today’s price == today’s expectation of tomorrow’s price

“today’s [3] price[1] equals today’s[3] expectation[2] of tomorrow’s price” — is a well-known catch phrase. Here are some learning notes I jotted down.

[1] we are talking about tradeable assets only. Counter examples – Interest rate and Dividend-paying stock are not tradeable by definition, and won’t follow this rule.

[2] expectation is always under some probability distribution (or probability “measure”). Here the probability distro is inferred from all market prices observable Today. The prices on various derivatives across different maturities enable us to infer such a probability distribution. Incidentally, the prices have to be real, not some poor bid/ask spread that no one would accept.

[3] we use Today’s prices of other securities to back out an estimated fair price (of the target security) that’s fair as of Today. Fair meaning consistent with other prices Today. This estimate is valid to the extent those “reference prices” are valid. As soon as reference prices change, our estimate must re-adjust.

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