# Options trading part 4: Theta/time decay risk

**Theta**, commonly known as the “**time decay**” of an option contract, is our third risk consideration while trading options & delta-hedging

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.

Understanding “**time decay**” or “theta” is essential to understanding where an option contract derives its value.

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

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

An option contract derives its value from the “**intrinsic value**” and the “**time value**.”

The “intrinsic value” is the amount by which an option contract is “in the money” (ITM) or not.

Meaning the difference between the “strike price” and the “current price” of the underlying (i.e., spot).

Disclaimer:

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.

We have a Tesla “call option” contract with a “strike price” of $300 while the share price trades at $400

Strike price: $300

Underlying (spot): $400

intrinsic value: underlying - strikeintrinsic value: $400 - $300 = $100

We have an “**intrinsic value**” of **$100. The** call option contract is “In the money.”

The “**time value**” measures the option’s odds of increasing value due to the passage of time and becoming “in the money.”

As time goes on, the option contract could increase in value and become “in the money.”

So “time value” refers to the probability that an option’s value will increase as time passes. The longer until the option’s expiration, the greater the time it will become “in the money.”

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

The closer the option contract gets to the expiration date, the higher the “**time value decay**” is.

That’s because there is less time remaining for the underlying asset to move enough to make the option contract swing “in the money.”

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

If you buy** options contracts**, your “theta Θ” or “time value” is **negative**. That means the option contract is losing value over time as expiration nears.

Theta is a measure of an option’s time value. **When you’re buying an option contract, your theta is negative.**

The option contract loses money over time as expiration nears. **So if you’re holding an option contract, you’re losing money as time passes.**

The closer you get to expiration, the greater the chance your option will expire worthlessly.

That is related to “theta decay,” which is the gradual loss of value of an option over time. As expiry approaches, “theta decay increases”, meaning the value of your option contract value erodes faster with increasing magnitude.

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

Therefore, “theta decay” refers to the deterioration of an option’s value over time. As expiry approaches, theta decay increases, meaning the value of your option contract drops at a quicker pace.

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 decay is becoming larger in magnitude, but it is also becoming more negative in direction.

As we get closer to expiry, the theta decay will be more negative. For example, it might start at -0.003 but be -0.1 by reaching the expiry.

# The theta Θ on the options chain

Let’s examine the “options chain” for bitcoin on Deribit. On the left are “call options,” and On the right are “put options.”

The maturity date selected is June 4 (2022)

For the call option contract with a strike price of $30k, you can see that the “theta Θ” is around -163

Now let’s select the maturity date for June 24 (2022)

For the call option contract with a strike price of $30k, you can see that the “theta Θ” is around -44

As you can see, in the option contracts with a $30k strike price, the closer an option is to expiration, the theta decay will be more negative than the option contracts further away from the expiration date.

The more time left to expiry, the greater the chance is for the option to become “in the money” or stay “in the money.”

If you don’t have a Deribit account yet for trading bitcoin, ethereum, and Solana options, I recommend signing up on Deribit.

Sign up on Deribit and receive 10% discount on fees for trading futures & options: https://www.deribit.com/reg-572.9826

# Theta Θ and Gamma Γ relationship

Theta measures how an option’s price changes over time, while gamma measures how an option’s price changes in response to changes in the underlying asset’s price.

There is an interesting relationship between “theta Θ” and “gamma Γ.”

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.

The relationship between “theta Θ” and “gamma Γ” is noteworthy because it demonstrates that.

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.”

Conversely, If you “**short-sell**” an **option contract**, you are “**short gamma**” and “**long theta**.”

**If you have a positive “theta,” you will have a “negative gamma.”**

To further explain and deepen our understanding:

**When you “short-sell” an option contract**

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.

So remember:

positive gamma = negative theta

negative gamma = positive theta

That’s the relationship between the “theta Θ” and “gamma.”

