Introduction to options


Options for hedging

Consider the following scenario: you are a pension fund manager, X, who has long exposure to BTC, that has the current price of $45,000, and would like to hedge against any downticks in it, while still benefiting from the upside. As such, X buys from a counterparty Y, a cash settled put option contract, with strike price $40,000 and date 1/1/22 This fixes the delivery price and date that X desires. When Jan next year arrives, X can (i.e. has the option to) sell 1 BTC at $40,000 to Y, despite whatever the prevailing market price is. If the market price is greater than $40,000, then X would not want to exercise it, and instead abandon the contract.

Suppose the price of BTC on 1/1/22 is $30,420, then X can make a profit by exercising the option. Since the strike price is $40,000, Y has to pay X $9580 in cash . We call this a hedge because the payoff offsets the loss X incurs on the value of their long BTC position, which dropped from $45,000 to $30,420.

Cash settlement means that a stablecoin rather than the underlying (the BTC in this case) will be delivered at expiration. When the underlying is delivered we say that the option is physically settled. In the case of digital assets, the underlying may exist on a blockchain different from where the option contract lives, so settling the option in a stablecoin is needed.

Why would someone take the other side of the put contract initially? In options terminology, the other party is called the writer. The writer is willing to collect the price (also called the premium) of the option contract today from the pension fund manager in exchange for increased exposure to the downside risk of BTC in the future.

Now to introduce the traditional finance definitions of an option:

An option contract (usually just termed an option) gives the holder the right, but not the obligation, to buy (call) or sell (put) the underlying asset (underlier or underlying) at a predetermined price (termed the strike price) at (European) or before (American) the contract expires.

To summarize:

The two most common expiration styles of options are:American: the option can be exercised any time before or at expirationEuropean: the option can be exercised at expiration

The two most common payoff types of options are:call: the right to buy the underlier from the writer at the strike priceput: the right to sell the underlier to the writer at the strike price

Next, we introduce payoff diagrams which we’ll be using a lot to represent what an option contract (or combination of them) will be worth at expiry for a given spot price.

This is the payoff and profit function of a call option, they differ by the option premium.


Similarly, this is the same graph for a put option:


Later on in this series, we will see how the current price of the underlier influences the option premium. An option can be:

a) in the money: if the current price is higher than the strike price for a call, and if the current price is lower than the strike price for a putb) at the money: if the current price is equal to the strike pricec) out of the money: if the current price is lower than the strike price for a call, and if the current price is higher than the strike price for a put

For next time

In the next post, we’ll look at put-call parity, a basic notion in options pricing. Meanwhile, follow our progress on the Arrow platform at arrowdfms.com, @arrowdfms on Twitter, on Telegram, or on the Arrow Discord.