Let B (t, T) denote the volatility structure of the return of a discount bond. The

Let σ_B(t, T) denote the volatility structure of the return of a discount bond. The Gaussian term structure models are characterized by (i) deterministic σ_B(t, T) and (ii) a Markov short rate process. Show that a necessary and sufficient condition for a one-factor HJM model to be Gaussian is given by (Hull and White, 1993a)

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where OB (t, T) = a(t)ß(t, T), B(t, T) = y(T) - y(t) y' (t)