Meet the Greeks: Options Basics and Daily Break-even

Options trading is a complex financial activity  that  involves  various  risk measures and factors affecting the pricing of options. One such set of measures, known as the "Greeks," is a vital concept for traders looking to understand the behavior of options in different market scenarios. The Greeks are so named after the Greek letters that  denote  them,  including  delta, vega, gamma and theta. These measures help traders assess the potential risk and reward of options positions, and their understanding is essential to making informed decisions when trading options strategies. In this report, we will give a brief explanation of these Greeks, creating an understanding of the price sensitivity of options to changes in the underlying asset  price.  We  will  explore  their definitions, properties, and implications for options trading. Finally, we will explain  how  Daily  Break-even  is calculated and why it is an important measure for the day trader/ gamma scalper.

Delta

Delta is a measure of the change in value of an option given a change in the underlying futures contract. This tells the trader how much the price of an option will change as the contract moves up or down. Option deltas are expressed as a value between 0 and 1.0 for calls, and as a value between 0 and -1.0 for puts. Delta also is used as a measure of the probability that a given option will expire in the money. At the money options have a 0.5 delta, that is a 50% probability of expiring in the money. Options that are out of the money will have a delta less than 0.5, while options in the money will have a delta greater than 0.5.

Delta proves helpful when determining directional risk. Long market assumptions are generally referred to as positive deltas and conversely, short market assumptions will have negative deltas. Delta is most useful to a trader when determining the number of option contracts required to hedge a position.

Vega

Vega is a measure of an option's price sensitivity to changes in implied volatility, whereas implied volatility is the market's expectation of how much an asset's price will fluctuate in the future. Vega measures the change in the option's price for every 1% change in implied volatility. Both call options and put options will increase in value when implied volatility rises. The Vega value is higher for options with a longer time to expiration since they are more sensitive to changes in implied volatility. As the expiration date approaches, the Vega of an option decreases, as the impact of implied volatility changes diminishes.

Similarly, when the underlying asset moves closer to the option's strike price, the Vega value increases, indicating a more significant impact of implied volatility changes on the option's price. Vega is an essential risk metric for options traders as it helps them understand the impact of volatility on the option's price. The higher the Vega, the more significant the impact of changes in implied volatility.

Gamma

Gamma is a measure of the rate of change in delta given a change in the underlying futures contract. Gamma is an important concept in options trading because it helps traders understand how much an option's delta will change in response to changes in the asset's price. High gamma values indicate that an option's delta will change rapidly in response to small movements in the underlying, while low gamma values suggest that an option's delta will change more slowly. This information is crucial for traders who use delta-hedging strategies to manage their risk and maximize their profits. By monitoring gamma values, traders can adjust their positions accordingly and ensure that they are properly hedged as price moves. Owning gamma enables the trader’s position to get long as futures rally and short as they move lower. Gamma will accelerate as time to expiration increases, as small changes in the underlying have a greater impact on delta changes. Regardless of the contract being a put or call, long positions will have positive gamma while short positions will have negative gamma.

Theta

Theta is a measure of the rate of decline in the value of an option over time. It gauges time decay and represents the amount by which an option's price will decrease each day. As an option approaches its maturity date, it loses value due to time decay, and the closer it gets to expiration, the more its value decreases. Theta is always negative because the time-related portion of an option's premium always decreases. This cost to own options will be relatively low on long dated options and will accelerate as expiration approaches – with passing time, the chance of an out of the money option expiring in the money decreases.

Therefore, traders need to consider theta when trading options, particularly if they hold options for longer periods. As theta can erode the value of an option over time, traders should take appropriate steps to hedge against this risk and maximize their profits.

Daily Break-even

For a gamma or day trader who may take less bets on vol or direction, one of the most important metrics to track is the daily break-even of a delta hedged portfolio. When you purchase an option, your exposure to the underlying increases as the stock moves away from its previous hedging level. This increase in exposure is proportional to the magnitude of the futures movement – if the futures rally, you become long and earn profits on the deltas you own. This positive outcome is due to the "convexity" of the option, which is directly related to gamma. This convexity operates in both up and down markets, meaning that you are not sensitive to market direction. However, to benefit from the option's convexity and earn profits when the futures move, you must own the option, and its value decreases every day due to theta. The erosion of the option is inversely proportional to gamma and is the “cost” a trader pays for the potential profits resulting from the option's convexity. So how can a trader know when to hedge their gamma effectively, making a profit despite the cost to own?

First, we must understand why volatility is proportional to time. The reason for this relationship has to do with the nature of randomness. When you look at the price of an asset over a short period of time, it may appear to be fairly stable. However, over a longer period, there  are more opportunities for unexpected events to occur that can cause the price to fluctuate wildly. Volatility is driven by random shocks to the system and as the time horizon increases, the number of these shocks increases as well, but their impact on volatility decreases at a rate proportional to the square root of time. This means that while volatility may increase as time horizon increases, it does so at a decreasing rate. Another means of defining volatility is as standard deviation.

Referencing Black-Scholes, when the underlying daily move reaches one standard deviation, gamma profits should offset theta losses, all else being equal. Arriving at this daily percentage is a matter of converting the annualized implied volatility to daily terms. Remembering that volatility is proportional to time, you can easily convert annual volatility to daily volatility by dividing it by the square root of the number of trading days per year. Assuming 365 trading days per year for BTC & ETH, we convert annual implied volatility to daily volatility by dividing it by the square root of 365(19.1).

For example, if BTC ATM Vol is 57.5%, we simply divide 57.5 by 19.1 = 3.01%. At an underlying price of $28,332, calculating break-even:

$28,332*3.01% = $850. This need not be only one direction but is the amount the trader needs to “ride” their gamma and capture to reach the break-even threshold versus daily theta.

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