whats does path dependency in monte carlo actually mean?

CFA Level III
#1

as per topic…

#2

Think of an interest rate tree for valuing MBS. If interest rates get really low, people will refinance their mortgages. But the second time they get really low fewer people will refinance because those who could will have already done so.

Therefore, to determine how many people will refinance in 8 years when interest rates are low, you have to now whether rates were low in 3 years: did interest rates follow a path of moderate-low-high-low, or did they follow a path of moderate-high-moderate-low? Path dependency.

#3

In lay man terms and thinking in terms of binary tree. Taking path 1 instead of path 2 (or vice versa) will impact the probability of an event occuring.

In terms of MBS, if rates go lower the probability of prepayment risk is higher due to high chance of people refinancing. If rates go high the probablity is reduced. Thus probability of prepayment event is path dependent.

#4

then what is the difference between path dependency and multi period way of looking at the portfolio?

#5

Please be more specific. Are you referring to the advantages of Monte Carlo simulation when it comes to asset allocation?

It takes a “path dependent” approach to determining final wealth. Meaning, you can incorporate changing inputs (tax rates, market expectations, external cash flows etc) specifically for an individual. It overcomes the static 1 period analysis provided by MVO.

#6

It takes into account the probability of A or B changes depending on what’s happened before. If mortgages rates go from 4 to 3 I would normally refinance, but if they were at 2% a year ago, or my mortgage is close to expiry, I’m less likely to. By running scenarios through Monte Carlo you can account for these changes in probabilities.

#7

Path-dependent is similar to this scenario.

Path 1: You have 100k then the market goes up by 50%. Your portfolio now have 150k.

Path 2. Withdraw 30k. You now have 120k. Then, the market goes down by 30%.

Final value is 84k.

In monte carlo, you can simulate a scenario where the 30% drop occur in Path 1 and then gain of 50% in Path 2.

Final value will be 60k.

#8

Mark it