# Options 101

Options can be intimidating, so we've put together an introduction to help you get acquainted with what they are, how they're priced, and how you can use them as part of a sophisticated trading strategy.

Options are immensely powerful financial instruments. Buyers of options can hedge their portfolios, generate leveraged upside returns, or simply cheaply get upside to an asset, all with limited downside. Sellers of options can generate high returns on their investments by selling both calls and puts, generating yield that is unmatched elsewhere in the world of finance. This is why options are a multi-trillion dollar market in traditional finance, with options traders often driving the movements of the stock market generally.

# Terminology

**Options**

An option gives the holder the right to buy or sell a particular asset at a specified price (the **strike price**) for a certain period of time. There are two kinds of options, calls and puts. **Calls** allow the holder to lock in a price at which to buy the asset. **Puts** allow the holder to lock in the selling price. You buy calls when you think the asset will go up, and you buy puts when you think it’ll go down. Options don’t last forever, though, they have an **expiration date**. After this date, the holder can no longer buy or sell the asset at the strike price and the option is worthless.

Options can have many different strike prices, and many expiries, giving traders a variety of potential hedging solutions. Let's introduce an imaginary asset called JaguarCoin (JAG), that promises to fund jaguar conservation by using DAO funds to flip used Jaguar cars.

If JAG coin is trading at $100, it may have options available which expire at the end of January, February and March, for strikes ranging from $50 to $150. The further away from the current price a strike is, the more expensive or cheaper options get, depending on whether they are ‘in the money’ or ‘out of the money’.

**In, At, or Out Of The Money**

Traders talk about options in three groups, ‘in the money’ (ITM), ‘at the money’ (ATM), and ‘out of the money’ (OTM).

**In the money**: options which currently give you the right to trade the asset at a better price than the current price.

For calls, it’s options with strikes that are lower than the asset price. (e.g. the JAG $80 call, if JAG is trading at $100).

For puts, it’s options with strikes that are higher than the asset price (e.g. the JAG $120 put, if JAG is trading at $100).

**Out of the money**: options which currently give you the right to trade the asset at a worse price than the current price.

For calls, it’s options with strikes that are higher than the asset price. (e.g. the JAG $120 call, if JAG is trading at $100).

For puts, it’s options with strikes that are lower than the asset price (e.g. the JAG $80 put, if JAG is trading at $100).

**At the money:** options with a strike price which is equal or close to the asset price. This often includes very slightly ITM and OTM options, since it’s rare for an asset to exactly equal a strike. For example the $100 strike if JAG is trading at $100.

# Payoff Graphs

Continuing the JAG token example from the previous section (trades at $100) we introduce the concept of a payoff graph. Payoff graphs are a great instrument to help gain an intuitive feel for options. We'll first example the payoff graphs that represent the potential profit or loss (P/L) for vanilla long/short asset positions. For example, if you are long an asset (such as ETH), the P/L graph is as follows:

You can see that your risk is proportional to how many tokens you buy. Buying 5 JAG tokens will mean that you make or lose $5 for every one dollar move in the token price. The maximum gain from being long a token is potentially unlimited, the maximum loss is the amount you purchase the token for.

Instead of buying first, and selling later, you can sell first and hope to buy back the token at a lower price, this is known as short selling (or shorting). The payoff graph for shorting is as follows:

The maximum gain for a short token position is the amount you sell the token for. The maximum loss is unlimited, as the price of a token can rise forever. Note that these payoffs are the inverse of a long token position. For example, Alice can borrow JAG tokens for $100, and sell it in the market. If the price falls to $90, Alice can buy it back, return the tokens to the person she borrowed them from whilst banking $10 in profit.

# Options Pricing

The three biggest factors that determine the price of an option are:

**Price**- the token price relative to the strike price.**Time**- the amount of time remaining until expiration.**Implied Volatility**- how much the token is expected to move until expiration.

**Price**

If **an option is in the money, then it is said to have intrinsic value**. For example, the $80 strike call for an asset worth $100 can be immediately exercised to realize a $20 gain. When you buy this call, the $20 intrinsic value is baked into the price of the option (you don’t get it for free).

