Sunday, January 8, 2017

option pricing - Joint distribution from expectations


Given two random variables X and Y and let K be a constant value. Assume the expectation E[X(YK)+] is given for all possible values of K0. Is there a way to derive the joint probability distribution of X and Y from this??


The expectation can be written as


E[X(YK)+]=x(yK)+dF(x,y) and when density exists =Kx(yK)f(x,y)dxdy


Both marginal distributions FX and FY are known and densities exists as well. Is there any way I can derive the joint distribution if the expected value is given for all values of K?


I have been stuck on this for a while now, even rough approximations would be of much use to me or a collection of properties that can be solved numerically.


Can someone please help me?




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