
Can the LEVEL, Steepness and Curvature change at the same time for a bond?

I know based on forward rate model, [1+f(1,2)] = [1+f(1,1)]* [1+f(2,1)]. But I still dont understand why. Can someone just explain a little on this, please?
Thank you!
Can the LEVEL, Steepness and Curvature change at the same time for a bond?
I know based on forward rate model, [1+f(1,2)] = [1+f(1,1)]* [1+f(2,1)]. But I still dont understand why. Can someone just explain a little on this, please?
Thank you!
Yes.
Arbitrage. If they were different, there would be an arbitrage opportunity. Say that 1 + f(1,2) is too small. You (A) buy a cash flow 3 years from now with payment due 2 years from now, (B) buy a cash flow 2 years from now with payment due 1 year from now, and © sell a cash flow 3 years from now with payment due 1 year from now. The present value of C is higher than the present values of A and B together; you’ve made an arbitrage profit.
Thanks for your answers! Makes sence now. Thank you!
You’re quite welcome.