Forward Curve
Overview
The Forward Price
{% f(t_1, t_2) = (r(t_2)t_2 - r(t_1)t_1) / (t_2 - t_1) %}
{% f(t_1, t_2) = r(t_2) + t_1 \times (r(t_2) - r(t_1))/(t_2 - t_1) %}
The Instantaneous Forward Rate
The instantaneous forward rate curve at time t is
{% f(t,T) = \lim_{S \rightarrow T} F(t,T,S) = -\frac{\partial}{\partial T} ln P(t,T) = -\frac{\partial P(t,T)/\partial T}{P(t,T)} %}
{% P(t,T) = exp[-\int_t ^T f(t,u) du] %}
