FRM 2006 PI q35 - American opiton and path dependence

[fullofquestions]

Which of the following options is strongly path-dependent?

a. An Asian option
b. A binary option
c. An American option
d. A European call option

ANSWER: A
‘A’ is correct. The payoff of an Asian option depends on the average price of the underlying asset. ‘B’, ‘C’ and ‘D’ are incorrect. Binary, American and European options are simple options whose payoff can be calculated using the price of the underlying asset at maturity only.



Isn't an American option also strongly path dependent? If you have an American put, then you want to exercise as early as possible, hence path dependence. Actually, the more I think about it, for the Asian option, the path isn't so important. It does not matter whether the underlying was priced at $100 either at t=1 or at t = T-1 or anywhere in between.
I can see how an Asian option can be considered path-dependent although may not 'strongly path-dependent.' I perceive the American option about as path-dependent as the Asian. Any thoughts?

 

[David Harper CFA FRM]

Hi FoQ,

The Asian is always considered strong path dependent, to my knowledge; i.e., you need the prior path information to compute the payoff. Unlike a vanilla Euro, you need more that just the asset information at expire. It's definitely the strongest path dependent listed among the choices.

I do agree that some classify American as weak path dependent, but I don't think it ever qualifies as strong. At most, the early exercise is like a barrier. But on the issue of weak path dependence, IMO, it begs the issue of how we are *technically* defining weak path dependence (IMO, depending on definitions, which turn on the coding implication--consistent with Wilmott's definition--you can say yes/no; e.g., not even weak dependent in the sense that you can backwardly induce/recurse nodes that each themselves do not require prior path information).

...so I would say based on the "strong," answer (A) is the only choice...David