LIBOR market (LM) model is an interest rate version of the BlackScholes
model of stock price. Extended LM models including constant elasticity
of volatility models and affine volatility models have been proposed to explain the
observation that implied volatilities of forward LIBOR rates depend on caps’ rates
in the LM model. This paper proposes methods of specifying the dimensionality
of Wiener process and the functional form on forward LIBOR rates’ volatilities in
the extended LM models, and presents a test for the extended LM models. The
result of the test using the Eurodollar future rates traded in the Chicago Mercantile
Exchange rejected all of the extended LM models.