**Time**

The more time to expiry, the more time there is for the token to move and the more expensive the option is. **The price of an option is strictly increasing with respect to time.**

**Implied Volatility**

The implied volatility (IV)* *of an asset expresses **how much the asset is expected to move until expiration as a percentage**. The *higher* the IV of an asset, the *more* it is expected to move, and the more expensive options are. Similarly, if IV is low, options will be cheaper. Since the price of an asset and the time to expiry are publicly available inputs,* ***the IV of the asset is the biggest driver of pricing differences between options traders**. Volatility is described in more detail in the next section.

# Volatility

Volatility is a measure of how much something moves. When traders discuss volatility, they’re referring to one of:

The price swings of an asset (market volatility)

The implied volatility of options (IV)

**Historical Volatility**

The market volatility of an asset is a result of the observed day to day swings in price. This is volatility that is in the past, and is why we say things like ‘crypto is a volatile asset class’ and ‘bonds are stable, safe yielding assets’. This is referred to as **‘historical’ or ‘realized’ volatility**.

With assets, historical volatility is a measure of how much the price changes over a given period of time. If an asset is expected to move 2% per day, and instead moves 10%, it would be referred to as having realized ‘high volatility’. Similarly, if an asset normally moves 5% per day, and only moves 2%, it would be realizing ‘low volatility’.

**Implied Volatility**

On the other hand, **implied volatility** is the market’s expectation of how much an asset will move, and is reflected in the price of options expiring in the future. This is effectively an estimate - the market can guess that an asset will move 10% over the next month, but it might move 50% (or not at all). An option with an implied volatility of 50% is saying that the underlying asset is expected to trade within a 50% range (high to low) within the next year.

Continuing our example of a JAG token which trades at $100 and has an IV of 50%. Options markets are therefore implying that JAG could move up or down 50% over the next year, creating an expected range of $50-$150. A good rule of thumb is to take the IV of an asset and divide by 20 to attain the average expected daily move. For example JAG (50% IV) is expected to move 50/20 = 2.5% per day. This means an asset with 20% IV is expected to move 1% per day, and an asset with 100% IV is expected to move 5% per day.

# Option Strategies

An overview of basic options strategies you can execute on Lyra.

# Long Call

You think the price of the asset is going up.

If Alice pays $5 to buy the JAG June 30th 110 call option, she is buying the right to pay $110 for one JAG token on or before June 30th. The $5 she pays is called the **premium**. Let’s compare the outcomes of buying one of these calls for $5 to buying JAG for $100. We'll examine three scenarios that could occur on June 30th:

The price of JAG rises to $130.

The price of JAG remains at $100.

The price of JAG falls to $70.

**Scenario 1:**

If Alice had bought one JAG for $100, she would make $30 on her investment (+30%)

If she had bought the June 30th 110 call for $5, she can purchase the coin for $110 and sell it for $130, netting $15 profit. Factoring in the $5 cost of the option, she has profited $20 - $5 = $15, making for a 300% (!!) return on her investment.

**Scenario 2:**

If Alice had bought one JAG for $100, she would be flat (price unchanged).

If she had bought the call for $5, so she would lose $5 (-100%). The option is worthless as the strike is greater than the token price.

**Scenario 3:**

If Alice had bought one JAG for $100, she would lose $30 (-30%).

If she had bought the call for $5, she would lose $5 (-100%).

These scenarios illustrate a couple of key points about options:

They are great sources of leverage: In Scenario 1 Alice makes a return 10x greater than had she simply purchased JAG

They protect buyers from downside: In Scenario 3 Alice only lost $5 compared to losing $30 had she bought the token. Note that she still retained the upside in the case that JAG had increased in value.

They do poorly when the price of asset doesn’t move much: In Scenario 2, Alice loses her entire investment (-100%) compared to being flat had she bought the token.

When you own a call your upside is unlimited (since stocks can go up indefinitely), and your downside is capped at the price you paid for the call.

