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A Common Market Measure For Libor And Pricing Caps, Floors And Swaps In A Field Theory Of Forward Interest Rates

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  • BELAL E. BAAQUIE

    (Department of Physics, 2 Science Drive 3, National University of Singapore, Singapore 117542, Singapore)

Abstract

The main result of this paper is that a martingale evolution can be chosen for LIBOR such that, by appropriately fixing the drift, all LIBOR interest rates have a common market measure. LIBOR is described using a quantum field theory model, and a common measure is seen to emerge naturally for such models. To elaborate how the martingale for the LIBOR belongs to the general class of numeraires for the forward interest rates, two other numeraires are considered, namely the money market measure that makes the evolution of the zero coupon bonds a martingale, and the forward measure for which the forward bond price is a martingale. The price of an interest rate cap is computed for all three numeraires, and is shown to be numeraire invariant. Put-call parity is discussed in some detail and shown to emerge due to some nontrivial properties of the numeraires. Some properties of swaps, and their relation to caps and floors, are briefly discussed.

Suggested Citation

  • Belal E. Baaquie, 2005. "A Common Market Measure For Libor And Pricing Caps, Floors And Swaps In A Field Theory Of Forward Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 999-1018.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:08:n:s0219024905003347
    DOI: 10.1142/S0219024905003347
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    Cited by:

    1. Baaquie, Belal E. & Liang, Cui, 2007. "Pricing American options for interest rate caps and coupon bonds in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 285-316.
    2. Baaquie, Belal E. & Liang, Cui, 2007. "Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 331-348.
    3. Baaquie, Belal E. & Liang, Cui & Warachka, Mitch C., 2007. "Hedging LIBOR derivatives in a field theory model of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 730-748.

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