2
$\begingroup$

Can you give some example of options that cannot be priced with least-square Monte Carlo?

Intuitively, this is any option for which a payoff depends on a previous exercise decision.
It's relatively easy to cook-up some example by hand.

Is there a name for such class of option?

Can you give the name of such options that are sold in financial market?

$\endgroup$
7
  • $\begingroup$ Why is your second statement intuitive? $\endgroup$
    – Olaf
    Commented Feb 2, 2016 at 10:21
  • $\begingroup$ @olaf LSMC uses the exercise date payoff to estimate the expectation function. If the computation of a payoff needs past infos and that past infos is dynamic, boom, you need nested simulations. $\endgroup$
    – user2688
    Commented Feb 2, 2016 at 13:57
  • $\begingroup$ But I first simulate N paths, then work my way backwards from the payoff date using LSMC. Along each path I "know" my past history, right? So where does the problem arise? $\endgroup$
    – Olaf
    Commented Feb 2, 2016 at 14:21
  • $\begingroup$ @olaf Say the option holder can choose between ten different strike prices at time 1, for a call exercisable at time 2. The exercise decision is not in the simulated path, so backward swimming is swimming in the wrong sea. $\endgroup$
    – user2688
    Commented Feb 2, 2016 at 14:47
  • $\begingroup$ Why is the exercise decision not part of the path? The decision could be simulated along each path as well, right? Just like e.g. the stock price. The decision would have to be represented by a state variable during your LSMC, of course. $\endgroup$
    – Olaf
    Commented Feb 2, 2016 at 15:01

1 Answer 1

1
$\begingroup$

you just add in any auxiliary variables accumulated along the path that determine the pay-off to the regression variables. So path-dependence is not a problem.

If you have previous decisions, you may need to do different regressions based on their possible values or make them into a continuous variables that can be used for regression.

$\endgroup$
2
  • $\begingroup$ Are there at least examples where LSMC becomes unfeasible or unreliable? $\endgroup$
    – Olaf
    Commented Feb 5, 2016 at 10:02
  • $\begingroup$ well, LSMC is often unreliable even for straight-forward cases. I have written a lot of papers on trying to improve it. see eg ssrn.com/abstract=1331904 or ssrn.com/abstract=2388415 $\endgroup$
    – Mark Joshi
    Commented Feb 6, 2016 at 2:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.