Essentials Series: Option Theta
By: Team Dopex
Tags: Decentralized Finance, Decentralized Exchange, Ethereum Blockchain, Options Greeks, Cryptocurrency

Trigger Warning: Numbers

Welcome back, we hope you’re enjoying the Dopex Essentials Series so far, in this article we will be discussing the Greek “Theta”, what it is and it’s significance in the options market.



There is a glossary of terms at the bottom of the article so if you come across any terms you are not familiar with just scroll down to the bottom.

Without further ado, let’s dive right in!

Movement of Time

Time Decay Graph

This Time Decay graph above depicts how the premium erodes as expiry approaches.

As you can see, as the time to expiry decreases the premium erodes faster and faster, i.e. — the time decay increases.

What does this mean for traders?

Well, consider this — would you be willing to pay the same amount towards time value for an option with 18 days until expiry as you would pay for an option with 2 days to expiry?

The answer is no! If you answered yes you’re ngmi. jk

With less time to expiry, traders will pay less towards time value.

The key takeaway is that — as we get closer to the expiry day, the time to expiry decreases. Meaning that option buyers will pay less and less towards time value. E.g. If the option buyer pays $10 towards the time value today, tomorrow they would probably pay less towards the time value.

With this information we can safely conclude that:

An option is a depreciating asset, due to the passage of time, an option’s premium erodes daily

But by how much would the premium decrease on a daily basis owing to the passage of time? That is where Theta comes in.

What is Theta?

As time progresses and expiration approaches, options tend to lose their value. The Theta (time decay factor) is the rate at which an option loses value as time passes.

Theta measures the rate of time decay in the value of an option or its premium

Time decay represents the decrease of an option’s value or price due to the passage of time. As time passes, the likelihood of an option being profitable or in-the-money at expiry decreases. As the expiration date of an option draws closer, time decay tends to accelerate as there is less time remaining to earn a profit from the trade.

Theta is always negative for a single option because time moves in the same direction (forward, just in case you didn’t know). The moment a trader purchases an option, the clock starts ticking, and the value of the option immediately begins to erode until it expires, worthless, at the expiration date.

In short, Theta is to the advantage of option sellers/writers and disadvantage of option buyers.

Analogy

Picture an hourglass, the top side is the option buyer, and the bottom side is the option seller. The buyer must decide whether to exercise the option before time runs out. Meanwhile, as the buyer is deciding what to do, the value is flowing from the buyer’s side to the seller’s side of the hourglass. Although the movement is not rapid, it is a continuous loss of value for the buyer.

Theta values appear smooth and linear over the long-term, but as the date of expiry draws nearer, the gradient becomes much steeper for at-the-money options. The extrinsic value/time value of the ITM and OTM options is very low near expiration because the probability of the price reaching the strike price is also low. In layman’s terms, as time runs out, there is less probability of earning a profit.

Key Points:

OTM options with a lot of implied volatility tend to have high values of Theta.

Theta is typically highest for at-the-money options since less time is needed to earn a profit with a price move in the underlying asset.

Theta will increase sharply as time decay accelerates in the last few weeks before expiration and can severely undermine a long option holder’s position, especially if implied volatility decreases at the same time.

Example Time

Consider the following situation — AnonToken is $1,000, you buy a $1,200 Call option (Option A) — what is the likelihood of “Option A” expiring in the money?

Let’s consider these scenarios:

Q: AnonToken is $1,000 today, what is the likelihood of it moving $250 in a certain number of days and therefore “Option A” expiring ITM?

30 days to expiry

The likelihood of AnonToken moving $250 over the next 30 days is quite high.

Likelihood “Option A” expiring ITM: VERY HIGH

15 days to expiry?

Assuming that AnonToken will move $250 over the next 15 days is reasonable.

Likelihood of “Option A” expiring ITM: HIGH

5 days to expiry?

Hmmm, it could happen but it’s on the less likely side.

Likelihood of “Option A” expiring ITM: LOW

1 day to expiry?

Unless Elon Musk tweets about it, the probability PumpToken moving $250 in 1 day is realistically speaking — very low.

Likelihood of “Option A” expiring ITM: LOW as [redacted]

Key Takeaway

What can we take from those probabilities? Well we can see that the greater the time period to expiry, the greater the probability of the option expiring In the Money (ITM).

GigaBrain ID: TztokChad99

The Silverback Odyssey

At this point, we should be all familiar with what an option writer does — they sell options and receive a premium for doing so.

Let’s assume there is an option seller/writer, we’ll call him Silverback. Silverback knows that when he sells an option he is exposed to unlimited risk and his reward potential is limited to the premium he receives for writing the option. He also knows that he only gets to keep the full value of the premium only if the option expires worthless. Let’s say Silverback decides to sell an option early in the month.

Here is what may be going through his mind:

He knows he carries unlimited risk and limited reward potential

He also knows that by virtue of time, there is a chance for the option he is selling to transition into ITM option, which means he will not get to retain the premium received for writing the option

Option traders should remember that because of time there is always the likelihood for an option to expire in the money and that this likelihood decreases as time the expiry date nears.

