A Probabilistic Approach to the Valuation of General Floating-Rate Notes with an Application to Interest Rate Swaps

ADVANCES IN FUTURES AND OPTIONS RESEARCH, Volume 7, 1994

Posted: 29 Dec 1998

See all articles by Hélyette Geman

Hélyette Geman

University of London - Economics, Mathematics and Statistics

Nicole El Karoui

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Abstract

This paper provides an exact formula for the pricing of floating-rate notes (FRNs) in the very general situation when the floater is not priced at par. In an earlier work, Ramaswamy and Sundaresan (1986) also addressed the pricing of FRNs in a stochastic interest rates environment: Their results relied on partial differential equations (PDEs) that did not result in analytical solutions. The model presented in this paper uses martingale theory in providing closed- formed solutions for the price of FRNs with discrete coupon payments and with an arbitrary lag between the reset dates and the ex-coupon dates. The two results are (1) a valuation formula that gives the price of the floater as the sum of discount factors multiplied by the expected future coupon payments, the expectation being taken under an appropriate probability measure; (2) the explicit expression of each expected coupon, which does not need any knowledge of the probability mentioned above, since it is exactly the forward rate plus a term only related to the volatility of the term structure. As a natural application, the paper provides an explicit solution to the pricing of interest rate swaps exchanging a sequence of fixed-rate cash flows in arrears for variable- rate cash flows.

JEL Classification: E43

Suggested Citation

Geman, Helyette and El Karoui, Nicole, A Probabilistic Approach to the Valuation of General Floating-Rate Notes with an Application to Interest Rate Swaps. ADVANCES IN FUTURES AND OPTIONS RESEARCH, Volume 7, 1994, Available at SSRN: https://ssrn.com/abstract=6019

Helyette Geman (Contact Author)

University of London - Economics, Mathematics and Statistics ( email )

Malet Street
London, WC1E 7HX
United Kingdom

Nicole El Karoui

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France
(33) 1 69 33 41 48 (Phone)
(33) 1 69 33 70 31 (Fax)

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