# Term Structure and short rates

If I have a term structure/yield curve given by: $$f(t, T) = f(0, T) + σ^2t(T − \frac{t}{2}) + σB_t$$

and want to find the short/spot rate $r_t$, is this simply:

$$f(t,t) = f(0,t) + \sigma^2t(t-\frac{t}{2}) + \sigma B_t$$

Can anything further be done?

• Yes. This is the definition. What's your question? – SmallChess May 11 '15 at 6:27
• What others you want? For example, the dynamics of $r_t$, or the bond price $B(t, T)$? You can actually have many things, depending on your appetite. – Gordon May 12 '15 at 19:45
• I was unsure if there was anyway to expand on the definition, as it turns out, there is not. Thanks. – elbarto May 13 '15 at 16:25