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Seems that the theory books are all integrals in continuous time, yet in practice, discrete estimations works fine.

As a newbie to this, when do you choose to use the continuous time finance vs discrete estimations?

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    $\begingroup$ This is very broad and not necessarily true for all theory books. I would suggest narrowing you question.. what specific aspect of pricing, which product are you interested in.. $\endgroup$ – Attack68 Jun 13 '18 at 15:26
  • $\begingroup$ I legitimately have no idea and am trying grasp the uses in the broad rates market. Just from what I've seen, IR derivatives/XVA quants use continuous time for pricing/hedging while sell traders use discrete time for easy estimations. Have no idea how the buy side does it $\endgroup$ – Bison Jun 14 '18 at 5:16
  • $\begingroup$ in my fixed income class, we learned the discrete model, but dabbled with instantaneous rates in cont.time. Most documentations are also in discrete time. $\endgroup$ – Bison Jun 14 '18 at 5:22
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There is no hard rule. Usually continuous time models are good because they allow for closed form expressions for the solution (where discrete time models do not allow). However, if a given model in continuous time does not allow for a closed form solution then you are better off going to discrete time as it is easier to solve numerically using grids for state variables rather than solving numerically stochastic differential equations.

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I tend to disagree with @phdstudent. In option pricing world, for example, continuous models are incapable to address early exercises on American options. Although there are some analytics models like Berjerksund-Stensland or Whaley model, which have closed-form formula, however, their accuracies are not as good as tree models or Monte Carlo simulation based model. Continuous models barely not work for exotic options. In my mind, continuous models only work well on European options.

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  • $\begingroup$ This is not very different from what I said. If a model has a closed form solution but its accuracy is not good then the model is not good and we are better off with discrete time models... $\endgroup$ – phdstudent Jun 14 '18 at 9:20

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