# The Greeks -- theta

Why is it for deep in the money put options as the option moves closer to maturity it can increase in value, but not for call option? I would think that if your deep in money (regardless if its put or call)…and it is almost about to expire, the probably of the stock moving an adverse direction will be significantly less. Help with the concept here?

not sure that your question is exactly clear, but for a put, if the underlying price approaches 0, the time value will be pretty much 0, and you are better off just exercising the option (you will be close to its max value of the strike price). is that what you are asking?

@ Kelleyc319, Where did you read this?

Schweser book 5, SS17, page 268. I guess what i am asking is …if a call option is DEEP in the money, why does the call value not increase as you get closer to expiration (similar to the put option that is deep in the money) sorry if i am unclear…

it does increase, but the increase is very marginal. this is measured by delta (change in option price/change in underlying) imagine that your option has a strike of 50 and the underlying is trading at 500. A change from 500-505 is going to have a small impact on the option price. Although Delta is essentially 1 at this point (as the call option is far in the money), the % change in the underlying is only 1%. If the price was closer to the strike and instead went from 55 to 60, the option price would change by 9% (5/55)

The thinking is that a call can always go DEEPER in the money… but there is a limit to a put.

Page 193 of the CFAI Text has the section on Theta… I don’t have schweser so it may or may not be clearer. It says essentially part of the option’s value is Time Value. And that the time value is a product of the option’s moneyness, time to expiriation, and its volatility. As expiration approaches, the option price moves toward the payoff value that will occur at expiration. This process is time value decay, and it makes sense… there is less time for things to go screwy, and so there is less value in the option. This is true for both calls and puts. There is a footnote on page 194 that describes how in certain instances the time value decay will be positive instead of negative for a European Put that is deep in the money, with low volatility, high interest rates, and the time to expriation is short. Meaning it will increase in value. In the text however, it makes a point to emphasize the most of the time, option prices decline the closer to expiration.

If the stock is at 0, then the put can’t have positive time value, because it is at its maximum value, and all it can really do is lose value. Therefore, you probably should exercise it before the company gets a federal bailout. I haven’t read the material, but the time value of a put for a stock at zero and with say a month to expiration might possibly be negative, to reflect the chance that if you hold it, you could lose money, but not gain it. That’s a negative expected value, and even though the value of an option isn’t the same as as its expected value, but you would never want to pay money for something that is expected to lose value.

I think you are asking why only a put would increase in value as we get closer to expiration, which is not the case with a call. The normal thing to happen is that the price of calls and puts *decreases* as you approach expiration, not increase as stated above. Let us say you have a call with a strike of \$20, with the stock now trading at \$19. If we have 10 days to go, you’d expect the call to be worth may be \$1. If the stock price does not change and we are now a day before expiration, the call will probably be worth \$0.05! Same thing would hold even if the call was deep in the money, say stock price=\$25. Ten days before expiration it might be worth \$5.50, closer to expiration it converges to \$5…in fact the bid might even be a little less than \$5. Same thing with puts. This is the concept of time decay. But then why would a deep in the money put would behave differently? An American style put behaves just like that, loses value as we approach expiration. It’s only European style deep in the money puts that have this wierd bahavior. Why? Because you can’t exercise them till expiration day. As it gets closer to expiration, it starts to have more value because you are about to be able to exercise and lock in your profit. Before that you can only sell the put, but the market for deep in the money puts is not very liquid. You’d either have to accept a rediculously low price, or you just hang on to your put.

Why would deep out of money call be worthless near maturity? If stock price is \$25, and strike price is \$20, I can also lock in a \$5 profit if I exercise it, no?

frangoya Wrote: ------------------------------------------------------- > Why would deep out of money call be worthless near > maturity? If stock price is \$25, and strike price > is \$20, I can also lock in a \$5 profit if I > exercise it, no? out of money call is far higher than your exercise price, in your example, if your stock price is \$25, your out of money call exercise price should be somewhere like \$40 or \$50

The option value will approach intrinsic value as time to maturity decreases. Someone please correct me if I’m wrong.

Opps, I mean, deep IN the money Why would deep in the money call be worthless near maturity? If stock price is \$25, and strike price is \$20, I can buy the stock for \$5 less and also lock in a \$5 profit if I exercise it, no?