question on bond valuation with embedded options valuation, corporate, question, interest, actual

YouCanDoIt

why do we use binomial risk free rate interest tree to value callable and putable corporate bonds? aren’t they overvalued like that?
and do we get the actual market price of the bonds when we value then with tree?

Analti_Calte

thanks a bunch..this really helped me clear my concepts about bond valuation

clearlycanadian

Not sure what notes you’re referring to. The CFA material is pretty clear (well, if you read between the lines ) about using the issuer’s on-the-run yield curve for the binomial model. Also, the term “treasury bond” is used loosely. For bond valuation, we use the spot rate curve (AKA term structure of interest rates) derived from zeroes.
When I was on the valuation reading, I actually had to go back to some of the level 1 material to figure out what was going on with the interest rates:
You start with the bond’s YTM.
Use YTM to derive spot rates (level 1 material).
Use spot rates to derive forward rates (level 1 material). The rates in the binomial tree are forward rates.
If OAS is introduced, it is added to each forward rate in the binomial tree to value the bond.
The market value is determined the same way it is for any other security… people trade. If we could value this crap with certainty, we’d be Gods on Wall Street, man! The CFA material even has examples covering the uncertainty of valuation models - one dealer may quote a lower rate than another, all because they used differing assumptions (volatility, their selection of on-the-run issue, etc.).

NakedPuts00

I really appreciate your detailed answer but I read in notes that you create tree by taking a treasury bond and then adjusting the node interest rates that will produce the current market value of that bond, then we value callable and putable bonds with the same tree by the assumptions you mentioned.
and if we value with our assumptions, how is the actual market value of that callable and putable corporate bond established?
Regards…

jacksparrow

First of all, it is not the “risk free interest tree.” The interest rates at each node are the forward rates (for option-free bonds) or the OAS-adjusted rates (for bonds with options). It is a binomial (“bi” meaning two) tree because each node has two outcomes. There’s nothing stopping you from using a trinomial tree, but the CFA material tries to keep it “simple.”
Why do you think the bonds will be overvalued?
As your first step, you’re finding the value of the bond without the option. Then, you setup the rules under which an issue can be called/put… this gives you the value of the bond with the option. In case of callable bonds, the value has to be lower than the option-free value. In case of putable bonds, the value has to be higher than the option-free value.
For an option-free bond, your volaitility assumptions and inputs for the interest tree must align so that the result of the binomial model is equal to the bond’s market value (i.e. arbitrage-free). Otherwise, your “base model” assumptions are flawed.
For an option-embedded bond, you’re making further assumptions with regards to when you think the bond will actually be called… these assumptions may be different than someone else’s assumptions, so the outcome could be different. At this point, it comes down to how accurate you think your assumptions are. One thing’s for sure: for callable (putable) bonds, you better get a value lower (higher) than the value of an option-free bond.
Hope this helps.