In finance, a **put** or **put option** is a financial market derivative instrument which gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the *underlying*), at a specified price (the *strike*), by (or at) a specified date (the *expiry* or *maturity*) to the *writer* (i.e. seller) of the put. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock.^{[1]} The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.

Put options are most commonly used in the stock market to protect against a fall in the price of a stock below a specified price. If the price of the stock declines below the strike price, the holder of the put has the right, but not the obligation, to sell the asset at the strike price, while the seller of the put has the obligation to purchase the asset at the strike price if the owner uses the right to do so (the holder is said to *exercise* the option). In this way the buyer of the put will receive at least the strike price specified, even if the asset is currently worthless.

If the strike is K, and at time t the value of the underlying is S(t), then in an *American option* the buyer can exercise the put for a payout of *K*-S(t) any time until the option's maturity date T. The put yields a positive return only if the underlying price falls below the strike when the option is exercised. A *European option* can only be exercised at time T rather than at any time until T, and a *Bermudan option* can be exercised only on specific dates listed in the terms of the contract. If the option is not exercised by maturity, it expires worthless. (The buyer will not usually exercise the option at an allowable date if the price of the underlying is greater than K.)

The most obvious use of a put option is as a type of insurance. In the protective put strategy, the investor buys enough puts to cover their holdings of the underlying so that if the price of the underlying falls sharply, they can still sell it at the strike price. Another use is for speculation: an investor can take a short position in the underlying stock without trading in it directly.

Puts may also be combined with other derivatives as part of more complex investment strategies, and in particular, may be useful for hedging. Holding a European put option is equivalent to holding the corresponding call option and selling an appropriate forward contract. This equivalence is called "put-call parity".

Trading options involves a constant monitoring of the option value, which is affected by changes in the base asset price, volatility and time decay. Moreover, the dependence of the put option value to those factors is not linear – which makes the analysis even more complex. One very useful way to analyze and track t

Trading options involves a constant monitoring of the option value, which is affected by changes in the base asset price, volatility and time decay.
Moreover, the dependence of the put option value to those factors is not linear – which makes the analysis even more complex.
One very useful way to analyze and track the value of an option position is by drawing a **Profit / Loss chart** that shows how the option value changes with changes in the base asset price and other factors. For example, this Profit / Loss chart shows the **profit / loss of a put option** position (with $100 strike and maturity of 30 days) purchased at a price of $3.34 (blue graph – the day of the purchase of the option; orange graph – at expiry).

The graph clearly shows the **non-linear dependence** of the option value to the base asset price.

As time passes, the blue graphs move "downward", until it reaches the orange graph (which is the profit / loss at expiry) – this loss of value by the option is called **"time decay"**.

As time passes, the blue graphs move "downward", until it reaches the orange graph (which is the profit / loss at expiry) – this loss of value by the option is called **"time decay"**.