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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

Abstract

The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally for such models. To elaborate how the martingale for the Libor belongs to the general class of numeraire for the forward interest rates, two other numeraire's 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 non-trivial 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," Papers physics/0503126, arXiv.org.
    • Handle: RePEc:arx:papers:physics/0503126
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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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