# Why does black scholes model give lower prices for puts with further time to expiry?

Consider BS-model with parameters: Stock = 100, Strike = 100, Texp = 1 year, Vol = 13%, Rf Rate = 3%. For these parameters the BS put price is 3.76. Then consider the same parameters but with Texp = 20 years. The new BS put price is 3.29. Consider now Texp = 100 years. The put price is even lower still at 0.09.

What gives? Does it make sense that longer expiry options can be valued less?

• Note that the upper bound of the put price is $K e^{-r T}$ and thus decreases with time-to-expiry. The forward on the other hand grows at $e^{r T}$. – LocalVolatility Sep 8 at 17:26
• how about 5 years? – Magic is in the chain Sep 8 at 18:04
• Is 5 years the turning point? – roz Sep 8 at 18:22
• turning point is slightly to the right of 5 in this case. – Magic is in the chain Sep 8 at 19:03
• I've been messing around with it. I guess this result is because at that long time span, the rf drift makes it so that all the paths almost surely are OTM for those puts regardless of the vol. Is this about right? Is there a better, more precise explanation? – roz Sep 8 at 19:05