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:
“Science is unflinchingly deterministic, and it has begun to force its determinism into morals. On some shining tomorrow a psychoanalyst may be put into the box to prove that perjury is simply a compulsion neurosis, like beating time with the foot at a concert or counting the lampposts along the highway.”
—H.L. (Henry Lewis)