# Term to Maturity when calculating discount function

I am just trying to understand what TTM (Term to Maturity) means in Page 8 of this PDF when calculating the discount function. Is it just the vector representing the difference between the time to maturity and the various coupon payments for the bonds? For example, if we are considering 1 year, 2 year, 5 year, 10 year and 30 year bonds and each has semi-annual coupons what would the TTM be?

Thank You

• Yes, each bond should have its own cash flow and cash flow times vector. The dimension of the matrices should be $N\times M$, where $N$ is the number of bonds, and $M$ is number of cash flows of the bond with the longest time to maturity. – Helin Jul 28 '15 at 0:37
• Thanks. And the discount vector that we multiply with the above matrix to get the prices would have a $M × 1$ dimension? But then, since the discount function is dependent on "TTM" and each bonds has its own "TTM" vector, doesn't that imply that the discount vector should actually be $N × 1$? – Jojo Jul 28 '15 at 0:43
• The discount factors would be $M\times1$. Keep in mind that this is a best-fit problem. You won't be able to price ALL the bonds perfectly. – Helin Jul 28 '15 at 1:10