I have learned this as taking the average of the two prices at the nodes, add back coupon and discounting back at the previous node rate.
We have the following (sorry hope it makes sense. Y1 and Y2 nodes). 2.5% Coupon
Y1…104.2876…Y2 103.2695
… X (Solve)…104.0168
…104.6350
Right, so surely X is (104.0168 + 2.5) + (104.6350+2.5) / 2 = 106.8259
Divide by the relevant Y1 node (which is 1.4925%) so 106.8259/1.014925 = 105.2549
The answer is saing 105.2917? What is with the small discrepency?
THanks
The answer is self explanatory
0.5 × [(104.0168/1.014925 + 104.6350/1.014925)] + 2.5
Track the numbers to Exhibits 3 and 4 and you will see the logic used.
P.S. Your answer incorrectly discounts the coupons as well. Take coupons out of the brackets.
Is the question referring to a floating bond?
2.5%, Four-Year, Option-Free, Annual Pay Bond
All tree examples I have done is the following:
Take Price at say Node 2-2 and add coupon
Take Price at say Node 2-3 and add coupon
Average these (x0.5)
Discount at rate before.
Is that not what I am doing in my explanation above?
The question says the prices are implied values for a 2.5% 4 year option free annual bond.
Sorry If im missing something obvious.
To clarify my confusion further. If you use the approach I have suggested above for Q10 a couple questions later I get the exact correct bond price?
“Pathwise valuation calculates the present value of a bond for each possible interest rate path and takes the average of these values across paths”. The key is present value. It means all relevant cash flows (including coupons) have already been accounted for in that particular node.
Q10 is a new question, with new exhibits and it explicitly asks to use a binomial tree. You can apply your method to a binomial tree (backward induction). Pathwise method is a little different but even simpler for reasons described above. The curriculum allocates only 3 pages to this method, of which 80% are tables.
thanks Krok, didnt realise it was a pathwise valuation question. Cheers