"Barrier option with American early exercise feature"?I agree that people abuse the terminology here, but in this case we seem to have on our hands two call options, both with a continuously monitored up-and-out barrier, with one being exercisable only at maturity and the other being exercisable at any time up to and including maturity as long as it has not been knocked out.
Thanks!. Now I know this particular scheme is good. It also implies that all the underlying maths has been stressed tested.
I think you are going off on a tangent here.Thanks!. Now I know this particular scheme is good. It also implies that all the underlying maths has been stressed tested.
That's not right. Let's say you're the supervisor of coding for an investment firm and hire an incompetent programmer to code this. He "forgets" to code for the lower barrier knock-out. You ask him to test his code on the example shown and he gets the answer discussed. Since the answer is "correct" to 6 digits, you conclude the scheme/code is good! The code is put into production. You get fired!
A minimal first test: code the exact sum solution and test it against your code for S0 running from the lower barrier to the upper barrier in fine increments. Is that difference uniformly below some required precision? Now, you can fire the incompetent programmer. Next, vary all the parameters over their defined domains. Next, test all the edge cases ....
By 'sum' you mean some kind of series solution as here? eq. 2.7, 2.8. I hate series, too many assumptions, how many terms to take, no guarantee of convergence, round-off error and ugly maths.Sorry, but I have other stuff going on. The hard part would be nailing down the putative exact sum.So, better exercise for students: what are the results to 30 digits? Now there's a benchmark.
No. Better to expose them to as many numerical methods as possible to many kinds of problems.
// 30 digits implies going down the multiprecision road. It is outside the scope.
edit: Alan, if you give 30 digits I can test it. You can probably do it in one line of MM. I don't have MM.