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LIBOR and swap market models and measures (*)

  • Farshid Jamshidian


    (New Products and Strategic Trading, Sakura Global Capital, 42 New Broad Street, London EC2M 1JX, UK)

A self-contained theory is presented for pricing and hedging LIBOR and swap derivatives by arbitrage. Appropriate payoff homogeneity and measurability conditions are identified which guarantee that a given payoff can be attained by a self-financing trading strategy. LIBOR and swap derivatives satisfy this condition, implying they can be priced and hedged with a finite number of zero-coupon bonds, even when there is no instantaneous saving bond. Notion of locally arbitrage-free price system is introduced and equivalent criteria established. Stochastic differential equations are derived for term structures of forward libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying existence of an arbitrage-free model with such volatility specification. The construction is explicit for the lognormal LIBOR and swap "market models", the former following Musiela and Rutkowski (1995). Primary examples of LIBOR and swap derivatives are discussed and appropriate practical models suggested for each.

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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 1 (1997)
Issue (Month): 4 ()
Pages: 293-330

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Handle: RePEc:spr:finsto:v:1:y:1997:i:4:p:293-330
Note: received: January 1996; final version received: May 1997
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