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 .
Read more about this topic: Put Option
Famous quotes containing the word put:
“There are many things children accept as “grown-up things” over when they have no control and for which they have no responsibility—for instance, weddings, having babies, buying houses, and driving cars. Parents who are separating really need to help their children put divorce on that grown-up list, so that children do not see themselves as the cause of their parents’ decision to live apart.”
—Fred Rogers (20th century)