# 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

It is simply the difference between "today" and the cash flow date in years. A 30-years bond paying semi-annual coupons has 60 cash flows, and each cash flow has its own "TTM".

• Thank you very much. This implies each bond has its own "TTM" Vector. And as a result, each bond would be associated with a different zero coupon rate and hence discount rate? And finally, does this mean if I've chosen 5 bonds, all of which have a semi-annual coupon and the 30 year bond has the max maturity, then shouldn't I have a discount vector which has the same number of rows as there are columns in the matrix of coupons and face values?.......
– Jojo
Commented Jul 28, 2015 at 0:31
• .....But each bond having its own discount factor vector implies that the number or rows of the discount matrix = number of rows in the matrix of coupons and face values? This is where my confusion really lies.
– Jojo
Commented Jul 28, 2015 at 0:31
• 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. Commented Jul 28, 2015 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
Commented Jul 28, 2015 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. Commented Jul 28, 2015 at 1:10