# How to bootstrap discount factor DF of the settlement period DF(today, today+settlement period)?

Consider an overnight rate $$r_{ON}$$ and a one-week rate $$r_{1W}$$.A settlement period of 2 days is associated to the rate $$r_{1W}$$.

In order to compute the overnight discount factor, since the first rate has 0 settlement period, I apply the simple compounding formula $$DF(t, t+1) = \frac{1}{1+\alpha_{0,1}r_{ON}}$$, where $$\alpha_{0,1}$$ is the accrual factor.

$$r_{1W}$$ is, to my knowledge, the discount rate I can use to compute the FORWARD discount factor $$DF(t, t+2, t+2+7)$$, am I right? How can I get the discount factor DF(t, t+2) in order to get DF(t, t+2+7)? What are the different solutions that can be used?

Thank you mr. Merlo

• Do you have both ON and TN rates? – Helin Sep 11 at 20:29
• I have only ON and 1 Week rate – mr. Merlo Sep 13 at 9:20