Options

Eva expects bitcoin to rise but does not want to commit to buying it immediately. A call gives her the right to buy at an agreed price in exchange for a premium paid upfront. A put gives her the right to sell and can help an owner worried about a decline. The underlying is what the right relates to; expiration is when it ends. An option is a derivative because its value comes from another asset. On the other side is the writer, the seller who accepts an obligation if assigned. Buying a put is therefore different from writing a call: Eva owns a right in the first case and would assume an obligation in the second. [1]

Before calculating anything, we need the quantity of underlying and the currency of the result. A standard equity option may cover 100 shares, although contract adjustments can change the deliverable. Exercising an option on futures can create a futures position, another contract with obligations of its own. For clarity, the examples below use our own fictional model for 1 BTC with linear cash settlement in USD. Here the price difference is multiplied directly by the quantity. This is not a particular exchange product or a universal formula for inverse or bitcoin-settled contracts. [1] [4]

In our model Eva pays a 2,000 USD call premium for a 60,000 USD strike. At expiration, an underlying price of 65,000 USD gives the right 5,000 USD of intrinsic value: the advantage over the agreed price. Subtracting the premium leaves a 3,000 USD profit before costs. If the price finishes at 61,000 USD, the right is worth 1,000 USD but Eva has lost 1,000 USD overall. Breakeven is 62,000 USD. “In the money” therefore means positive intrinsic value, not necessarily a profit. These are expiration outcomes; selling the option earlier involves a different market price. [2]

Consider a put instead, with the same 60,000 USD strike and a 1,500 USD premium for 1 BTC. At a final price of 55,000 USD its intrinsic value is 5,000 USD, leaving a 3,500 USD profit after the premium and before costs. At 60,000 USD or above this put expires worthless and the premium is gone. In our model, which assumes a non-negative underlying price, a fall to zero produces a maximum net option profit of 58,500 USD, not infinity. If Eva also holds bitcoin, the put can offset some of its loss. The option’s result is not the entire portfolio’s result, however; protection also costs money and eventually ends. [1]

Eva can lose the entire premium on a standalone, fully paid long option. A small premium does not mean a small probability of loss: all the money committed can disappear. This limit concerns the option itself before additional costs. If she exercises a different, delivery-settled contract and receives shares or a futures position, their subsequent losses are not capped by that premium. Distinguish the price of the right, the funds needed for settlement and the risk of what remains in the account afterward. Automatic exercise and instruction deadlines also depend on the broker and contract. [2] [6]

The writer receives money at the outset, but that is not the end of the trade. With an uncovered call, the writer promises performance without holding the necessary underlying. A sharp price rise can produce a theoretically unlimited loss, while the premium received is fixed. A broker may demand additional margin, collateral securing the obligation, or forcibly close the position. A later price recovery does not help if the trader ran out of collateral first. An expiration payoff diagram therefore leaves out the journey. The writer’s risk must not be confused with the buyer’s loss limit. [3]

Eva may sell her option before it ends if she finds a buyer; the selling price may not recover her original premium. Exercising instead triggers the agreed performance. That may mean a cash difference, delivery of shares or creation of a futures position. American style permits exercise before expiration; European style restricts it to the specified date. These names do not describe where the trader lives. Assignment allocates the obligation to a particular writer. With centrally cleared options, this need not be the person Eva originally bought from. Quantity, settlement and instruction cutoff are therefore part of what the contract means, not incidental small print. [4] [6]

Before expiration, the right also has value because further price movements remain possible. As time runs out, that opportunity shrinks; other things equal, this hurts a typical long call. Price also depends on Implied Volatility, the expected scale of fluctuations inferred from option prices, rather than a certain forecast. A decline in it can outweigh a favorable bitcoin move. For more advanced reading, Delta, Gamma, Theta and Vega estimate sensitivity to the underlying price, changes in that sensitivity, time and implied volatility. They depend on assumptions and change continually. The initial Delta cannot simply be extended across an arbitrarily large move. An option involves more than direction: the size of the move, timing and price paid also matter. [5] [2]