In the last chapter, we went through fundamental terms of options as well as some basic strategies. We are glad to see you here in this article because options trading has clearly drawn your interest!
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In the world of cryptocurrency, another popular derivative is Perpetual Futures. A futures contract is a binding agreement to trade a specific asset, such as bitcoin or ether, at a certain price and at a predetermined time in the future. Perpetual futures, as its name indicates, do not have an expiration date and the exchanges use special mechanisms (as we will discuss later, funding rate), to close the price difference between futures and spot prices. Perpetual contracts are popular because they are timeless and traders get the chance to perform either long or short trades without the constraint of the market condition. In addition, they can be highly levered - some exchanges allow users to borrow money and trade up to 100x leverage.
Options, in the meantime, provide some additional benefits that perpetual futures fail to offer. The high leverage of perpetual futures can be a double-edged sword - if the market goes against your initial expectation, even at a very small scale, the position can be liquidated forcefully and you can lose your entire fund. Even if the market eventually moves to align with your initial plan, you can no longer benefit because you have been knocked out.
On the other hand, if you own an option, which still can be highly levered as well, after paying the initial premium, you will never get knocked out as long as the contract is not expired. You still keep your chance of coming back, as long as the asset moves in your favor before expiration! Note that if you sell an option, you still have liquidation risk, but options do provide more flexibility for your investment needs.
Furthermore, if utilizing options tactically, you can isolate risk factors and make a profit in almost every imaginable scenario. You can benefit from the market's ups and downs, from the market going sideways, from volatility fluctuation, and from the passage of time, whereas you can only bet on market direction using futures. In summary, options are a more powerful and efficient tool for sophisticated traders. And we will show you how you can achieve these goals in the sections below.
In the previous article, we briefly mentioned the value of an option
Option Price = Intrinsic Value + Time Value
And in this section, we would like to go in-depth on how the market really prices the option of an asset and what affects the option price.
Intrinsic Value is fairly easy to explain - it is how far the option is in-the-money. For ATM or OTM options, the intrinsic value is simply zero.
Time Value is a little more difficult to understand than intrinsic value. It can be considered as the value of possible movement of the underlying asset price from now till expiration. And the exposure or the risk can be mostly broken down into factors below - any movements in each of the factors can impact the time value of the option, therefore changing the price of the option
The value of calls and puts is affected by changes in the underlying asset price in a relatively straightforward manner. As the underlying price becomes closer to (or further from) the strike price, the chance of the option becoming ITM and having positive intrinsic value gets higher (or lower), so the option price goes higher (or lower).
Generally, all else equal, when the asset price goes up, calls should gain in value, and puts should decrease; likewise, put options should increase in value and calls should drop as the asset price falls.
The effect of time is easy to conceptualize - a longer time frame offers the option owner higher chances to reach the desired outcome or provides longer protection. So the further away an option contract is from expiration time, the more value it usually brings to the option owner.
On the other hand, time can be the enemy of the buyer of the option because, if days pass without a significant change in the price of the underlying, the value of the option will decline. In addition, the value of an option will decline more rapidly as it approaches the expiration date. On the expiration date, the time value is totally diminished, leaving only intrinsic value.
The volatility used in an option's price may be the hardest concept for beginners to understand. It is defined as the uncertainty of asset return at a certain moment. However, it can't be estimated precisely. In practice, it relies on an estimator called Realized Volatility (RV), which looks at past actual price movements of the asset over a given period of time decided by traders, usually on a scale of days.
Option pricing models require the trader to input future volatility during the life of the option. Naturally, options traders don't really know what it will be and have to guess based on historical data and other inputs. These inputs form the core of Implied Volatility (IV), a key measure used by options traders. It is called implied volatility because it allows traders to determine what they think future volatility is likely to be. Apparently, the higher IV (or the expected future uncertainty) is, the more expensive the option will be, just as health insurance premium is always higher for riskier individuals who smoke and drink heavily, even though such individuals may not actually have health issues at the moment.
On a side note, traders can also use IV to gauge if options are cheap or expensive. It is more useful than price as it neglects strike, time to expiry, and all other inputs, allowing traders to compare among different contracts. You may hear option traders say that premium levels are high or that premium levels are low. What they really mean is that the current IV is high or low.
