An option with no intrinsic value. In so far as the options above have any value at all, it consists in their time value. All that means is that, while there is still some time before the expiry of the option, there is always a chance that the price of the share will move in favour of the option holder. Using the examples above, the holder of the put option might be saved if the price of the share rises to 90p, and the holder of the put option might be saved if the price of the share drops to 60p.
Time value lessens the nearer the option gets to expiry.