Introduction to Bitcoin Options Profit/Loss

This will be the first in a series of articles aimed at people new to options, and in particular the Bitcoin options on Deribit. If you already trade cryptocurrencies you are probably familiar with both spot markets and futures markets. Options however are a largely unknown product to many traders, particularly those whose first exposure to trading was cryptocurrencies. Even options on Bitcoin, by far the best known and widely traded cryptocurrency, only exist in a small number of places.

Options have a steeper learning curve than simple buying and selling which along with availability is the main reason they are underutilised. However, once you get over the initial hurdle of learning the basics they are an extremely useful instrument as you can build positions that simply aren’t possible with futures/spot. They can be used alongside futures/spot to complement existing strategies, or they can be traded in isolation.

This article won’t be going into strategy, for now we’ll just give an understanding of what call and put options are and how they work in terms of profit and loss.

First let’s get some definitions out of the way.

What Is An Options Contract?
Every option has a buyer and a seller. The buyer is buying from the seller the option to trade the underlying asset at the strike price on the expiry date.

Each option consists of the following:
Underlying asset — The asset being traded, in this case Bitcoin. (For the purpose of pricing calculations on Deribit the underlying asset is either the Deribit BTC index or the closest BTC future).
Option Type — Either a call (the right to buy at the strike price on the expiry date) or a put (the right to sell at the strike price on the expiry date).
Strike Price — The price at which the buyer has the option to buy (for calls) or sell (for puts) Bitcoin. For a call option to have value at expiry the BTC price must be higher than the strike price. For a put option to have value at expiry the BTC price must be lower than the strike price.
Expiry Date — The date at which the option is automatically exercised. After this date the option is no longer valid and can no longer be exercised.
Option Price (aka Premium) — The price the buyer pays to the seller for the option to buy (call) or sell (put) Bitcoin at the strike price on the expiry date.

The options on Deribit are European style and cash settled.

European style — Options cannot be exercised before the expiration date. However it’s worth noting that they can still be traded prior to expiry (i.e. you do not have to hold it until expiry).
Exercising an option means putting the right specified in the contract into effect i.e. buying at the strike price of a call or selling at the strike price of a put.
Cash settled — When the option is exercised any value the option has is paid from the seller to the buyer in cash (in this case Bitcoin). The Deribit options are exercised automatically on expiration so you don’t actually need to worry about how or when to do this.

Let’s look at how buying a call or buying a put compares to longing or shorting futures.

As you can see by the green lines, when buying a call or put you limit your losses to a fixed amount (unlike longing/shorting futures). In exchange for this protection you pay a premium to the option seller shifting the whole profit/loss line down the chart by the amount of the premium paid.

It’s also possible to combine more than one option to create a wide variety of different payoff curves. We will save these multi-leg positions for the next article though. For now let’s move on to the profit and loss of Bitcoin options and how to calculate it.

Bitcoin Call Option Visualisation

A BTC call option is the right but not obligation to buy 1 BTC on the expiry date at the strike price. If you are the buyer of a call option you want the BTC price to go up, as the more it goes up the more your call option is now worth.

Let’s look at an example of a call option with a premium of 0.1BTC and a strike price of $4000. The following chart shows what the profit/loss of that option would look like if you held it to expiry:

The x axis is the price of Bitcoin at expiry, the y axis is the corresponding profit of the position in BTC. Blue is the buyer’s profit/loss, red is the seller’s profit/loss. We’ll go through some examples of how to actually calculate this later.

Bitcoin Put Option Visualisation

A BTC put option is the right but not obligation to sell 1 BTC on the expiry date at the strike price. If you are the buyer of a put option you want the BTC price to go down, as the more it goes down the more your put option is now worth.

Let’s look at an example of a put option with a premium of 0.1BTC and a strike price of $4000. The following chart shows what the profit/loss of that option would look like if you held it to expiry:

The x axis is the price of Bitcoin at expiry, the y axis is the corresponding profit of the position in BTC. Blue is the buyer’s profit/loss, red is the seller’s profit/loss.

How to Calculate Profit/Loss of Bitcoin Options

If an option expires out of the money then this option expires worthless and no further transfer will occur between buyer and seller. The buyer’s only loss is the premium they paid for the option, and the seller gets to keep the premium they collected.

A call option is out of the money (OTM) when BTC Price < Strike Price
A put option is out of the money (OTM) when BTC Price > Strike Price

However if an option expires in the money (ITM), this option’s value is determined by the difference between the BTC price at expiration and the strike price according to the following formulas:

Call Example

You buy a call with the following attributes:
Strike Price: $4000
Option price: 0.1 BTC
At the time of expiry the price of Bitcoin is $5000.

