# Calculating discount factors using Nelson Siegel Svensson model

I am trying to understand how to calculate the discount factors $disc(TTM)$ mentioned on Page 9 of this pdf. When I'm calculating the discount factors, mentioned each bond has its own cash flow and cash flow time vector. Wouldn't this imply that since there are as many TTM Vectors as there are bonds, there will be as many $disc(TTM)$ values as there are bonds, and as a result the discount vector will have as many rows as there are bonds? However, shouldn't it have as many rows as the number of cash flows of the bond with the longest time to maturity (Only then would we be able to multiply the matrix of coupons and face values ($A$) with the discount vector ($P$) as listed here?

Edit: I apologize if I've asked a question similar to this one. But I'm trying to gather as much information as I can and ask this question thats been plaguing me as clearly as possible.

Thank You

For each bond, you have a list of cash flows ($c_i$'s). For each cash flow, you can compute the corresponding discount factor ($d(t_i)$'s). Sum up the discounted cash flows gets you the theoretical price: $P = \sum_i c_i d(t_i)$.
• Thank you very much. And if I was calculating the theoretical Yields directly from the discount factors using the equation $Y(t) = P(t)^{-1/t}-1$, where $P(t)$ is the discount function and $Y(t)$ are the yields, what would I take $t$ to be given that I have the discount factor matrix you described above? – Jojo Jul 28 '15 at 14:18