Options trading part 4: Theta/time decay risk

Theta (Θ) is an important risk to consider when trading options is time decay which is the loss in value of an option contract over time.

“Theta Θ” is also known as the time decay of an option contract.

“Θ” is the symbol used to represent “theta.”


You have learned in school, on television, or YouTube how to visualize atoms, protons, neutrons, electrons, etc.

This model is entirely inaccurate, yet we use it because it helps us visualize the specifics of these abstract subjects.

Consider everything in this article to be an oversimplification to assist you with more advanced reading about options trading

Don’t feel intimidated if you don’t understand this article after the first time reading. It took me a while too to understand.

You’ll probably need to read this and the previous articles multiple times over a few weeks or months. Don’t try to understand it within one day. “Sleep on it.” Sleep can help your brain form connections.

Time value

Let’s take an example.

Strike price: $300
Underlying (spot): $400
intrinsic value: underlying - strike
intrinsic value: $400 - $300 = $100
We have an “intrinsic value” of $100. The call option contract is “In the money.”

The value of options contracts tends to diminish as they approach expiry, due to the effects of time value decay.

Time decay/Theta

Time value decay is a key consideration when trading options contracts.

In addition, the time decay accelerates as your option contracts approach “At the money” (ATM)

The closer you are to expiry, the greater the likelihood that your option will expire worthless since the option contract will have less time to recover its value.

The theta Θ on the options chain

BTC June 4 (2022)
June 24 (20220)

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Theta Θ and Gamma Γ relationship

The relationship between theta Θ and gamma Γ is interesting because it can be used to help predict how an option’s price will change over time.

when you buy an option contract, you will have negative “theta Θ” but positive “gamma Γ.”

The option contract “negative theta Θ” represents the amount by which the option contract’s value will decline over time,

while the option contract “positive gamma Γ” represents how the option contract’s “delta Δ” will change in reaction to changes in the price of the underlying asset.

When you buy an option contract, you have a “negative theta Θ” but a positive “gamma Γ” your option contract will lose value over time, but you will profit from large price movements in the underlying asset.

Because a high positive “gamma Γ” indicates that the option contract’s delta will grow when the underlying asset’s price rises, it is more probable that the option contract will become “in the money.”

You sell the right to buy or sell an underlying asset at a specific price on or before a specific date.

Because you are selling an option contract that has not yet expired, you are “short gamma.”

Additionally, you are “long theta Θ” as you bet that the option will expire worthless.

If the option expires worthless, your “theta ” will be positive, and if your “theta” is positive, your “gamma” will be negative.

positive gamma = negative theta

negative gamma = positive theta

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BTC-24JUN22-50000C (10 call options)total delta:0.03
total gamma: 0.000019
total theta: -15.83
PNL call option position if it would expire today
There is no “intrinsic value” left at expiry, only “intrinsic value.”

Definition of Theta

Typically, the “theta” represents the value lost per day, assuming that all other market circumstances stay constant.

Is it ever possible for an option contract to have a positive “theta,” meaning that if nothing changes, the option contract will be worth more tomorrow than it is today?

Short-selling options

However, the short seller also earns the “time decay”, or “theta”, on the options contracts, which offsets some of the risks.

Delta hedging is a way of offsetting the risk of price fluctuations in the underlying asset by trading in the derivatives market.

0.0033 * $29723 = ~$98.08
positive theta of 13.45

Interesting paper for advanced options trader:


The yield of shorting a put option. Our maximum yield is the premium
You can see the yield by selling a “put option” for example

This options strategy is called “overwriting”

Tesla "Out of the money" call optionPremium: $12.50
Current share price: $700
Strike price: $900
expiration date: July 17th 2022
delta: 0.16
gamma: 0.0015
theta: -0.0457
delta: -0.16
gamma: -0.0015
theta: 0.0457 (our theta is positive)
Short-selling 10 call optionsTotal delta of position:-1.6
Total gamma of position: -0.015
Total theta of position: 0.457 (our theta is positive)

Volatility and gamma

In a short gamma position we will profit from reduced market volatility.

In a long gamma position we will profit from a rise in market volatility.

what determines the “time decay” or “theta” of an option contract?

The “implied volatility determines the “time decay” of an option contract.”

The higher the “implied volatility,” the greater the anticipated price volatility of the underlying asset, and the greater the “time decay” of the option.

If we anticipate that the market will move more than the “implied volatility” being priced, we should be “long-gamma.” That means that a rise in market volatility is advantageous for us.

If we anticipate the market to move less than the implied volatility, we should be “short-gamma.” Thus, we profit from a reduction in market volatility.

Together, these two factors determine our overall PNL due to realized volatility.

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FTX MOVE Contracts

If you short an FTX MOVE contract, you are “short-gamma,”

If you long an FTX MOVE contract, you’re “long-gamma.”

Your delta: 0.771
Your gamma: 0.00014
Your theta: -159.92 (time decay will erode the value)To delta hedge: short 0.771 BTC
Adjust your short when delta changes
Your delta: -0.771
Your gamma: -0.00014
Your theta: +159.92 (time decay will work in your favor)To delta hedge: long 0.771 BTC
Adjust your long when delta changes

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Efficiency gamma/theta


Efficiency gamma/theta

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ByBit options trading

ByBit option chain

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Trading platform: Delta exchange

Delta exchange

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