Understanding Option Greeks for Trading

Today I'm going to help you master your understanding of the option Greeks using helpful visualizations, examples, and logical explanations when possible. The option Greeks are essential to learn as an options trading beginner because they inform you of the risks that your option positions are exposed to. The first option Greek you need to understand is called Delta and Delta predicts an options price change relative to a $1 shift in the stock price. In essence, it's the sensitivity of your options price relative to changes in the stock price. We can visualize delta by using an options pricing calculator plotting the call prices at various stock prices. So consider a call option with a strike price of $200 and 90 days until expiration. As you'll see the call price increases when the stock price rises and the call price falls when the stock price declines. This is because call options have positive deltas and that means that the call options price will move in the same direction as the stock price. Let's say you have a call option with a delta of positive 0.5. This implies that if the stock price goes up by $1, your call option will experience a 50 cent price gain. Conversely, if the stock price goes down by $1, this call option should lose about 50 cents. Let's look at a real life example using Apple data. In this Apple call chart, note the relationship between the stock price, the price of the $1.35 call, and the call's delta. Initially, the call's delta was approximately 0.47, suggesting the call's price would change by about $0.47 for the initial $1 changes in the stock price. When Apple shares rose from $132 to $136, an increase of $4, the call's price climbed from around $7 to $9, or a $2 increase. And this is consistent. with that positive 0.47 delta that the call had at the beginning of this period. Now put options have negative deltas and this means that their prices move in the opposite direction as the stock price. So if the stock price goes up a put options price will fall and if the stock price goes down a put options price will increase. And again we can visualize this using an options pricing calculator to plot the put option price at various stock prices. So here we see the put options price is increasing as the stock price goes down and the put options price is decreasing as the stock price goes up and this visualizes negative delta call option deltas can range from zero to positive one and put option deltas can range from zero to negative one so an options price can only be as sensitive as a share of stock itself but option deltas do not remain constant they do change and this brings us to our second option greek to understand which is called gamma Gamma is the option Greek that estimates how an option's delta will change given a $1 shift in the stock price. So as delta is predicting how the option's price will change given a $1 shift in the stock price, gamma is predicting how the option's delta will change when that stock price movement occurs. Let's go back to our earlier Apple example to visualize this. In this example, you'll see the call's delta rising alongside the stock price. Gamma predicts this rate of change, estimating the adjustment in an options delta for a $1 movement in the stock price. Consider a call with a delta of 0.5 and a gamma of 0.05. Here, if the stock price increases by $1, the call's delta would become a positive 0.55. Conversely, if the stock price drops by $1, the delta would decrease to a positive 0.45. So what this means is, if you own a call option and the stock price increases, Your new call option delta is going to be higher than it was before and therefore your options price will be more sensitive to changes in the stock price compared to when the stock price was lower. And conversely, if you own a call option and the stock price falls, your call option is going to become less sensitive to changes in the stock price than it was before. The opposite is true for put options because a put options delta will get closer to negative one as the stock price falls, meaning its price will become more sensitive to changes in the stock price. And if the stock price increases, put option deltas will move towards zero, which means they will become less sensitive to changes in the stock price than they were before. In the Apple example, the call began with a delta of positive 0.5. indicating a 50 cent change for each $1 shift in the stock price at the beginning of the period. However, by the end of the period, the call's delta was positive 1, suggesting a $1 change in the call price for each $1 shift in the stock price. And this implies that the call option is behaving more like shares of stock, because if the stock price rises by $1 and the option price rises by $1, this means that the option is trading just like shares of stock. And this is expected because in the Apple example, the stock price far exceeded the call's strike price at the end of the period. And this indicated a high likelihood that the call option would expire in the money. And when a call option expires in the money, it becomes 100 shares of stock. And so what that means is this call option was starting to trade like what it would become. And that's because with a stock price way above the strike price, this call option had a high likelihood of becoming or expiring in the money and converting into shares of stock. and so before the call option even became shares of stock it started to trade like what it would become i hope that makes sense in this sense we can understand delta as the probability of an option becoming shares or expiring in the money if an option has a low delta or close to zero it has a small probability of becoming shares and will behave less like them or be less sensitive to changes in the stock price conversely if an option has a high delta meaning it is close to positive or negative one It has a high probability of becoming shares at expiration and therefore it will trade much more like shares of stock experiencing a one dollar change in the option price for a one dollar change in the stock price. So if we interpret delta as the estimated probability of an option expiring in the money which it sometimes is used as that proxy then we can understand gamma as the change in the options probability of expiring in the money as the stock price changes. So for example, if we have a call with a delta of 0.5 and a gamma of 0.05, this tells us that if the stock price goes up by $1, the delta is going to increase to 0.55, indicating a higher chance of expiring in the money at expiration. This makes sense because if the stock price is increasing towards that call option strike price or even above it, that means that the probability of the stock price being above that call's strike price is 0.55. at expiration is increasing and so therefore the delta increases making the option more sensitive to changes in the stock price since it has a higher probability of becoming shares of