**Where buying an option contract gains value from large movements with magnitude, it doesn’t benefit from the passage of time.**

Using Deribit tool: https://pb.deribit.com

If you don’t have an account on Deribit, you can sign up and receive a 10% discount on fees for trading futures & options: https://www.deribit.com/reg-572.9826

Let’s look at a simulation. We buy 10 “Out of the money” call options

BTC-24JUN22-50000C (10 call options)total delta:0.03

total gamma: 0.000019

total theta: -15.83

If I use the slider to move 15 days closer to expiration, you will see that the time will erode the option contract value.

you will see that “the time” will erode the option contract value.

If there’s no time value left, when we reach expiry, you see we are only left with the “intrinsic value.”

# Definition of Theta

The theta (Θ), or time decay of an option contract, is the rate at which the option contract’s value gradually decreases over time.

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

The “theta” is crucial for options traders to understand since it reflects the time value lost as the contract’s expiry date approaches.

The time value of an option is the amount by which its price exceeds its “intrinsic value” (i.e., the amount of compensation the option holder would receive if they exercised the option today).

The more the passage of time, the less time value an option has. Therefore, the theta measures the rate at which an option’s time value is decaying.

An option contract with a “theta” of -0.05 will lose 0.05 in value each day due to time decay and no underlying movement.

If the notional value of the option contract is $4 today, it will be worth $3.95 one day later and $3.90 two days later.

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?

However, this subject is beyond the scope of this article, but it’s worth mentioning.

## trade-offs of buying/long options and delta hedging

In my second article on alternatives, I said that a “long-gamma” position created by buying options contracts causes the delta to move in the correct direction, resulting in the profitable trading of shares and staying “delta hedged.”

However, this may not always ensure profits since time decay might cause losses.

To get a “long-gamma” position, a trader buys option contracts to benefit from delta changes and trading shares to neutralize his delta.

That exposes option contract buyers to the danger of time decay, which may erode the position’s value and result in losses.

So the trade-offs of buying an options contract are that while **we may profit** from market movements **by delta hedging**, we will also have to **pay** the “**time decay**” or “theta.” That’s the downside of being “long” on an option contract.

# Short-selling options

Shorting options contract involves selling options contracts in hopes that the price of the underlying asset will move to a price so that the options will expire “out of the money” and therefore worthless.

When we “short-sell” an option contract short, we are “short gamma” and “long theta.” That indicates that we profit from “time decay” due to the “premium” of the option contract we sell. The “time value” of an option contract decreases as time passes.

The term “short-gamma” refers to a position in which an option trader earns the time decay of an option contract by “short-selling.” That happens because the option contract is sold as a “time value,” which gets smaller as time passes. When an options trader is short-gamma, they effectively earn the option contract’s “ premium. “

Short-selling option contracts expose the trader to short-gamma risk, which is the risk of losing money if the market moves too much. Theta, or time decay, is the amount by which the value of an option declines over time.

**That exposes the short seller of an option contract to the risk of a dramatic, unexpected change in the underlying asset price, which might result in significant losses.**

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.

When an options trader is short-gamma, they effectively earn the option contract’s “premium. “

Let’s go over an example, we “short-sell” a put option contract with a “strike price” of $20k

**The current price of bitcoin is $29723**

We paid an average price of 0.0033 BTC

`0.0033 * $29723 = ~$98.08`

**Notice, when trading bitcoin options on Deribit, our collateral is in BTC. To hedge our BTC exposure, we short 0.0033 BTC (the premium) within the derivatives market by trading shorting futures.**

Interesting paper for advanced options trader:

https://www.researchgate.net/publication/353478878_Inverse_Options_in_a_Black-Scholes_World

As you can see, if BTC remains above $20,000 at expiry, we “yield” the put option premium!

However, since we are a “short seller” of this put option contract, the risk of a dramatic, unexpected change in the underlying asset price might result in significant losses.

If we witness a sharp move to the downside within a few days, our unrealized loss will be $1280. However, if we hold until expiry, we still yield a profit.

However, delta hedging is a way of offsetting the risk of price fluctuations in the underlying asset by trading in the derivatives market and limiting our loss.

