The Effect of Time to Expiration

The Effect of Time to Expiration

Consider two American puts, one with a time to expiration of T₁ and the other with time to expiration of T₂, where T₂ > T_1.

Now assume today is the expiration date of the shorter-lived put. The stock price is S_T1. The expiring put is worth Max(0, X – S_T1). The other put, which has a remaining time to expiration of T₂ - T₁, is worth at least Max(0, X – S₀). Consequently, it must be true that at time 0, we must have:

                                      P_a(S₀, T₂, X) ≥ P_a(S₀, T₁, X)

Note that the two puts could be worth the same, however, this would only occur if both puts were very deep-in or out-of-the-money. The principles that underlie the time value of a put are the same as those that underlie the time value of a call. As the following figure shows, as expiration approaches, the put price curve approaches the intrinsic value, which is due to time value decay. At expiration the put price equals the intrinsic value.