# LIBOR with different tenor

Let $F(t;S,T)$ be the forward rate from $S$ to $T$ seen at time $t$, and $I$ be one of tenors, i.e. $I$ is one of {1M, 3M, 6M, 12M}. Then the forward curve $t\mapsto F(0;t,t+I)$ is $I$-forward curve.

I understand that the forward curve above is easy to calibrate to market values that involves LIBOR of tenor $I$, such as swaps. But how can I get $I$-discounting curve (zero coupon curve) from the forward curve? Is it simply to find the function $P_I(0,t)$ that satisfies the following equation? $$F(0;t,t+I)=\frac{1}{I}\bigg(\frac{P_I(0,t)}{P_I(0,t+I)}-1\bigg)$$

If this is the case, what is the meaning of the value $P_I(0,t)$? Is it simply a function gives the forward curve back?

• Didn't you already ask this once? What happened to that question? – experquisite Jun 18 '15 at 17:40

Your $P_I(t,T)$ is the formula for the so-called "pseudo" discount curve. It can be used to compute relevant LIBOR forward rates and LIBOR zero rates.