algorithm for the libor market model. Forthcoming in: Journal of Derivatives
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The LIBOR Market Model (LMM or BGM) has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround.
|Item Type:||MPRA Paper|
|Original Title:||An efficient lattice algorithm for the libor market model|
|Keywords:||LIBOR Market Model, LMM, BGM, lattice model, tree model, shifted forward measure, drift approximation, risk management, calibration, callable exotics, callable bond, callable capped floater swap, callable inverse floater swap, callable range accrual swap|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling
D - Microeconomics > D4 - Market Structure, Pricing, and Design
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing
|Depositing User:||Tim Xiao|
|Date Deposited:||26. Aug 2011 01:58|
|Last Modified:||03. Jan 2016 18:55|
Amin, K. “Jump diffusion option valuation in discrete time.” Journal of Finance, Vol. 48, No. 5 (1993), pp. 1833-1863.
Brace, A., D. Gatarek, and M. Musiela. “The market model of interest rate dynamics.” Mathematical Finance, Vol. 7, No. 4 (1997), pp. 127-155.
Brigo, D., and F. Mercurio. “Interest Rate Models – Theory and Practice with Smiles, Inflation and Credit.” Second Edition, Springer Finance, 2006.
Das, S. “Random lattices for option pricing problems in finance.” Journal of Investment Management, Vol. 9, No.2 (2011), pp. 134-152.
Gandhi, S. and P. Hunt. “Numerical option pricing using conditioned diffusions,” Mathematics of Derivative Securities, Cambridge University Press, Cambridge, 1997.
Hagan, P. “Accrual swaps and range notes.” Bloomberg Technical Report, 2005. Hull. J., and A. White. “Forward rate volatilities, swap rate volatilities and the implementation of the Libor Market Model.” Journal of Fixed Income, Vol. 10, No. 2 (2000), 46-62.
Martzoukos, H., and L. Trigeorgis. “Real (investment) options with multiple sources of rare events.” European Journal of Operational Research, 136 (2002), 696-706. Piterbarg, V. “A Practitioner’s guide to pricing and hedging callable LIBOR exotics in LIBOR Market Models.” SSRN Working paper, 2003.
Rebonato, R. “Calibrating the BGM model.” RISK, March (1999), 74-79.