Like most other financial assets, option prices are influenced by prevailing interest rates. Oftentimes, Risk-Free Rate, such as the short-term U.S. Treasury Bill (T-Bill) rate, is used as the benchmark, because T-Bills are extremely safe and its rate is very easy to observe. Call option and put option premiums are impacted inversely as interest rates change: calls benefit from rising rates while puts lose value because rising rates can be seen as decreasing present underlying prices. The opposite is true when interest rates fall.
Notably, in the world of cryptocurrency, the interest rate risk profile is a bit different from the traditional financial asset. The interest rate is decided by futures price at each expiration and perpetual price. Futures prices can be seen as investors' desired underlying prices at each expiration, given the current spot level. The higher the difference between futures and the underlying price (also called Futures Premium), the higher the interest rate will be.
In the SignalPlus Toolkit, we provide Forward Curve tool to display interest rates at different expirations. You can find all the information including futures price, index price, perpetual price, and interest rate easily.
Another interesting thing to know is that the underlying price is not denoted by the crypto index. Instead, it is replaced by a special kind of futures called Perpetual which never expiry! It works in a special way to stay around the crypto index as close as possible by Funding Rate.
When a gap exists between the crypto index and perpetual futures, the funding rate is adjusted by the exchanges to reduce (even eliminate) the arbitrage opportunity, thus closing the gap.
To elaborate, assuming perpetual is above spot price and the funding rate is 0.01% at the moment, this means individuals with long positions need to pay individuals with short positions, for 0.01% of the position sizes, each funding period (usually every 8 hours). By applying such a mechanism, traders are incentivized to close their long positions or open short positions, so the perpetual price would come down to the spot price. In the opposite scenario, the funding rate would be negative and short positions pay long.
After all the concepts we learned previously, we now have a good understanding of how each factor influences option price qualitatively and directionally. But how does the price of an option change quantitatively as these variables change? If volatility goes up by 2%, how much does your call go up? If the asset increases by $10, how much does mine go down? The Greeks offer an answer to these questions by measuring the sensitivity of an option’s price to changes in the input parameters. Below we will go over some of the common and useful Greeks in detail.
Option Delta is perhaps one of the most vital measurements of all, as it can measure the sensitivity of an option's price to a change in the underlying asset price. It indicates the amount of an option price should move based on the change in the underlying asset, given all other factors stay the same. Mathematically, it is the first derivative of the value of the option with respect to the underlying price.
For example, if a call has a delta of 0.85 and the token goes up $1, in theory, the price of the call will go up about $0.85. The range of delta is between -1 and 1, where calls have a positive delta (between 0 and 1) and puts have a negative delta (between -1 and 0).
Another way to think about the absolute value of delta is a rough estimate of the probability of the asset ending up in the money at expiration. Please note that this is not perfect math but a frequently used synonym for probability in the options world. Usually, the ATM option will have an absolute value of delta 0.5 (call with 0.5 deltas and put with -0.5 delta), because there is a 50/50 chance the option will wind up in- or out-of-the-money at expiration.
As an option contract becomes more in the money, the probability of the option finishing up in the money at expiration gets higher, so the absolute value of delta approaches 1. In contrast, as an option contract gets more out of the money, the probability of the option finishing up in the money at expiration gets lower, so the delta goes to 0. In other words, when an option gets very deep in the money*,* it will begin to trade like the underlying asset, moving almost dollar-for-dollar with the underlying price. Meanwhile, far-out-of-the-money options won't move much in absolute dollar terms.
In addition, we can apply delta not only on a single position but also on a complex portfolio with the same underlying asset - simply taking the sum of the deltas for each individual position. In addition, the delta of owning an asset is always 1 because the price of the asset always moves (obviously!) 1:1 to a change in the underlying asset price. Therefore, a trader can create a Delta-Neutral portfolio (meaning the total delta of the portfolio is 0), using options and their corresponding underlying asset, such that positive and negative deltas offset. In this case, the portfolio's value can be relatively insensitive to changes in the price of the underlying asset, and be more dependent on the exposure of other factors (such as time to expiry and IV).
In SignalPlus Toolkit, we provide an automatic delta-neutral method. By ticking on Delta Exchange (another expression of Delta Neutral), perpetual will be added into the selected portfolio to make the whole portfolio zero deltas. Below is an example of how the portfolio payoff changes from left to right through checking Delta Exchange.