So why would anyone want to sell options? Theoretically risk outweighs reward and because of time there is always a chance they lose on the trade. We can conclude that time — in the option writer’s context — is essentially a risk factor. Which is why in order to incentivize or perhaps lure Silverback into selling options, the buyer offers to compensate for the ‘time risk’ that Silverback undertakes. With this in mind, before making the decision to sell a particular option, Silverback would evaluate the time risk : reward ratio.

When you pay a premium for options, you are paying towards:

Time Induced Risk The option’s intrinsic value

Option Premium = Time Value + Intrinsic Value

Intrinsic Value

Let’s do a quick recap on intrinsic value.

Intrinsic value is the value any given option would have if it were exercised today.

So in essence, the intrinsic value of an option is the amount by which the strike price of an option is profitable or in-the-money as compared to the underlying assets price in the market.

Example

Assuming that Pump Token is trading at $1,423 — let us calculate the value of the following options:

$1,350 Call Option $1,450 Call Option $1,400 Put Option $1,450 Put Option

First remember these points

The intrinsic value can never go below 0. If the value is negative then the intrinsic value is considered to be zero. Intrinsic value for Call options is calculated in the following way “Spot Price — Strike Price” Intrinsic value for Put options is calculated in the following way “Strike Price — Spot Price”

With that in mind, we can calculate the intrinsic values of the aforementioned options

$1,350 Call Option = $1,423 — $1,350 = +73 $1,450 Call Option = $1,423 — $1,450 = 0 (negative value) $1,400 Put Option = $1,400 — $1,423 = 0 (negative value) $1,450 Put Option = $1,450 — $1,423 = + 27

Since we know how to calculate intrinsic value. Lets calculate the premium and extract time value and intrinsic value

Consider the following details:

Underlying Asset Price = $1,531

= $1,531 Strike Price = $1,600

= $1,600 Option Type = Call Option

= Call Option Option Moneyness = OTM

= OTM Option Premium = 99.4

= 99.4 Date of purchase = 6th July 2021

= 6th July 2021 Date of Expiry = 30th July 2021

Calculations

Intrinsic value of the call option = Spot Price — Strike Price Intrinsic value of Option X: $1,531 — $1,600 = 0 (negative value) Option Premium = Time + Intrinsic Value Option Premium of Option X: 99.4 = Time Value + 0

Conclusion

As you can see, this implies that the time value is 99.4. In essence this means that the market is willing to pay a premium of $99.4 for an option that has no intrinsic value but a lot of time value.

Let us take another example

Underlying Asset Price = $1,514

= $1,514 Strike Price = $1,450

= $1,450 Option Type: Call Option

Call Option Option Moneyness = ITM

= ITM Option Premium = 160

= 160 Date of purchase = 6th July 2021

= 6th July 2021 Date of Expiry = 30th July 2021

Calculations

Intrinsic value of the call option = Spot Price — Strike Price Intrinsic value of Option Y: $1,514 — $1,450 = +64 Option Premium = Time Value + Intrinsic Value Option Premium of Option Y: 160 = Time Value + 64

Conclusion

This would imply that the time value would be:

160–64 = 96

With that in mind we can deduce that out of the total premium of $160, traders are paying $64 towards intrinsic value and $96 towards the time value.

For both calls and puts you can repeat these calculations and dissect the premium into the Time value and intrinsic value.

Final Thoughts

Overall, an options seller can choose to sell options that are closer to the expiry, they will get a lower premium but the drop in premium (time decay) is high/fast, which ultimately — is advantageous to the options seller.

If you have any further questions, do not hesitate to reach out to us in the Dopex Discord server or via Twitter.

Glossary of terms

Underlying asset — The underlying asset, the price of which is being speculated on, for example, Bitcoin.

Expiry date — The date the option will expire and be exercised, after this date, the contract is no longer valid.

Strike price — The price at which the buyer has the right to buy or sell the underlying asset at expiry.

Option price (premium) — The price the buyer pays to the seller for the right to buy or sell the asset at the strike price on the expiry date.

In the money (ITM):

For a call — this term is used when the strike price is lower than the current price of the underlying asset.

For a put — this term is used when the strike is higher than the current price.

At the money (ATM):

For both a call and a put — this term is used when the strike is equal to the current price.

Out of the money (OTM):

For a call — this term is used when the strike price is higher than the current price of the underlying asset.

For a put — this term is used when the strike is lower than the current price.

All options on Dopex are European style, which means they can only be exercised at expiry, unlike American style options that can be exercised any time until expiry

About Dopex

Dopex is a decentralized options protocol which aims to maximize liquidity, minimize losses for option writers and maximize gains for option buyers — all in a passive manner.

Dopex uses option pools to allow anyone to earn a yield passively. Offering value to both option sellers and buyers by ensuring fair and optimized option prices across all strike prices and expiries. This is thanks to our own innovative and state-of-the-art option pricing model that replicates volatility smiles.

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