In the previous page we have explained why time value of at the money call options is higher than time value of deep in the money call options (other factors being equal). The reason is that the closer to at the money an option is, the more it limits your maximum risk from holding it, as there is less intrinsic value you can lose. Let's now look at put options.
Maximum risk for an option's owner
Concerning maximum risk of an option's owner, it is the same with put options as with call options. You can theoretically lose only as much as you have paid for buying the option ? the options's market price which consists of intrinsic value and time value.
The difference between calls and puts is only in the calculation of intrinsic value. While for call options the lower the strike price the higher their intrinsic value is, for put options it is exactly the opposite. The higher the strike price, the higher the intrinsic value of a put option (as a put option gives you the right to sell and you want to sell as high as possible).
Deep in the money put options
While in the money call options are on the low end of the strike prices range, deep in the money put options are those with high strikes.
In the previous article we have explained that buying the underlying stock itself can be considered buying the deepest in the money call option with stike price of zero, intrinsic value equal to the stock's market price, and no time value. We have no example like this available for put options, as here the deepest in the money strike price would be theoretically infinite (in reality the further up you go in the strike price, the less liquid the puts are and eventually there are no options traded for very high strikes).
Time value is greatest at the money for both calls and puts
The idea of maximum risk is the same with puts as with calls. The lower the market price of the option you hold, the less you can lose. At the money options have lower market prices than in the money options, as there is no intrinsic value to pay for.
With at the money options you have less on the table and your maximum risk is lower. Therefore, the market is willing to pay more for the time value of at the money option, as people prefer less risk to more risk. The extra time value is the price for limiting the risk.
Interest rates and time value of options
Besides the risk factor, interest rates and time value of money are another reason. When you buy an at the money option, you get the same exposure in terms of profit potential as with a deep in the money option, but you need less cash to pay for the option. This means you either have to borrow the cash for the time you will be holding the option (and pay interest for it) or if you use your own cash you give up the opportunity to deposit or invest it somewhere else (opportunity cost). It doesn't play any role when you are trading options in hundreds of dollars, but with millions the interest can already be significant.