Delta tells us the sensitivity of the option price to a change in the underlying asset price. However, as the underlying asset price further deviates from the initial point, the delta is also shifting. This is due to the fact that any movements in the underlying price would impact the probability of the option ending up ITM, thus changing the delta.
Unfortunately, this shift is not linear. To better estimate the option price movement in a larger underlying price range, Gamma is introduced as the rate of the change in the delta for an option as the underlying price changes. Since it measures the sensitivity of the first-order Greeks (such as Delta, Theta, and Vega), it is also known as one of the second-order Greeks. Mathematically, it is the second-order partial derivative of the option price with respect to the underlying price.
Positive gamma means that as the underlying rises, the option’s price will be more sensitive to further underlying changes. Negative gamma means the opposite: underlying price rises cause options to be less sensitive. Gamma is the largest approximately at the money and diminishes the further out the option goes, either ITM or OTM.
When a trader tries to establish a delta-hedge strategy for a portfolio, the trader may also seek to neutralize the portfolio's Gamma, as this will ensure that the hedge will be effective over a wider range of underlying price movements.
Theta represents the sensitivity of the value of the option to the passage of time. And this number shows the dollar amount that an option premium should decrease as a result of time decay. Theta is almost always negative for long positions as times only move in one direction. Apparently, theta is good for sellers and bad for buyers, because as the clock is ticking, the value of the option diminishes continuously until it expires.
In general, the further out in time you go, the less impactful the time decay will be for an option. Another way of saying this is that the time decay accelerates closer to expiration. So through reviewing theta, traders could pick the proper tenure of the options based on their strategies.
Vega is a measure of an option's sensitivity to changes in implied volatility. As IV is derived from option price under current market conditions, any changes in IV are also a reflection of changes in market expectations.
As we discussed before, for long option positions regardless of calls or puts, the value of the contracts increases as IV increases, because buyers will have more chance to be ITM and make more profit while sellers want to be compensated more for elevated future risk. So vega is always positive for long option positions.
Historically, IV tends to mean reverting to RV, so some short-term IV deviation could produce a correcting movement in the near future. Traders could make bets on this most efficiently by constructing a portfolio with high vega (usually near the money) while managing other risks.
Rho is the amount an option value will change in theory based on the change in interest rates. However, please note that even though rho is one of the primary inputs in option pricing, it generally has a very minor impact on the pricing of the options.
In the last chapter, we discussed the five most commonly used Greeks in option trading, delta, gamma, theta, vega and rho. Traders usually measure these Greeks to gauge their positions' risk. As we mentioned before, if a trader doesn't want the portfolio value to change along with the underlying price, he or she would adjust positions to make the total delta zero. This action is called Delta Hedge or Delta Exchange. Another example is that if a trader believes the volatility is about to go up, he or she would want portfolio's vega to remain positive.
However, even when these five Greeks are in good positions, traders are also worried how these Greeks would change when the market changes. In some cases, they may lose their desired risk exposure again. Thus, higher ordered Greeks were introduced to assist traders to measure how fiercely delta, gamma, vega, etc. can change and how soon they would need to readjust positions again. Furthermore, these risk factors take into consideration how directional, time to expiry, volatility, interest rate interact with each other. Traders would also want to see these interactions, like how implied volatility influences delta.
**Volga (also known as Vomma) is a second-order Greek. It tells us the sensitivity of vega to the change of the implied volatility of the underlying asset. A positive volga means that the vega increases when the volatility increases; a negative volga means that the vega decreases when the volatility increases. Similar to vega, vomma is positive for long positions and negative for short positions.
Vega provides a good estimate of the relationship between price and volatility, in a narrow interval. By combining vega and vomma, traders can estimate the price movement more accurately, especially for larger changes in volatility. The relationship between vega and vomma is similar to the relationship between delta and gamma in this sense.
Vanna is another second-order Greek derived from the delta. It tells us the change in delta for any changes in the level of the implied volatility of the underlying asset. It can also be understood as the change in vega for any changes in the underlying price. This concept is introduced because delta and vega will change depending on both underlying price moves and IV shifts.
OTM call and ITM put options have positive vanna, and OTM put and ITM call options have negative vanna.
Vanna is extremely important for a market maker who manages inventory across multiple strikes, expirations, and underlying tokens. However, for the average investor who speculates on the simple movement of the market and only owns a few options at a time, it is much less relevant.
