# Theta - sensitivity of option price to passage of time

Can somebody explain to me concept of theta - sensitivity of option price to the passage of time. I understand passage of time is different from time to maturity. But why does the option price decrease on passage of time. I feel any option that is in the money should be more valuable as time passes. Also, how can deep in the money European put option but not call option be the only exception to the rule?

You have a call option trading at \$1 now on a stock with a strike of \$20, trading at \$19, with 2 weeks to expiration. The reason teh option is worth \$1 and not zero, because it is out of the money, is because there is still time that teh stock could move higher. The \$1 is entirely time value. Intrinsic value is zero. But if it is going to epire tomorrow, while the stock is still traing at \$19, time value has eroded, and it might actually be trading at \$0.05, all of which is time value.

The exception to this is deep in the money European put option. Assume the same stock as before witha strike of \$20 and you purchased the \$20 put on the stock. Assume the stock is now trading at \$15, so your put is worth at least \$5. Since you cannot exercise until expiration day, proceeds of \$5 cannot be realized via exercising, so in theory the closer we get to expiration the more valuable the option becomes! However (someone feel free to correct me), you can sell the option for \$5 any time you like. So, I guess I don’t agree that with a European put, the put price does not decrease with passage of time.

Even if you take the extreme case and assume the stock is now trading near \$0.00, true you cannot excercise, but you should be able to sell the put for about \$20. Again, passage of time will decrease any option price, that’s my thesis.

Thanks. But I am still consfused. Consider a call that is in the money. Strike of \$15 and stock trading at \$20 (if thats wat deep in the money). As time passes the call becomes more valuable right? Why is this not considered? I know i must be thinking it wrongly somehow. But where

Think of volatility as similar to the effects of duration: its like a slinky. The longer it is, the more it can hurt. Basically, the longer your time horizon, the more that can occur, eg, the more your underlying can go up or down, ergo, the more your option can be worth during the time that you hold it (because your hoped-for scenario has more time to come to fruition.) The less time to expiry, the less time your monetary dreams have to come true. As such, the potential for value starts to ebb. Got it? With deep in-the-money puts, this relationship doesn’t hold because, looking at the put call parity equation, you don’t have to figure in the weight of the risk free rate, which in theory, weighs on the value of the option, because when you hold a put you’re short the stock. An in-the-money call will have a significantly shorter theta horizon than an out-of-the-money call.

Strike \$15, stock at \$20. If you have 6 months to go, this option will be worth probably \$7, with \$5 for intrinsic value + \$2 for time value. As time passes, and assuming the stock stays fixed at \$20, the intrinsic value doesn’t change…it is still \$5, but the time of \$2 will shrink. On the day of expiration, time value = \$0, and the option is worth only \$5.

Thanks Dreary. That explanation helped a lot.