The Minimum Value of a Put

The Minimum Value of a Put

A put is an option to sell a stock. A put holder is not obligated to exercise it and will not do so if exercising will decrease wealth. Thus, a put can never have negative value:

                                      P(S₀, T, X) ≥ 0

An American put can be exercised early. Therefore:

                                      P(S₀, T, X) ≥ Max(0, X- S₀)

The value, Max(0, X- S₀), is called the put's intrinsic value. An in-the-money put has a positive intrinsic value, while an out-of-the-money put has an intrinsic value of zero. The difference between the put price and the intrinsic value is the time value speculative value. The time value is defined as P(S₀, T, X) - Max(0, X- S₀). As with calls, the time value reflects what an investor is willing to pay for the uncertainty of the final outcome.