Charm is a second-order Greek measuring how much delta will change as time passes by. It is mostly useful to decide how much positions' delta will change after a certain period. Thus, Charm is also called Delta Bleed or Delta Decay.
As time passes, OTM delta approaches 0 and ITM delta becomes more and more like the underlying, meaning ITM call delta approaches 1 and ITM put delta approaches -1. This leads to the conclusion that ITM call and OTM put have positive charm while OTM call and ITM put have negative charm.
Zomma is a third-order Greek measuring how much gamma will change as implied volatility changes. It is usually used in a gamma-hedged portfolio to anticipate the degree of influence implied volatility can have on the hedge effectiveness.
Speed is also a third-order Greek measuring how much gamma will change as the underlying price changes. Similar with zomma, it is also used in gamma-hedged portfolio but to anticipate the influence of underlying price change on the hedge effectiveness. There is one thing to be noted here: We know that Gamma itself measures how much delta will change as the underlying price changes. So the ultimate purpose of using speed is to control Delta.
In SignalPlus Toolkit, we further divide speed into speed+, speed-. Mathematically speaking, these Greeks are calculated using infinite small underlying price movement, implied volatility change, etc. However, in real market, infinite small steps are unachievable. This means the up movement and down movement may lead to different changes and different Greeks. For lower order Greeks, the difference is small. But when it comes to a third order derivative all on underlying price, the difference can be quite large. So when gauging the influence of underlying price increase and underlying price decrease, it is better to use different speeds called speed+ and speed-.
For the same reason, we also provide Gamma+ and Gamma- for users to choose based on their own needs.
Option Greeks quantitatively measure changes in underlying asset parameters and determine the value of an option contract. They include almost every aspect of option pricing, such as price movement, loss of time value, volatility fluctuation, etc. With this tool, traders can make well-informed decisions about options trading while understanding the risks involved.
There are definitely more Greeks that can be useful for traders, but what we have shown above is the most common ones that a lot of people refer to every time they do trades. The math behind the Greeks may be cumbersome, but fortunately, some of the Greeks are readily available for you to use in SignalPlus Toolkit. And you can even isolate your return and risk by different Greeks.
In this chapter, we covered a good deal of intermediate knowledge of options. After reading, you should be able to understand the pricing of the options and the Greeks affecting the value of the options.
In the next chapter, we will show you all the built-in strategies in SignalPlus Toolkit, so you can start making profit efficiently and/or hedging risk effectively.
In the last bonus section regarding the history and development of options, we briefly mentioned Black-Scholes Model, which is used to derive a theoretical price for standardized options. Since it is one of the most important concepts in modern financial history and one of the best ways to price options contracts, we are spending more time here to show you the details behind it.
The key assumption of the model is that financial instruments, such as stocks, tokens, or futures contracts, will have a lognormal distribution of prices following a random walk with constant drift and volatility. This means changes in asset prices are independent of each other and the historical trend does not predict future movement. Factoring in other important variables, the equation can derive the price of a European-style call option.
As we saw in the section How are Option Priced, there are 5 input variables needed to calculate the value of an option: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.
Knowing the variables, the Black-Scholes call option formula is calculated by multiplying the stock price by the cumulative standard normal probability distribution function. Thereafter, the net present value (NPV) of the strike price multiplied by the cumulative standard normal distribution is subtracted from the resulting value of the previous calculation.
In mathematical notation
However, this model does have some drawbacks, as it is intended to work under extremely tight scenarios. In the real world, especially in the cryptocurrency market, these conditions may not hold true. As stated previously, the Black-Scholes model is only used to price European options and does not take into account that U.S. options or exotic options have different expiration/exercise mechanisms. In addition, considering the early stage of the cryptocurrency market, the transaction costs are not negligible - in fact, the commission and gas costs could be excessive; and there are certain riskless arbitrage opportunities among different CEX and DEX, due to low liquidity in the market from time to time; not to mention the market is heavily event-driven and people's expectation of volatility is constantly changing. All of these instances can deviate theoretical prices from the real world.
Regardless, the model is still exceptionally useful for estimating the value of an option in most cases. Most market participants customize the model with adjustments, which usually relax and generalize the assumptions in many directions, to conclude a fair price under different market circumstances.
