Reading 61.i, Schweser Fixed Income P.169 Having read the Schweser and CFAI textbook several times, I still do not understand why OAS with “binomial model” should be used for value fixed income security when its cash flow is independent with interest rate; OAS with “Monte Carlo” should be used for value fixed income security when its cash flow is interest rate path dependent. Can anybody explain?
This is what I think, but I might be way-off-track to explain what you expected. So , When we are calculating OAS for Fixed Income securities like Callable/ Puttable Bonds we use the Binomial Model to derive a value for the OAS, we do this be calculating the value of the bond at each node and getting to the conclusion if its going to be called at that price or not!! So it’s basically MIN(call price, calculated nodal value) to be the final node value, likewise we keep going backward and calculate the Vo and get the value of OAS. Here we never consider what happened to interest rates in the past (i.e. the Interest Rate Paths that lead to this node) all we believe is that once the value of the callable bond is greater than call value, it’s called-off. PERIOD!! But when calculating the OAS for implicit prepay call optionality of MBS, we need to consider the past rates. Suppose in 2006, rates went down to 5% and most of the mortgage owners refinance their homes in 2006, Then-on from 2006 and whole of 2007 the Interest rates remained at around 6% and not much home loans were issues during that time. If now in this case, at year 2008, again the rates fall to 5%, we would be hardly having any owner to refinance their homes as the bull-run of refinancing already occurred in 2006 and we are now experiencing prepayment burnout. All such scenarios can well be stimulated using the MC model and hence we use it for path-dependent cash-flows.
to make it short and sweet… for bonds with embedded options the cash flows are not dependent on the path that interest rates have taken in the past… for things like Mbs/abs etc…the path that the interest rate follwed “in the past” predicts the cash flows in the future…so you have to use the Monte Carlo - because this model simulates thousands of different paths that interest rates could take…
path dependent -> Monte Carlo
maratikus Wrote: ------------------------------------------------------- > path dependent -> Monte Carlo I know. But why?
mumukada Wrote: ------------------------------------------------------- > to make it short and sweet… > > for bonds with embedded options the cash flows are > not dependent on the path that interest rates have > taken in the past… > > for things like Mbs/abs etc…the path that the > interest rate follwed “in the past” predicts the > cash flows in the future…so you have to use the > Monte Carlo - because this model simulates > thousands of different paths that interest rates > could take… To sum up, Monte Carlo takes into account of the whole path of interest rate. So path dependence of the MBS is considered. Binomial model values the MBS by the interest rate at one time. Binomial model does not consider the effect of the past interest rate on MBS. As a result, Monte Carlo should be employed for interest rate path dependent MBS.
Binomial model can not be used for path-dependent problems because it uses backward reduction (doesn’t know about past, only assumes to know the future). MBS prepayment is very path-dependent, if there was a drop in interest rates two years ago, there probably will be no spike in prepayments this year if interest rates go down. However, if interest rates are at the low over the last 10 years after staying at a high level for 10 years, prepayments will probably be high.
exactly…
And, to add to the fine comments above, the Monte Carlo approach could be used for the non-path dependent ones but it should just converge to the answer of the binomial model while doing lots more work.
Good explanations!
With all due respect, this simply isn’t true. (And, by the way it’s induction, not reduction.)
In the articles I wrote on valuing floating rate bonds (http://financialexamhelp123.com/valuing-floating-rate-bonds/) and valuing caps and floors (http://financialexamhelp123.com/interest-rate-caps-and-floors/) I demonstrate clearly the use of binomial interest rate trees in path-dependent problems.
Granted, the analysis of these securities is only a little path dependent (the cash flow at one node depends on the interest value of the preceeding node), but it’s still path dependent.
The fact is that you can use binomial interest rate trees with backward induction or with forward induction; there’s nothing in the binomial interest rate tree methodology that prevents that.
The reason we use Monte Carlo simulation for most path-dependent analyses isn’t that they’re path-dependent; it’s that the number of paths is so absurdly huge that it’s impractical to use all of them in the analysis. A 30-year, monthly binomial interest rate tree (such as you would use to analyze a 30-year MBS) has 2.35 × 10^108 paths: a ridiculously large number. Thus, we use Monte Carlo simulation to randomly create 500, or 1,000, or 10,000 paths through the tree, then use forward induction or backward induction on only those paths (after we’ve calibrated the simulation, of course).
Of course, there’s something intrinsically silly about arguing with posts that are 8 years old. 
Does anyone know if it says anything different in the curriculum re: bionomial trees not being used for path-dependent cash flows? I don’t see it anywhere but based on the threads seems to be a common misconception. I can only find that it says that Monte Carlo is usually used for path-dependent cash flows not that binomial trees can not be used…
The whole idea of path dependence (as referred to in ABS, which by the way is not in the curriculum this year) is this; If interest rates go from 5% down to 4%, then come up again to 5% things will not be the same ever again. Mathematically (think binomial trees) nothing has changed, 5%=5% but the market has already changed, people have changed minds and preferences. They have already refinanced loans so going back to 5% does not prompt them to undo their refinance etc.
At the end of the reading on The Arbitrage-free Valuation Framework, example 7 ends with the comment “The paths (generated by Monte Carlo) are now different enough such that path dependent securities, such as MBS, can be analyzed in ways that provide insights not possible in binomial trees.”