Option Greek Theta and its role in Options Trading Strategies

This is a continuation of series of post on options trading. If you are new to Options trading you should first read my post on Options Trading Examples, Options Premium Price and Implied Volatility. Read a gentle introduction to Option Greeks first or directly jump to Option Greek Theta.

What are Options Greeks?

In order to understand Option greeks and in particular Option greek Theta, let us first recall how Options premium is calculated. In addition to risk free interest rate and strike price of the option, (which are constant till expiry) The price of an option or options premium is dependent on the following factors :

Price of the underlying.
Volatility of the underlying.
Time remaining for expiry.

Each of the above factors has a very specific impact on the price of the Options and this impact or influence is measured by Options Greeks. For example the influence of time remaining for expiry on the price of the option is measure by Option Greek Theta which will be discussed in this article.

What is Option Greek Theta?

As time remaining for expiry decreases, the price of the option decreases more or less in an exponential manner. This behavior is measured by Options Greek Theta. The formal definition of Theta is as follows:

Theta is the change in price of the option caused by one day. In other words Theta measures how fast the Options premium decays with time.

If the concept of theta is still not clear, then it is best understood by an example.

Example of Option Greek Theta: Suppose you buy a call option for price $2 for a particular stock whose current price is $50. The strike price of your option is $55. The number of days remaining for the expiry are 25 when you bought this option. The next day after you buy this call option you realise that the price of the underlying is still $50 but the price of the option you bought has decreased to $1.95. This is because as the expiry date approaches, the price of the option tends to decrease. In our example, everything else, in particular the stock price ($50) was constant. So the reduction in the option premium from $2 to $1.95 is purely due to decreasing of the time by one unit (or one day). Thus in this case theta of the option is $0.05. Had you known the theta of this option before, you would have been able to predict by how much the price of the option will decay as time passes.

Options Greek Theta is always negative !

This question has already been answered above. Options premium decreases as the number of days remaining for the expiry of the option decrease. This means Options Theta is always negative.

Options Greek Theta and Options trading strategies

The fact that Theta is negative can be exploited in options trading strategies. I will explain two options strategies which can be used effectively once you understand Options Greek Theta.

Simple Covered Options Strategy benefits from negative theta: I have already discussed covered call and covered put. Take for example Covered Call. The covered call writer always gains from the decay in the options premium due to negative value of theta. This is because lets say you write a covered call when you do not expect a significant up or down movement in the price of the underlying. After a few days, if according to your expectation the price of the underlying has not moved significantly in the downward direction, you can by simply squaring off your position because the price at which you wrote the call options will be higher than the price at which you will square it off. Thus Covered Call Strategy benefits even if the price of the underlying does not move. Similar statement holds for covered put options strategy. Remember that this fact is not visible from the standard graphs of covered call or covered put that people usually draw.
Writing Delta Neutral Options benefits from negative value of Theta : This is an options trading strategy based on the understanding of Options Greek Delta as well as Options greek theta. You write an out of the money call option and an out of the money put option. The Option strike prices are chosen in such a way that their 'Option Greek Delta' are the same. Thus if the price of the underlying moves up the price of the Call Option you wrote will increase. But not to worry, since you wrote a carefully chosen Put Option, the price of the Put Option will decrease by approximately the same amount. The benefit of this Options Strategy is that if you write it when you do not expect large movements in the price of the underlying, you make profit by squaring off after a few days. Because small movements do not influence any net increase in the price of options you wrote and as time passes, the sum total of the price of Options written by you decreases due to time decay.
This strategy should not be used in unstable markets where large movements in price are likely.

How to Calculate Options Greek Theta?

The formula to Calculate Options Greeks is a bit complicated. However you can download the following Options Greeks Calculator (Excel Spreadsheet Format) which uses Black-Scholes Method and is good for European style Options.

Download Options Greek Calculator Excel Spreadsheet or Preview
(can be used to calculate Options Greeks Theta, Delta, Vega, Rho and also Options Premium ).

Options Greeks

Option Greeks for Beginners (with free Options Calculator)

Option Greek Delta and Delta Neutral Options Trading Strategy

Option Greek Theta and its role in Options Trading Strategies

Option Greek Vega and implied volatility

Option Greek Rho - does it really matter in your Options Trading Strategies?

Stock Market Derivatives: Futures, Options

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Stock Options trading examples - Call Option Example and Put Option example.

Covered Call and Covered Put - Simplest Options trading strategy.

Volatility and Options Pricing - How is Option premium priced?