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I see a lot of academic papers talking about accuracy in pricing American Options (and finding analytic solutions). Why is there so much interest in this topic? Isn't the option price set by the market? From what I can understand, accuracy in pricing gives accuracy in implied volatility, which gives you a sense of which options are expensive relative to others (eg. A listed puts for the same underlying, same maturity but varying strike may have different volatilities, even though they should be the same). I don't see why as an option trader accuracy is important, since the market already decided the fair price.

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  • $\begingroup$ What about simulating future credit risks or market risk where you need to estimate portfolio value? Today option price can’t be used for future, $\endgroup$ – SmallChess Oct 18 '17 at 2:34
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    $\begingroup$ A pricer is useful for 2 things essentially: computing a price and calculating Greeks. If you cannot price the option with sufficient accuracy (+speed) you a fortiori have no means of computing your Greeks accurately (and fast), or put differently, no means of knowing the exact risks you are exposed to and thus decide the ones you want hedge vs. those you're comfortable with. Also a pricer can be useful to price non listed options (e.g. 5Y American call trading OTC) $\endgroup$ – Quantuple Oct 18 '17 at 7:13
  • $\begingroup$ The effect of "Americanness" is small. You can get a rough idea of an American price just by taking the European (i.e. Black Scholes) price so to improve on that you need an accurate algorithm, and for some reason this has proven difficult. There are already a lot of modestly accurate ones in journals... you have to claim you can do better if you want to get published. $\endgroup$ – noob2 Oct 18 '17 at 14:02
  • $\begingroup$ @SmallChess Thank you for replying, what do you mean by that, and how does accuracy in option pricing help? Suppose you did have a purely analytic pricing of American Options. What could you do with that? $\endgroup$ – Spent Death Oct 29 '17 at 5:15
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The market creates price quotes only for some standard products. But maybe you have some products in your portfolio that are non standard (e.g. because the market has changed since you bought it).

Now you want to know what your assets are worth. What to write to your balance sheet? Or maybe you want to sell it. how much should you be payed? The market doesn't tell you directly. You have to to calculate it. And typically you want to know it exactly.

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  • $\begingroup$ Aren't pricing models kind of subjective? Why should I trust the Black-Scholes equation? $\endgroup$ – Spent Death Jul 1 '18 at 15:14

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