**Why trade it?**You think the asset is going up within a certain time frame.**Optimal conditions?**Cheap volatility, bullish asset.**Example**: Buy 10x September 100 Call for $5.**Cost**: The premium you pay, in this example 10 x $5 = $50.**Theoretical Max Profit**: Unlimited. It’s not likely an asset will go to infinity, but it’s theoretically possible.**Theoretical Max Loss**: The price you paid for the call, in this example $50.**Breakeven at expiration**: The strike plus the price you paid for the call (100 + $5 = $105).

# Long Put

You think the price of an asset is going down.

Let’s re-run the three scenarios described in the previous section, this time comparing the purchase of the JAG June 30th 90 strike put for $5, against short selling one JAG token. Reiterating, the scenarios are:

The price of JAG rises to $130.

The price of JAG remains at $100.

The price of JAG falls to $70.

**Scenario 1:**

If Alice had short sold one JAG for $100, she'd lose $30 (-30%).

If she had bought the put, she would lose the $5 premium as the asset price is greater than the strike price (-100%).

**Scenario 2:**

If Alice had short sold one JAG for $100, she would remain flat.

If she had bought the put, she would lose the $5 premium paid for the put (-100%).

**Scenario 3:**

If Alice had short sold one JAG for $100, she'd make $30 (+30%)

If she had bought the put, she could exercise the put to sell JAG at $90 and buy it back for $70. After factoring in the put premium, this is a profit of $15 (+300%).

**Why trade it?**You think the asset is going down within a certain time frame.**Optimal conditions?**Cheap volatility, bearish asset.**Example**: Buy 10x September 100 Put for $5.**Cost**: The premium you pay, in this example 10 x $5 = $50.**Theoretical Max Profit**: If the asset goes to zero, you make the difference between the strike and zero, minus the premium you paid, (100 - $5) x 10 = $950.**Theoretical Max Loss**: The price you paid for the put, in this example $50.**Breakeven at expiration**: The strike minus the price you paid for the put (100 - $5 = $95).

# Covered Call

**Covered calls versus naked short calls**

In a sentence: a covered call writer owns the underlying asset, and a naked short call writer does not.

A covered call differs from a '**naked short**' call, where the option is partially collateralized by cash (and *not* the underlying asset). To write a covered call the writer must first purchase the underlying asset, which means they are *long* the asset itself. The accompanying short call position offsets this somewhat, but unless the call is 100 delta, the option seller remains net long the underlying asset (whereas they would be net short with a short call position).

**Why trade it?**You think an asset is going up, is going to trend sideways, or take a small dip in price.**Optimal conditions:**Lower realized volatility than IV, small bullish to sideways asset.**Example:**Long 1 ETH for $2000 against short a 2500 strike call for $300 with 30 days to expiration.**Cost:**Share of asset, less premium received for call ($2000 - $300 = $1700).**Theoretical Max Profit:**The maximum profit occurs when the price of the asset rises to the strike price on expiration, so the call you sold is worthless and your asset appreciates in value. In this example, if ETH rose from $2000 to $2500 on expiration the profit would be $800 ($2500 - $2000 + $300).**Theoretical Max Loss:**If the price of the asset goes to 0, you lose the amount you paid for the asset less the call premium. In this example it would be $1700 ($2000 - $300).**Breakeven At Expiration:**The asset price minus the premium collected ($2000 - $300 = $1700).

# Cash Secured Put

**Why trade it?**If you think a stock is going up, staying where it is, or only going down a small amount.**Setup:**Sell a put short, post the strike price as collateral (in cash)**Example:**Selling the ETH 2000 put expiring in 15 days for $150.**Cost:**The collateral posted minus the premium received from the put ($2000 - $150 = $1850).**Max Profit:**The premium received for the put ($150).**Max Loss:**The difference between the strike price and zero, minus the premium received for the put ($2000 - $0 - $150 = $1850).**Breakeven at expiration:**The strike minus the premium received ($2000 - $150 = $1850).