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1. Lecture No 68
Option Greek
Theta
Rohan Sharma (Coach)

2. What is Theta ?
Options generally lose value with passing time.
For example, an option which is worth $4.83 today may only
be worth $4.79 tomorrow and $4.55 next week, without the
market moving.
 This process is known as time decay.
Theta measures the speed of time decay – how much option
premium will decrease in one day.

3. Example - Theta
Consider a $100 strike call option with 3 weeks (21 days) left
to expiration.
Its underlying stock is trading at $101. The option’s
premium, currently at $4.83, consists of intrinsic value (101 –
100 = $1) and time value (4.83 – 1 = $3.83).
 The option’s theta is -0.04.
It means the option premium will decrease by 0.04 to $4.79
until the next day (as number of days to expiration decreases
by 1), if everything else remains the same.

4. Example - Theta
We could also say the option’s time value will decrease by
0.04 to $3.79, because passing time only affects time value;
intrinsic value can change only if underlying stock moves.
 Let’s assume nothing happens in the market until the next
day. The stock stays at $101 and the option is indeed trading
at $4.79.
Now it has 55 days left to expiration and theta of -0.04,
indicating that the premium will decrease to $4.75 until the
next day.

5. Theta Values
Options generally have negative theta – lose value with passing
time.
There are some rare exceptions, but for now it is safe to take it as a
universal rule.
Short option positions have positive theta and benefit from time
decay (unless other factors like underlying price or volatility move
against them).
• In general, at the money options have greatest (most negative)
theta, as they have more time value to decay than out of the money
or in the money options.
• Moneyness (the relationship between underlying price and strike
price) is only one of several factors affecting theta.

6. Theta Units
 Long time horizon may measure theta in weeks, while short term
traders or those working with options very close to expiration may
measure theta in hours or shorter intervals.
Calendar or Trading Days?
When using calendar days, theta means how much the option or
portfolio value will change in one calendar day.
When using trading days, it is per one trading day.
 We take 252 Trading Days as Saturday & Sunday .

7. Theta for Option Buyers vs. Option Writers
 If all else remains equal, the time decay causes an option to lose extrinsic
value as it approaches its expiration date.
 Option buyers should worry about since time is working against long option
holders.
Conversely, time decay is favorable to an investor who writes options.
 Option writers benefit from time decay because the options that were
written become less valuable as the time to expiration approaches.
Consequently, it is cheaper for option writers to buy back the options to close
out the short position.
 It can also be referred to as an option's time decay. If everything is held
constant, the option loses value as time moves closer to the maturity of the
option.

8. How Theta Changes with Passing Time
 Theta of options which are near or at the money tends to increase (in
absolute terms) with passing time.
When there are still several months left before expiration, the rate of
time decay is relatively slow, and it accelerates as expiration
approaches.
 At the money options have greatest theta in the final days before
expiration.
 Options which are further out of the money or deeper in the money
tend to lose most of their time value earlier.
How Theta Changes with Volatility
The effect of volatility on theta is simple: Higher volatility means more
time value and higher theta, other things being equal.

9. Theta Trading Considerations
 The idea of making money “automatically” from passing time can
tempt some inexperienced traders to treating positive theta
strategies as sure ways to profits.
 Understand that mere passage of time can never, on its own,
generate returns higher than the risk-free interest rate.
Options on many underlying tend to trade at inflated prices, higher
than what actual realized volatility would justify. This is called
volatility risk premium.
 The source of their profits is not passage of time itself; it is passage
of time combined with mispriced volatility.

10. Theta and Gamma Relationship
•Long option positions generally have negative theta and
positive gamma (you pay for buying optionality).
•Short option positions have positive theta and negative
gamma (you get paid for providing optionality).
•Positive theta is good: you make money with passing time.
Negative theta is bad.
•An ideal position would have positive gamma and positive
theta. Unfortunately, there is no such option strategy.

11. Theta and Gamma Relationship
•Positive gamma is good: if the underlying price moves in
your favor, your profits accelerate; if it moves against you,
your losses slow down.
•Negative gamma is bad: accelerating losses and decelerating
profits.
•Every strategy has strengths and weaknesses. It can position
you favorably to either market moves or passage of time –
but not both, as one pays for the other.
•Option theta and gamma provide quick information on
where you are in this tradeoff.

12. Conclusion
• Theta measures how much an option’s price will change in one day.
• All options (with some rare exceptions) have negative theta – lose
value with passing time.
• Theta is greatest at the money. At the money theta is greatest just
before expiration.
• An increase in volatility increases time value and thereby theta.
• Short option positions have positive theta and profit from passing
time.
• Positive theta goes hand in hand with negative gamma. There is no
free lunch.