[color=#242729][size=100][font=Arial, Helvetica Neue, Helvetica, sans-serif][size=100][font=Arial, Helvetica Neue, Helvetica, sans-serif]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. If you had a purely analytical way to price options, how does that benefit you?[/font][/size][/font][/size][/color]



[color=#242729][size=100][font=Arial, Helvetica Neue, Helvetica, sans-serif][size=100][font=Arial, Helvetica Neue, Helvetica, sans-serif]EDIT: Why does my post have random tags on it?[/font][/size][/font][/size][/color]

In general analytical means fast (faster than trees, PDEs and Monte Carlo). That's why analytical solutions "have a good sound to them". Recently though people have been presenting more and more complicated "analytical" solutions that blur the traditional distinction between analytical and numerical. I think that the first analytical solutions(approximations) for American options were sufficiently inaccurate to matter, so I guess that's why new papers stress accuracy? Not sure.

The market is web of products that all have constraints on relative prices. Proffessional traders try to exploit that, they can eg sell American options and hedge them with european options, have some residual exposure. That way they can maybe .01% on that .. if it's priced correctly..

So accurate models are needed to be able to accurately relate products. If one product changes in price due to market demand then other related product will follow due to the mitigation of risk into highly related products based on arbitrage trading. Models connect products.

Options are derivatives, that is, their value is determined by reference to the price of something else. Isn't it natural to want to link the two prices in a logical, systemic way?

I was an OTC option trader and without some form of model to lean on for insight my hair would surely have turned prematurely grey. Option models yield useful things for risk management like the Greeks.

In a more humorous and cynical vein, obsession with models provides endless hours of entertainment for people who clearly do not have much else to do (can you imagine who I have in mind here?). Models also provide publications for academics and sales for consultants and software vendors.

But I think the real answer to your question is the same answer to another question - Why does a dog lick its genitals? Because it can.