AuthorTopic: Fixed income questions
russian
@2014-12-28 12:22:12
I am having a little trouble understanding that concept so I am gonna write it out here and please let me know whether I am wrong or right:

Question 1:

Ex. Nominal Spread is 100, OAS is 25

Does that mean, that if I add 25 bp to every short rate on the node, I will get a value for an option free bond that has a credit and liquidity risk (providing the issuers rates are Treasuries), which would also mean it would have a smaller value than the option-free Treasury. Naturally this would also mean that the cost of a, callable option for example, is 75 basis points. Am I correct?

OR is the OAS the actual cost of the option (i.e., the 75 basis points)?

Also, lets say you have an Option Free Treasury that is worth a 100, and a callable AAA corporate bond that is 97.5 and is identical with respect to the coupon and maturity. That means that the difference of the 2.50 is the cost of the option, credit risk and liquidity risk. Now if I value that same bond using the backward induction method and adding the OAS, knowing the OAS is an X amount of BP's, and now the bond is 99.50, that means the option is 2.00 dollars and the other 2 risks are .50 cents or is it vice-versa (i.e., the option is 50 cents and the credit risk and liqidity risk, and all other risks are 2.00 dollars).

Question 2:

In determining effective maturity and effective convexity using the backward induction method, the book tells you to shock the yield curve by an X amount of BP's, CREATE A NEW I-RATE TREE, add the OAS and then you get the value.

However, the binomial valuation method in constructing and I-Rate tree, requires that you make sure that the rates that you get in the model get the current market values of the on-the-run Treasuries. However, if you shock the yield curve up or down by a X amount of BP's then you would not be able to determine the current market values of the on-the-run Treasuries, i.e. the model could theoretically be wrong. Which rates do you shock? The bottom one (as the top ones adjust themselves based on volatility)?

A little confused on these issues, any help would be appriciated. Thanks in advance.
hughhurt
@2015-01-12 17:13:58
Russian:

Question 1

First of all nominal spread means nothing. Perhaps you meant the z-spread. Then, yes 75bp would be the purchase price of the option by the issuer. You sold it, it is not a cost to you. Suppose a binomial tree spits out OAS of 25bp, then you compare that to other liquid issues of the same company and normally it should not diverge too much. If it does there is value in there.

Question 2

Well yes, when you shock the spot rates you also shock the prices of the underlying instruments obviously. First you get your fair market curve (spot curve). Plug it into your model, add the spread, it spits out the value for your bond. Get the bond values for parallel shifts in the curve. The shifted curve is obviously not your fair market curve. It is a hypothetical curve. Duration for parallel shifts is a reporting requirement, however it is not extremely useful. You wanna model what is likely to happen, a bullish flattening or a steepening, FED on the short end etc...

Treasury spot curve is slowly becoming irrelevant with the gov't redeeming lot of issues. Swap curve is future and it makes much more sense too...

### CFA Discussion Topic: Fixed income questions 