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:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)