Your net profit can be calculated as:
=((BTC Price — Strike Price)/BTC Price) — Option Price
=((5000–4000)/5000) — 0.1
=0.2–0.1
=0.1

So when you first purchased the call option you paid 0.1 BTC to the seller. The option was worth 0.2 BTC at expiry so you then receive this amount into your account. Leading to your net profit of 0.2–0.1 = 0.1 BTC.

Put Example

You buy a put with the following attributes:
Strike Price: $4000
Option price: 0.1 BTC
At the time of expiry the price of Bitcoin is $3000.

Your net profit can be calculated as:
=((Strike Price — BTC Price)/BTC Price) — Option Price
=((4000–3000)/3000) — 0.1
=0.3333–0.1
=0.2333

So when you first purchased the put option you paid 0.1 BTC to the seller. The option was worth 0.3333 BTC at expiry so you then receive this into your account. Leading to your net profit of 0.3333–0.1 = 0.2333 BTC.

I’ve created a free Google sheet you can use to test some more examples of options profit and loss for yourself. Feel free to save a copy for to your own drive here:
Bitcoin Option Profit/Loss Google Sheet

Maximum Profit and Loss
As you may have guessed from the profit and loss formulas, buyers of options always have a maximum loss of the premium they paid for the option. As your risk is very well defined when buying, it makes this a much safer side of the trade to be on, particularly if you’re new to options. (Though selling does have other advantages that we’ll go into in another article)

Below is the maximum profit and loss for buying and selling either puts or calls. One interesting thing worth mentioning about the Deribit options in particular is the collateral used for these options is BTC. This means your collateral gains in value as the BTC price goes up, and loses value as the BTC price goes down. This leads to a difference in how the BTC profit/loss charts look compared to how a USD profit/loss chart would look for traditional stock options.

Breakeven Points
Contrary to what is quite a common assumption with people new to options, the breakeven point is not the strike price. This would of course only be true if the option had cost nothing at all. Thankfully the calculation is quite simple, and is the same for both buyer and seller.

Breakeven for a call = Strike Price / (1 — Option Price )

Breakeven for a put = Strike Price / (1 + Option Price )

As you can see you need to account for how much you pay for the option to determine the price at which you breakeven. As a buyer the more you pay for an option the further away from the strike price your breakeven price will be, and therefore the more price needs to move for your position to make money.

Some Reasons to Trade Options
1. When buying either a call or put option your risk is fixed to the price you paid for the option, no matter how much the price moves against you. With futures/spot your risk is not fixed, and even with a stop loss in place you can’t guarantee these will execute at the price you intend. Slippage is often an issue, particularly on violent moves.
This fixed risk feature of buying options of course has the benefit that you cannot be stopped out or liquidated. It is important to note though that this is NOT true when selling options.

2. Options are much more versatile in terms of what kind of position you can build. With futures/spot you either buy or sell and the price either goes in the direction you need it to or it doesn’t. With options you can still profit from those same movements, but you can also profit from sideways markets by for example selling straddles or strangles (we’ll go into more detail about this in future articles).

3. You can trade volatility using options without having to pick the direction correctly. If IV is high and you think it’s going to fall you can short both puts and calls, if IV is low and you think it is going to increase soon you can buy both a call and a put to benefit from an increase in volatility no matter which way it goes.

4. Option sellers benefit from the markets tendency to overestimate future volatility. This means implied volatility (on average) is slightly higher than realised volatility. Sellers get to capture this difference in the extra premium they charge. We’ll go into much more detail about this in future articles as well.

It’s not all good news though. When buying options you have a time limit for your trade to work out. If you buy a call for example and by the expiry date the price still hasn’t got up to your breakeven point, that’s it the trade is over.
If a future expires at the same price you bought it for your position will be break even (minus fees), however any options bought would have lost any extrinsic value they initially had.
When selling options your profit is limited to the premium you collected, you do not receive anything extra for being very right like you would with a futures trade.

Despite this options can be extremely useful instruments to trade in a variety of circumstances.

I wanted to keep this first article as simple as possible so we’ll save subjects like options pricing, volatility and multi leg positions for another day.

If you have any questions at all feel free to comment on here, hit me up on twitter @cryptarbitrage or in the Deribit telegram chat here: https://t.me/deribit

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