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2#
发表于 2013-4-28 09:19
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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. |
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) 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.