Payoff of A Put
These examples lead to the following formal reasoning. Fix an underlying financial instrument. Let be a put option for this instrument, purchased at time, expiring at time, with exercise (strike) price of ; and let be the price of the underlying instrument.
Assume the owner of the option, wants to not take a loss, and does not want to actually possess the underlying instrument, . Then either (i) the person will purchase at expiry, and then immediately exercise the selling option; or (ii) the person will not exercise the option (which subsequently becomes worthless).
In (i), the pay-off would be ; in (ii) the pay-off would be . So if (i) or (ii) occurs; if then (ii) occurs.
Hence the pay-off, i.e. the value of the put option at expiry, is
which is alternatively written or .
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Famous quotes containing the word put:
“The magnanimous know very well that they who give time, or money, or shelter, to the stranger—so it be done for love, and not for ostentation—do, as it were, put God under obligation to them, so perfect are the compensations of the universe.”
—Ralph Waldo Emerson (1803–1882)