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It seems like there is a contradiction between the fact the option pricing is risk-neutral and the large amount of option trading that is done for speculation.

Since the option is risk-neutral, a trader cannot expect to make a profit. He could use the option as a form of insurance, but in practice a lot of options are used for speculation. Since the expectation is zero, but the option costs a fee, this seems like a bad choice for the investor.

Edit: There is an related answer to another question which helped me a lot: http://quant.stackexchange.com/a/1116/1157

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possible duplicate of How does the "risk-neutral pricing framework" work? –  phi Sep 22 '13 at 11:24
    
I guess the question was not presented well enough. The question is why people would buy an option which was priced risk-neutally other than as insurance? The linked question discusses how risk neutral pricing works, but not why these options are a useful investment. –  Anna Sep 22 '13 at 15:31
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The models for option prices work on the assumption of arbitrage free markets, in which speculation in general is not expected to make a profit. These are different interpretations of the markets, pricing of derivatives is based on other hypotheses as speculative trading. –  Arne Sep 22 '13 at 16:03
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Its been some time that I took these lectures, but as far as I remember the risk neural-measure is based on the assumption of abitrage-free and complete markets (where a derivate can be replicated with other assets), such that a risk-neutrality can be assumed, even if investors aren't. These are simplifications which are preconditions for the know pricing models like BS. In reality, markets may behave completely different and their efficiency is heavily discussed since decades. E.g., if a speculator thinks that the buy of the derivative is beneficial, he trades on a perceived inefficiency. –  Arne Sep 22 '13 at 16:58
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2 Answers

up vote 8 down vote accepted

You may need to differentiate between the use of options and the pricing of options. How options are used has no bearing on the price of such options. Options can be used as leveraged investments or as insurance or as hedges. Any such use does not change the fair value derived for the option. By the way you are in fact compensated the risk premium but it is already built into the underlying and risk neutral pricing is just an apparatus which simplifies pricing mechanics.

Who says that options cannot be used for speculative purpose. If you have a better model that derives a different implied volatility than the value the option is priced at then you can speculate and make money and yet the risk neutral pricing framework still holds up

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The option price is a martingale only because of that speculative activity. if there is any reason for the prices to move, there is some speculator(s) who is putting in money to cash in on that.

When you have to price the option, you also consider any reason for the trend to exist in the price. So you have two components. One is your own speculative component and the other is the component of the rest of the market which is a martingale. You use the pricing theory for the martingale part as relative pricing applies to that. For your own speculation, you have to make adjustments.

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