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This may seem like a dumb question, but if the EMH is generally true, wouldn't options already be correctly priced? Why do we need all these intricate formulas, unless we think the prices are wrong or that the prices can be improved? Lets say I develop an option pricing formula for pricing option under the event of natural disasters. How is this useful?

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A first usage that you already probably thought of is that the markets are not perfectly efficient, so the options are slightly mispriced. Then you need to know in which side you should invest. And that is true, most option contracts are not liquid enough to be perfectly priced by the markets.

Other use is when you issue a new option (for example if there is no option at this strike or at this maturity).

And last but not least, they can be useful to calculate other things than the price. If you consider the price (market price) as an input, you can get a parameter as an output. This is done for finding the implied volatility with the Black Scholes pricing formula.

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My 10 cents is the formulas aren't super intricate: they attempt to reflect certain realities. At the simplest level, simply intrinsic value + time value. You could make up your price just from that.

But if you did just intrinsic value + a time value and put your price out there then you face the EMH risks, and if your price is off market you'd get instantly put into a losing position. So you have to manage that.

Therefore EMH means every provider has to follow the same price range... Like there's a picture where the practical reality of EMH means all options everywhere can become underpriced or overpriced. Then providers and clients alike can take advantage of a theoretical price edge.

I think the models simply try and break down the valuations. Intrinsic value is always basically fixed, right? Between price of underlying and strike price.

Whereas time value means a time decay, a volatility component, and an interest rate risk, and then there's the delta of the current position against the assumption of a random walk of underlying prices, and the expected speed of change of those prices.

Then to further manage risk there's a whole load of second derivative colours and charms.

That is the use of option pricing formulae. Each aspect of option risk can be categorised and even traded separately. Also think about pricing 100's of strikes, maturity dates, and 1000's of underlying instruments...

But the use of pricing an option in the event of natural disasters is what, like, laying off the cost of writing insurance policies. Like running the spread between insurance policies and option premiums?

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