Topic · Derivatives & Volatility
← All topicsOptions Theory
28 articles · 4 checkpoints · 18 deeper reads · 6 reference notes
Every article, in reading order
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Before any model tells you what an option is worth, pure logic tells you what it cannot be worth. A handful of inequalities pin every option price into a band, and a quote outside that band is free money you can collect without a forecast.
The whole option chain at one expiry contains the market's entire probability distribution for where the underlying will land, not just its average and its spread. Differentiate the call price twice with respect to strike and the distribution falls out.
An option's bent payoff can be manufactured out of shares and cash, provided you keep adjusting the mix as the price moves and never add or remove money along the way. The cost of setting that machine running on day one is the option's fair price.
A set of prices contains no free money if and only if you can find a set of made-up probabilities that reprices everything as a fair bet. That equivalence is the theorem the whole derivatives industry stands on, and a second half tells you when those probabilities are unique.
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