By the way, Deribit has a nice tool for

Just one thing that would be nice to mention is that your collateral on Deribit will be in BTC if you trade bitcoin options. Your collateral will be in ETH if you trade ethereum options. Your collateral will be in SOL if you trade Solana options.

You have to hedge your exposure by shorting futures, as mentioned before.

## Options overwriting

Let’s take an example of short-selling an “Out of the money” call option

This options strategy is called “overwriting”

Overwriting is an options strategy that is a common one used by traders to make a profit. It involves selling overpriced option contracts or way too far “Out of the money.”

with the hope that they won’t get exercised before they expire. In other words, we hope that the share price won’t expire “in the money” (above our “strike price”)

Overwriting options can be a l**ucrative strategy**, but it is also **risky**. If the options do get exercised, we end up losing money.

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

Since we are “short-selling,” we hope that on the day of expiration, Tesla trades below $900. The current share price of Tesla is $700

We will short-sell 10 of these “Out of the money” call options.

So our greeks will be the opposite.

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)

Since our theta is positive and assuming all market circumstances stay the same, we make $0.457 per day on theta, assuming all market conditions remain unchanged.

If the price of the options declines as time passes due to the lower probability of expiring “in the money,” we can repurchase those 10 call options back before expiration. We earned the time decay.

However, if we wait until expiration and Tesla trades below $900 on the day of expiration, we will gain the premium of $12.50. Still, because we sold 10 call option contracts, we would earn $125, the entire “premium” of these 10 call option contracts.

# Volatility and gamma

A volatility trader may take a “long-gamma” position by buying options contracts or a “short-gamma” position by selling options contracts, depending on their expectations for the market’s volatility.

The gamma of an option contract indicates how much the contract’s price will change in response to a change in the underlying asset’s price.

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.

You probably understand the concept if you have been trading FTX MOVE contracts or option straddles.

We may either choose to be “long-gamma” to collect enough profit from delta hedging by trading on the derivatives market to offset the negative “theta” or “time decay” that erodes the option contract’s value.

Or, decide to be “short-gamma” and receive “theta” and delta hedging to offset the risk of price swings in the underlying asset by trading in the derivatives market.

You may wonder

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

The answer

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

The “Implied volatility” reflects the volatility expectations of the market “realized volatility” for the underlying asset.

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.

**Suppose our view of an increase in volatility is correct and long-gamma. If our prediction of a rise in volatility is accurate, we will earn a greater return. In that case,** we will make more profit by delta hedging is a way of “delta hedging” is a method of mitigating the risk of “time decay” or “theta” by trading the underlying asset on the derivatives market.

The way that “delta hedging” works is we have a long option contract or “long gamma” position and then offset that position with trades in the derivatives market (i.e., futures).

We “delta hedge” to mitigate the risk associated with a long option position. By using “delta hedging,” we can limit the risk of holding an option contract. Our option position will profit when the underlying price moves, but our directional hedging strategy will lose the same amount of money in the futures market.

**Suppose we are correct that volatility will decrease, and we have a short gamma position. In that case,** we will earn more from “theta” than we would lose from delta hedging to offset the risk of price swings in the underlying asset by trading in the derivatives market.

Our “short sell” option PNL with a short gamma will increase. This is because gamma measures the rate of change of an option’s delta, and a decrease in volatility will cause the delta to become less negative (move closer to 0).

Therefore, a “short gamma position” will benefit from a decrease in volatility. On the other hand, delta hedging involves trading the underlying asset when it increases in price and buying it when it decreases in price.

So if the underlying asset’s price decreases, the delta hedge will lose money. Therefore, if we are correct that volatility will decrease, we will make more money from theta decay than we would lose from delta hedging. Therefore, it makes sense to trade on the derivatives market to offset our delta hedging.

The “gamma” PNL measures the change in our PNL resulting from changes in the underlying asset’s price.

The “theta” PNL measures the change in our PNL due to the passing of time (i.e., the decay in the options’ value over time).

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

In part 5 of the options trading series, we will examine the fourth risk consideration, the “Vega” risk, and delve deeper into “implied volatility.”

I highly recommend you create a medium account and follow me. Turn on email notifications.

