Proof that under simple assumptions, such as con- straints of Put-Call Parity, the probability measure for the valuation of a European option has the mean of the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets  . We confirm that the heuristics used by traders for centuries are both more robust  and more rigorous than held in the economics literature  .
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets and other strong assumptions . We confirm that the heuristics used by traders for centuries are both more robust , more consistent, and more rigorous than held in the economics literature . We also show that options can be priced using infinite variance (finite mean) distributions .
R
con- straints
constraints
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of the
derived from the forward price which can, but does not have to be the
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and other strong assumptions
A
, more consistent,
A
. We also show that options can be priced using infinite variance (finite mean) distributions