stock at expiration. The third option Greek to understand is called theta. Theta predicts the expected decrease in an option's price over time assuming no change in the stock price or expected volatility. So consider this option price simulation with a 90-day call option and a $200 strike price analysis. and a volatility of 20%. If we keep the stock price and expected volatility constant, the call's price diminishes from $8 to $0 over the 90-day period. Theta gauges the estimated daily depreciation of an option's price if the stock price and expected volatility remain unchanged. Option prices are essentially a function of how likely they are to be valuable at the time of expiration. Generally speaking, option prices will fall as they get closer to expiration because with less and less time before those options expire, we have a smaller probability of seeing big stock price movements. And with a smaller probability of big stock price movements comes a smaller probability of big option price movements. And therefore, the options price will get smaller and smaller as expiration approaches. The fourth option Greek to understand is called vega, and vega indicates the expected changes in an option's price. corresponding to a 1% shift in implied volatility. Implied volatility reflects the anticipated fluctuations in a stock's price over a specific period as implied from option prices. For instance, consider two $100 stocks and we're looking at 30-day call options with the same strike price on each of these stocks. Let's say the first stock has a call priced at $5 and the other stock has the same call priced at $10. The second scenario results in higher implied volatility because the elevated option price suggests that the market is anticipating more stock volatility over the next month in that second scenario as opposed to the first stock scenario. Vega is the option Greek that informs us how an options price is expected to change given a change in implied volatility. So look at this 60-day Tesla call option with a Vega of 0.31. This suggests that if the implied volatility increases by 1%, the options price is expected to rise by 31 cents. If the implied volatility decreases by 1%, the options price is anticipated to fall by 31 cents. Earlier, I mentioned that option prices is are essentially a function of how likely they are to be valuable at the time of expiration. And so an increase in expected stock volatility will inflate all option prices because with larger anticipated stock price movements comes larger potential option price movements as well. And on the other hand, if the expected stock volatility decreases, that means there is smaller potential option price changes and therefore a decrease in expected stock volatility will deflate all option prices. So using an option pricing simulator, let's look at a 200 strike call option on a $200 stock, and let's plot the prices of these two different call options, assuming different levels of expected volatility. Assuming the stock price remains constant and no time passes, if you bought the call when implied volatility was 20% and it immediately rose to 30%, you'd profit from the increase in option prices. However, if you bought the call when IV was 30% and it dropped to 20%, you would lose money due to the deflation in option prices as the market factors in lower expected stock price volatility. Of course, volatility changes will coincide with some passage of time and sometimes significant stock price changes, but this simulation shows us just how the option price is expected to change given changes in volatility expectations. So far, we've talked about the individual option Greeks, meaning the expected price changes of an option as related to various factors. But now I want to look at position level Greeks which tells us how much we can expect an entire option position to make or lose given a change in the stock price, the passage of time, or a change in volatility. So for instance this position here has a delta of plus 175, gamma of plus 7, theta of negative 2.8, and vega of plus 81. This translates to a potential gain of $175 if the stock price goes up by $1 and a $175 loss if the stock price falls by $1. The gamma of plus 7 indicates that if the stock price goes up by $1, the position delta will increase by 7 points. And if the stock price goes down by $1, the position delta will decrease by 7 points. The theta of negative 2.8... tells us that if the stock price and volatility remain the same, then this overall position should lose $2.80 with the passage of one day. Finally, the vega of plus 81 suggests that if implied volatility goes up by 1%, this position should make $81. And if implied volatility falls by 1%, this position should lose $81. Now this might be a little confusing to you because earlier I mentioned that call deltas can only range from zero to positive one and put deltas can only range from zero to negative one. So how do we get a delta of plus 175? The answer is that we have to account for the option contract multiplier. What I mean by that is if we have an option that is worth two dollars and fifty cents, we actually have to buy that option with $250 because we have to multiply that listed price by 100 since each option corresponds to 100 shares of stock. And a 50 cent change in an option price is actually a $50 profit or loss when you have a position in that option. So if you buy a call option for $2.50 and its price increases to $3, that represents an actual $50 profit on that option position. So the position delta in that case would be positive 50. Another example, if an options trader buys five call options and that call option has a delta. of 0.5, that means they will make or lose $50 for a $1 change in the stock price. And therefore, their delta or position delta would be a positive 250. Because if the stock price goes up by $1, they will have a $50 gain per option times five contracts, which gives them a $250 gain if the stock price goes up by $1 and a $250 loss if the stock price goes down by $1. The next thing I want to do is to go a little bit deeper. on theta and vega because the greek's theta and vega only affect the option's extrinsic value, not its intrinsic value. So time decay or the loss of an option's value over time only impacts extrinsic value, not intrinsic value. The intrinsic value of an option or the amount that it is in the money remains unaffected by the passage of time. This means if we have a call strike of $135 and the stock price is at $150, this call option will have intrinsic value of $15 since it has the ability to purchase shares of stock for $15 less than the current market price of the shares and the value of that will never change no matter how much time passes or no matter how much volatility changes. Changes in implied volatility also only relate to extrinsic value, not intrinsic value. I really hope you enjoyed this option Greeks for beginners tutorial. My name is Chris from Project Finance, and I will see you in the next video.

