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Built some tree methods to price american options with discrete dividends. But I have no way to really verify my work. Questions below:

  1. Does it make sense to build a Monte Carlo pricer to use as a benchmark to measure the results of the trees against.
  2. What is the best way to build such a Monte Carlo pricer for american options with discrete dividends ?

Please help.

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    $\begingroup$ Why build your own when there are so many existing ones online? $\endgroup$ – Brian B Dec 1 '20 at 16:05
  • $\begingroup$ I second @BrianB : validate against an outside view, e.g. QuantLib. I think it should be able to consider discrete dividends ... $\endgroup$ – Kermittfrog Dec 1 '20 at 16:19
  • $\begingroup$ Thanks @BrianB but who has one that i can use for discrete divs ? $\endgroup$ – JBerstein Dec 1 '20 at 16:46
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    $\begingroup$ Could this help: quant.stackexchange.com/questions/37237/… $\endgroup$ – Kermittfrog Dec 1 '20 at 17:40
  • $\begingroup$ @Kermittfrog Yes that would be very helpful; only the code presented in that post has a constructor error and does not work despite the author saying he fixed it. I can't seem to debug it; might post about that. $\endgroup$ – JBerstein Dec 1 '20 at 20:40
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  1. No, it doesn't.

Monte Carlo is a forward-simulation method, whereas trees propagate backwards. This is a problem for valuing American options: at every timestep you have to take the $max()$ of the payoff and the current option price - but you don't know the option price.

  1. There are 'American MC' models to circumvent this but they are pretty heavy.

Practitioners of course hit this problem. What they do is test the discrete dividend model on real market data. The market is large enough, and market makers are now advanced enough, to find most holes in any new model you've built.

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