[math-fun] Computational complexity of financial derivatives
If this new (Oct. 2009) paper is correct, there isn't enough computational power on the planet to properly price financial derivatives. This paper compares financial derivatives to used cars (!). Suppose that the buyer of a used car estimates that 20% of used cars are lemons & therefore is willing to pay only 80% of the value of a non-lemon. If the seller knows that he is selling a non-lemon, he is unwilling to sell it for 80% of its true value. The market seizes up due to the lack of information. The paper shows how the information to properly evaluate the derivative may be lying ("lie-ing" !) in plain sight, but due to computational complexity, cannot be utilized. The paper also contemplates a "factor derivative" that pays off on a specific date if the unemployment rate at that date (rounded to an integer) is the last digit of a factor of a large (public) integer. If the person selling such a derivative already knows the factorization of this integer, (s)he is in a much better position to evaluate the derivative than an arbitrary buyer. "Computational Complexity and Information Asymmetry in Financial Products": http://www.cs.princeton.edu/~rongge/ http://www.cs.princeton.edu/~rongge/derivativeFAQ.html http://www.cs.princeton.edu/~rongge/derivative.pdf
participants (1)
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Henry Baker