I am searching on real-option pricing deficiencies to encounter risk-neutrality. As we know risk-neutrality assumption, is not hold in real situations. The problem is that I could not classified literature solutions to this problem. In financial market and real market. I really appreciate each piece of information.

  • $\begingroup$ Hi zahra, welcome to Quant.SE! It's difficult to follow your question. Can you please revise it. $\endgroup$ – Bob Jansen Oct 26 '14 at 16:23
  • $\begingroup$ Could you explain what you mean by risk-neutrality here? What literature says the market is risk neutral? $\endgroup$ – user59 Oct 26 '14 at 16:25

This goes back to the so-called First Fundamental Theorem of Asset Pricing saying that markets are arbitrage free if and only if there exists at least an equivalent risk neutral measure. So the reason why we are using risk neutral measures to price options is because it allows us to represent discounted stock diffusions as martingales and therefore express the price of any derivative, whose payoff is a deterministic function of the final price of the stock, as an expected value under the risk neutral measure, for instance for a call option: $$C(S_t,t) = \mathbb{E}_t^{\mathbb{Q}}[(S_T - K)^+e^{-r(T-t)}]=S_tN(d_1) - Ke^{-r(T-t)}N(d_2) $$ $$d_1=\left[log\frac{S_t}{K} + (r+\frac{\sigma^2}{2})(T-t)\right]\frac{1}{\sigma\sqrt{T-t}}$$ $$d_2 = d_1 - \sigma\sqrt{T-t}$$ So risk neutral valuation is just a trick to use no arbitrage arguments to price derivatives, but of course it’s well known markets participants are risk averse and it would be actually particularly interesting to know the physical measures they use.

Some references:

-Harrison, Michael J. and Kreps, David M, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, Volume 20, Issue 3, June 1979, Pages 381–408

-Harrison, Michael J. and Pliska, Stanley R., Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications, Volume 11, Issue 3, August 1981, Pages 215–260

-Ross, Steve , The Recovery Theorem, Journal of Finance, forthcoming

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