# Theta for options

What i understood that Theta is negative for put options and positive for call options

But why did i see in one of the TT’s that Theta is negative for options ? without specifying the kind of option ( shall i treat it as negative for both for the exam purpose?

Thanks Thanks

The sign on theta is (usually) the same for calls and puts, but part of the problem is how, exactly, theta is defined. Or, more specifically, how we’re measuring time.

If we measure time as time-remaining-till-expiration (so that if t is 3 today, it will be 2 tomorrow), then theta is (usually) positive for both calls and puts: the more time till expiration, the greater the value of the option.

If we measure time according to the calendar (so that if t is 27 today, it will be 28 tomorrow), then theta is (usually) negative for both calls and puts: tomorrow’s time value is less than today’s time value.

Theta is always negative for long options. As t declines, the option price declines (less time for the option to be in the money).

This is true for both calls and puts.

Theta is positive for short options (i.e. when you write calls or puts). This is because you’ve sold them and collected money on them, and you want them to expire out of the money (and there is less time for them to suddenly be in the money).

Hope that helps.

While we’re on the topic of second order effects, Gamma is always positive for long call/put, and negative for short call/put.

Not always.

For deep in-the-money put options, time value can be negative, so theta would have the opposite-of-normal sign.

If price (p) declines when t declines, then,

θ = ∂_p_/∂_t_ = negative/negative = positive

This is inconsistent with your statement that θ < 0.

It is certainly true that the sign on θ is generally the same for both calls and puts.

Again, it is certainly true that θ for short positions is the opposite sign of θ for long positions.

Maybe not as much as you’d hoped.

Theta is a first-order effect, not a second-order effect.

Absolutely correct!

Ending on a high note!

So lets go with your first defintion

can I say now that today’s option value is \$ 9 30 days after it will be \$7 (mainly due to TVM ?)

so now we can say that the option value decrease when time to expiration decrease , therefore it is positive relationship ?

But the absolute value of theta (measuring the speed or the sensitivity of this decrease in value) will increase as time to expiration decrease (negative relationship)

*Hoping for answer of yes otherwise i need to jump in a cold shower to wake up*

Works for me.

Not necessarily. How has the price of the underlying changed?

That’s what we agreed.

I’m not sure I understand the question. Are you asking about how theta will change over time?

Well . . . I didn’t answer, “Yes.”

Dry off before you reply. I wouldn’t want you to short circuit your keyboard.

Yes ! The change in theta over time

I honestly have no idea how theta changes over time.

After the exam, maybe I’ll investigate that.

This exhibit is from an answer to one of the newly added TT questions

Typically, theta is negative for options. The speed of the option value decline increases, however, as time to expiration decreases. Vega is high when options are at or near the money. During the next 30 days, the options will approach expiration and approach being at the money

So they’re not measuring time as time-to-expiration; they’re measuring it as time-since-inception.

Whatever. Either way works, you simply have to know whether you’re driving on the right side of the road or driving on the left side.

That’s what I want to investigate.

Another thing to investigate . . . after the exam.

Options always approach expiration. At a rate of one. Weird statement: what do they think, that time might start running backward?

Another weird statement. How do they know that the price of the underlying will approach the strike price of the options? If I have two options with the same expiration and different strike prices, will it cause a rift in the space-time continuum, ending life as we know it?