OAS on bond

CFA Level II Fixed Income
#1

So the question below, I’ve spent a lot of time on but still not following whats going on. I understand that lowering the interest rate volatility will lower the embedded put option which will lower the value of put bond. So if the value is lower, shouldn’t the OAS needed to to force the tree to make the value equal the market price be higher (since oas is in the denominator for each branch ==> market value = X / (interest + oas) ). I think I’m doing something wrong with the market price. To solve this problem, am I adjusting the market price down or am I adjusting the interest rate down.

Why is the answer < 50bps

Sharon Rogner, CFA is evaluating three bonds for inclusion in fixed income portfolio for one of her pension fund clients. All three bonds have a coupon rate of 3%, maturity of five years and are generally identical in every respect except that bond A is an option-free bond, bond B is callable in two years and bond C is putable in two years. Rogner computes the OAS of bond A to be 50bps using a binomial tree with an assumed interest rate volatility of 15%.

If Rogner revises her estimate of interest rate volatility to 10%, the computed OAS of Bond C would most likely be:

a. higher than 50bps.

b. equal to 50bps.

c. lower than 50bps.

#2

The market price doesn’t change: the market doesn’t know what volatility Sharon’s using (and wouldn’t care even if it did know).

I wrote an article on using binomial trees to calculate OAS here: Option-Adjusted Spread (OAS) | Financial Exam Help 123

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website. You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

The reasoning, in short, is that when the volatility decreases:

  1. The high interest rates in the tree will be lower, and the low interest rates in the tree will be higher.
  2. The lower the high interest rates, the higher the present value of the remaining cash flows.
  3. The higher the present value of the remaining cash flows, the less likely it is that the bond will be put.
  4. When the bond is put, the higher the cash flow at that node, so the less likely it is to be put, the lower the average cash flows for the entire tree.
  5. The lower the average cash flow, the lower the average discount rate needed to get to the same present value.
  6. The lower the average discount rate, the lower the required spread (OAS).
1 Like
#3

Ahhhhh that makes perfect sense! Thank YOU!

I was trying to lower the market price, and when that didn’t work, I tried to lower the interest rate, which also didn’t work – because didnt factor if the interest rate branch was low or high in the tree.

#4

My pleasure.