# Time value of option not always leading to an increased option value

My understanding was that as you increase the time to expiry of an option, the value of the option increases. However, I have run a bunch of scenarios and have realized that if you assume a dividend yield > 0%, the value of the option starts decreasing after x number of years. In other words, in the first z years, the value of the option increases, and after x years, it starts to decrease. This is even the case if the risk free rate > dividend yield. Can someone please explain to me intuitively why the dividend yield causes the value of the option to decrease after a certain number of years and why the time value of the option doesn't outweigh the effects of the dividend?

Thanks very much.

• Which option valuation model did you use? – emcor Jun 6 '15 at 21:16
• He was obviously talking about the standard BS model with a non-zero dividend. – SmallChess Jun 7 '15 at 15:29

let $q t$ be big (t goes to infinity where q is the yield) and you will see why . The first part of the BS formula becomes zero.