Module 8: Crypto Options
Call Options
Chapter 2 of 14 · about 5 minutes
2.1 Bullish, with a safety limit
Mint was bullish on Bitcoin over the next month but nervous after learning about liquidations in Module 7. "I want to profit if it rises, but I don't want to be wiped out by a sudden dip first."
"Then a call option might fit," said Hash. "You pay a fixed amount up front. If Bitcoin rises enough, you profit. If it crashes, or wicks down for a moment, you can't be liquidated. Your loss is capped at what you paid."
2.2 Buying a call
Bitcoin is at $100,000. Mint buys a $100,000 strike call expiring in 30 days, for a premium of $6,284. This option is "at the money" because its strike equals the current price (Chapter 4).
At expiry, the call is worth:
Call value at expiry = maximum of (price at expiry − strike, 0)
Profit = call value at expiry − premium paid
Break-even = strike + premium = $100,000 + $6,284 = $106,284
| BTC at expiry | Call value | Mint's profit or loss |
|---|---|---|
| $85,000 | $0 | −$6,284 |
| $100,000 | $0 | −$6,284 |
| $106,284 | $6,284 | $0 (break-even) |
| $110,000 | $10,000 | +$3,716 |
| $120,000 | $20,000 | +$13,716 |
| $130,000 | $30,000 | +$23,716 |
The shape of this payoff is the classic hockey stick: flat at a fixed loss below the strike, then rising one-for-one with the price above it.
"So BTC has to rise more than 6.3% just for me to break even," said Mint.
"By expiry, yes," said Hash. "That's the cost of the insurance against the downside. Buying options means you need to be right about direction and about the size and timing of the move."
Chapter 2 · The payoff of a call
Below the strike, a call buyer loses only the premium paid, a flat line. Above the strike, profit rises one-for-one with the price. The break-even is the strike plus the premium, so the call pays off only once the price exceeds that level.
2.3 Compared with spot and perps
Here's how the call compares with buying 1 BTC spot or opening a 1 BTC long perp at 10x, over the same 30 days.
| BTC at expiry | 1 BTC spot | 1 BTC perp at 10x ($10,000 margin) | $100,000 call ($6,284 premium) |
|---|---|---|---|
| $85,000 | −$15,000 | Liquidated: −$10,000 | −$6,284 |
| $95,000 | −$5,000 | −$5,000 | −$6,284 |
| $100,000 | $0 | $0 (before funding and fees) | −$6,284 |
| $110,000 | +$10,000 | +$10,000 | +$3,716 |
| $120,000 | +$20,000 | +$20,000 | +$13,716 |
Each has trade-offs. Spot ties up the most capital but can't be liquidated. The perp risks liquidation and pays funding. The call costs a premium that's lost if the price doesn't rise enough, but its maximum loss is fixed, and it can't be liquidated on a wick.
Notice also that a perp position can be liquidated by a temporary dip even if the price recovers by expiry. The call only cares where the price is at expiry, or what the option is worth when Mint sells it.
2.4 Choosing a strike
Different strikes offer different trade-offs.
| Strike (30 days, BTC at $100,000) | Premium | Break-even | Character |
|---|---|---|---|
| $100,000 | $6,284 | $106,284 | Moderate cost; profits from moderate rises |
| $105,000 | $4,246 | $109,246 | Cheaper; needs a larger rise |
| $110,000 | $2,765 | $112,765 | Cheaper still; needs a strong rise |
| $120,000 | $1,057 | $121,057 | Very cheap; needs a very large rise |
Cheaper calls look tempting because the potential percentage return is huge. But they're cheap because the market thinks the required move is less likely. Many traders lose repeatedly buying cheap, far out-of-the-money calls that expire worthless.
"So a $1,057 call isn't a bargain," said Node. "It's a long shot priced like a long shot."
"Usually," said Hash. "Cheap options are cheap for a reason."
2.5 Selling before expiry
Mint doesn't have to hold until expiry. If Bitcoin rises quickly, the call's market value rises, and Mint can sell it for a profit before expiry. If Bitcoin falls, Mint can sell it to recover part of the premium rather than risk losing all of it.
The value of an option before expiry depends not just on the current price, but also on time remaining and expected volatility, covered in Chapters 4 to 8.
2.6 Selling a call
The other side of Mint's trade is the call seller. The seller receives the $6,284 premium and takes on the obligation to pay the call's value at expiry.
| BTC at expiry | Seller's profit or loss on the $100,000 call |
|---|---|
| $85,000 | +$6,284 |
| $100,000 | +$6,284 |
| $106,284 | $0 |
| $120,000 | −$13,716 |
| $150,000 | −$43,716 |
The seller's maximum profit is the premium. Their potential loss grows as the price rises, with no fixed limit. That's why selling a call without owning the underlying, called a naked call, is one of the riskiest positions in options.
Selling a call while holding the underlying, a covered call, is very different, because the holding offsets the obligation. Chapter 12 covers this popular income strategy.
2.7 Calls as leverage with a cap on losses
A call can provide leveraged exposure. For $6,284, Mint gains about the same upside as owning 1 BTC above $106,284. But unlike leverage in perps, the loss is capped at the premium, and there's no liquidation.
The trade-off is that the premium is a certain cost if the price doesn't rise enough by expiry. In perps, you pay funding over time; in options, you pay the premium up front, and it shrinks with time (Chapter 8).
2.8 Try it yourself
On an options chain, find the 30-day BTC call closest to today's price and one about 10% above. For each, calculate the break-even price. Then calculate the profit or loss at expiry for each if BTC ends 5% lower, flat, 10% higher, and 20% higher. Which strike would you choose if you expected a 10% rise? A 25% rise?
Key takeaways from this chapter
- A call's value at expiry is the price above the strike, or zero; profit subtracts the premium.
- Break-even for a call buyer is the strike plus the premium.
- Call buyers have a capped loss and open-ended upside, and can't be liquidated by wicks.
- Cheaper, higher-strike calls need bigger moves and often expire worthless.
- Options can be sold before expiry; their value then depends on price, time, and volatility.
- Call sellers earn the premium but face open-ended losses on naked calls.
- Calls offer leveraged upside with a fixed maximum loss, paid for through the premium.