# What is option theta?

By Simon Gleadall, CEO of Volcube.

If you have the option to do something, that option is more valuable, the longer it is valid. If you have the option to borrow my umbrella whenever you like for the next 10 years, that is a more valuable option than it would be if you can only use my umbrella for the next 24 hours. So with financial options, the longer they have until they expire, the more they are generally worth. But, the flip side to this is that with each day that passes, options become *less* valuable. This risk is known as time decay and it is measured by *option theta*.

Option theta tells us how much our option’s value will change as time passes. To make it an easy number to use, it is typically standardised to show the change in option value for each *day* that passes. For example, if an option is worth $1.50 and it has a theta of 0.05, this means that the option will lose 5 cents in value over the next 24 hours, other things being equal. So if nothing else happens at all (the spot product doesn’t move in price, the implied volatility stays the same etc.), when we look at our option’s theoretical value tomorrow, the pricing model should say $1.45.

The theta of options is additive, regardless of the underlying product, their strike or their expiration date. This means the theta from every option in your portfolio can be added and subtracted to give your total portfolio ‘theta bill’. If you own options, it means you will be ‘paying’ a theta bill. In other words, your portfolio will be worth less tomorrow than it is worth today, other things being equal. If on the other hand you have written options and are *short* options, you will be *collecting* theta. As time passes, you will profit from being short options, if nothing else changes.

So why would you ever be long options? Why not just short options and collect time decay from the guy who buys the options and pays a theta bill? The reason is that by owning options, you own gamma. And it is possible to make money from owning gamma by gamma trading and gamma hedging. When you are short gamma, gamma hedging only loses money; it can never make money. So, there is a trade-off here. By owning options, you will be paying a theta bill, but you can make money by scalping your gamma. By shorting options, you will be collecting theta, but you may lose money via *negative * gamma hedges. Remember too that the payoffs are not necessarily symmetrical. The theta bill will not vary a lot from the theoretical theta number. The option premium (value) can only fall so far (to zero) so there is a limit to the amount of theta. But the profits/losses from gamma hedging are potentially almost limitless. This is because the underlying product could become incredibly volatile and so the amount of gamma hedging the trader might do could lead to very large profits/losses. So there is an asymmetry in the potential payoff from being long or short theta versus short or long gamma.

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