I will try to release part 5 as soon as possible.

# FTX MOVE Contracts

Check out the link below for anyone familiar with my article about FTX MOVE contracts.

If you still didn’t make the connection, allow me to explain

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

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

Now you also know at which delta the gamma is at its highest ;)

If you long BTC-MOVE-WK-0603

`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

If you short BTC-MOVE-WK-0603

`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

I shouldn’t have to explain this since it should have been obvious after reading this post, but I chose to do it anyway because some people may not be able to grasp and draw the connection/relationship.

Keep in mind that FTX MOVE contracts are option straddles. To trade FTX MOVE contracts, you must first understand options trading.

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My referral link will give you a 10% discount instead of the usual 5% discount for anyone who wishes to give it a go.

# Efficiency gamma/theta

Some traders assess the relative riskiness of various trading strategies by examining the risk-reward ratio or the effectiveness of the strategies.

A trader may examine 2 different spreads, both of which have **positive** “gamma” and **negative** “theta”.

The reward is the possible profit from “gamma” when a trader hedges against the underlying asset’s movement by trading derivatives. The risk is represented by “theta,” which is the amount of money lost over time if the underlying market does not move significantly enough.

Ideally, the trader would prefer the reward to be far greater than the risk. This connection is quantifiable as a ratio.

gamma/theta

The greater this ratio’s absolute value, the more efficient the position.

However, a trader with a **negative** “gamma” and a **positive** “theta” wants the risk (the “gamma”) to be as little as possible relative to the potential reward (the “theta”). Therefore, they want the absolute value of the gamma/theta ratio to be as large as possible.

Because each spread has a negative gamma and positive theta, we want the efficiency to be as small as possible.

When all options expire all at the same, efficiency is an excellent approach to evaluating strategies rapidly. “Spread 3” is the optimal choice since it has the smallest efficiency. That’s important since it means the gamma and theta risks are minimized.

Nonetheless, if a strategy comprises of options contracts with different expiration dates, (ie FTX MOVE Contracts)

Then the “Vega” risk becomes important and a more detailed analysis is necessary.

In part 5 of these options trading article series, we will delve deeper into “vega” or volatility risk.

I highly recommend you create a medium account and follow me. Turn on email notifications.

**ByBit options trading**

If you are now trading futures on ByBit or planning to, you will also be able to trade options.

Options trading on ByBit is easier than on Deribit for beginners.

Why? may you wonder? When trading on Deribit, the collateral is in BTC, but on ByBit, it is held in USDC.

Typically, when new traders join Deribit, they forget that their collateral is in BTC, resulting in incorrect hedges and computations.

As some of you may recall, trading on Bitmex with 1x leverage is equivalent to 2x leverage since your collateral exposes you to 1x leverage already.

Some of you might remember this tweet from Flood.

Liquidity still has to improve, but that will happen in the future.

ByBit Options (Discount on fees and $100 deposit bonus):https://www.bybit.com/register?affiliate_id=6776&group_id=1653&group_type=1

# Trading platform: Delta exchange

Another new exchange called “Delta exchange” has options trading for multiple altcoins. You could use these options to hedge your portfolio for altcoins. Here we can see the options chain for Avax.

Your collateral will be stablecoins rather than BTC or ETH is an additional incentive to favor Delta Exchange over Deribit and the availability of altcoin trading choices.

If you are new to options trading, I would recommend Delta Exchange and ByBit over Deribit. After learning how to hedge your collateral on Deribit, you can use Deribit.

Delta exchange

If you’re seeking to signup and want a 10% discount

You can use my referral link

# Final words

Leave a clap for the algorithm on medium if you enjoyed it.

Feel free to leave a comment if you enjoyed it.

I highly recommend you create a medium account and follow me. Turn on email notifications.

Part 5 of options trading will be released soon, our fourth risk consideration: “Vega”

*More medium articles?*

If you are looking for more medium articles like this written by me, you can find them here.

Twitter: https://twitter.com/RNR_0

If you liked this article, you will probably also love this article about FTX MOVE contracts.

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