CFA CFA Level 2 Theta in a option.

# Theta in a option.

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• vincentt
Participant
• CFA Level 3
0

In level 2 syllabus, it mentioned that as time to maturity gets lesser the value of a call and put option will decrease towards \$0.

However, there’s no mention of whether that would be applicable for a call/put option that’s deeply in the money (from a logically thinking since it’s deeply-in-the-money, there’s lesser uncertainty of losing hence the option price should be slightly less than the value gained from exercising the option or the difference between the market price and the exercise price).

So why would a deeply-in-the-money call/put option losses it’s value as time theta is reaching 0?

• vincentt
Participant
• CFA Level 3
5

I understand the part about IV and TV, but I thought you mentioned that even if the option is ITM as theta gets close to 0 (very close to maturity) the option value would be approaching 0?

Sorry @sophie i’m a little confused here.

• vincentt
Participant
• CFA Level 3
4

@sophie so is option price the same as option value?

Because based on the diagram in schweser (the BSM model) as theta approaches 0 (expiring soon), the option price approaches \$0.

I guess that model assumes the option isn’t ITM?

• 3

@vincenttall else constant, an option theta measures the fall in value of a given option as it nears it’s maturity/expiry. This relationship is one way (always negative, unlike delta).

So even for a deeply ITM options, assuming all else is constant, it loses value over time as it loses the time/opportunity to get more/deeper ITM.

• 3

Theta doesn’t lose value, the option value does. Sorry I wasn’t clear above. Theta is just the measurement of option value’s sensitivity to time, i.e. change in option value due to change in time.

Your reasoning seems fine. Option value comprises of intrinsic value and time value. For the call option example above, as it’s deep in the money when it’s so near expiry, the option value (\$40 as you mentioned above) is mostly comprised of intrinsic value and theta is near 0 since it’s so near maturity.

• 3

As the option approaches maturity and it is in the money you are usually only left with the intrinsic value with is the difference between the stock price and the strike price due to the certainty.

• vincentt
Participant
• CFA Level 3
3

@sophie ahhh so the model assumes there’s no intrinsic value at inception and all the way through.

Because I was thinking, I’m sure someone could sell an call option at a higher price with some intrinsic value and quite a bit of time to maturity.

thank you once again. ^:)^

• vincentt
Participant
• CFA Level 3
2

when you mention “it loses value” are you referring to theta loses it’s value?

For example a dealer is selling a call option with an exercise price of \$40 (current market price of the underlying is \$35) with say 6 months to maturity.

So obviously, you have got quite a bit of time for the stock to fluctuates towards a gain or a loss.

However, if the current market price is at \$80 and there’s 1 day left to maturity, shouldn’t it be pretty certain that the call option buyer would be able to gain from the call option hence the current market price of the option (if the dealer is still selling it) would cost slightly less than \$40 (\$80-\$40) as that would be the value anyone could secure by purchasing the call option.

Am I on the right track?

• 2

The assumption of whether it’s ITM, OTM or ATM of the option is important for the theta relationship. So i’m not sure what the model assumed, any idea?

That statement ‘option price approaches 0’ is not entirely clear to me as I don’t have much context.

• vincentt
Participant
• CFA Level 3
2

@sophie
This is the only part that explains the theta in the book

@diya if you have got schweser i’m sure you’ve seen that as well, there’s no mention on whether it’s ITM, OTM or ATM.

• 2

Yes, these graphs assume all else constant. So, for a given strike price and stock price (fixed), we expect the option price (which in this sense is mainly time value of the option, since intrinsic value doesn’t change as the value is fixed) will reduce as it nears maturity, to 0 eventually. I guess I can see why you got confused with the labels

• 1

No problem @vincentt – it means my explanation is bad too! :))

If the option is ITM and near maturity, theta is near 0 but option value should be the intrinsic value (since it’s ITM) and not 0.

• 0

No problem! It assumes it’s constant. They like to do that in econs, it helps analysis. If all else is constant (or ceteris paribus) is a common term. Glad I could help!