In essence, it's the sensitivity of your options price relative to changes in the stock price. We can visualize delta by using an options pricing calculator plotting the call prices at various stock prices. So consider a call option with a strike price of $200 and 90 days until expiration.

As you'll see the call price increases when the stock price rises and the call price falls when the stock price declines. This is because call options have positive deltas and that means that the call options price will move in the same direction as the stock price. Let's say you have a call option with a delta of positive 0.5.

This implies that if the stock price goes up by $1, your call option will experience a 50 cent price gain. Conversely, if the stock price goes down by $1, this call option should lose about 50 cents. Let's look at a real life example using Apple data. In this Apple call chart, note the relationship between the stock price, the price of the $1.35 call, and the call's delta.

Initially, the call's delta was approximately 0.47, suggesting the call's price would change by about $0.47 for the initial $1 changes in the stock price. When Apple shares rose from $132 to $136, an increase of $4, the call's price climbed from around $7 to $9, or a $2 increase. And this is consistent.

with that positive 0.47 delta that the call had at the beginning of this period. Now put options have negative deltas and this means that their prices move in the opposite direction as the stock price. So if the stock price goes up a put options price will fall and if the stock price goes down a put options price will increase. And again we can visualize this using an options pricing calculator to plot the put option price at various stock prices. So here we see the put options price is increasing as the stock price goes down and the put options price is decreasing as the stock price goes up and this visualizes negative delta call option deltas can range from zero to positive one and put option deltas can range from zero to negative one so an options price can only be as sensitive as a share of stock itself but option deltas do not remain constant they do change and this brings us to our second option greek to understand which is called gamma Gamma is the option Greek that estimates how an option's delta will change given a $1 shift in the stock price.

So as delta is predicting how the option's price will change given a $1 shift in the stock price, gamma is predicting how the option's delta will change when that stock price movement occurs. Let's go back to our earlier Apple example to visualize this. In this example, you'll see the call's delta rising alongside the stock price. Gamma predicts this rate of change, estimating the adjustment in an options delta for a $1 movement in the stock price. Consider a call with a delta of 0.5 and a gamma of 0.05.

Here, if the stock price increases by $1, the call's delta would become a positive 0.55. Conversely, if the stock price drops by $1, the delta would decrease to a positive 0.45. So what this means is, if you own a call option and the stock price increases, Your new call option delta is going to be higher than it was before and therefore your options price will be more sensitive to changes in the stock price compared to when the stock price was lower. And conversely, if you own a call option and the stock price falls, your call option is going to become less sensitive to changes in the stock price than it was before. The opposite is true for put options because a put options delta will get closer to negative one as the stock price falls, meaning its price will become more sensitive to changes in the stock price.

And if the stock price increases, put option deltas will move towards zero, which means they will become less sensitive to changes in the stock price than they were before. In the Apple example, the call began with a delta of positive 0.5. indicating a 50 cent change for each $1 shift in the stock price at the beginning of the period. However, by the end of the period, the call's delta was positive 1, suggesting a $1 change in the call price for each $1 shift in the stock price.

And this implies that the call option is behaving more like shares of stock, because if the stock price rises by $1 and the option price rises by $1, this means that the option is trading just like shares of stock. And this is expected because in the Apple example, the stock price far exceeded the call's strike price at the end of the period. And this indicated a high likelihood that the call option would expire in the money.

And when a call option expires in the money, it becomes 100 shares of stock. And so what that means is this call option was starting to trade like what it would become. And that's because with a stock price way above the strike price, this call option had a high likelihood of becoming or expiring in the money and converting into shares of stock. and so before the call option even became shares of stock it started to trade like what it would become i hope that makes sense in this sense we can understand delta as the probability of an option becoming shares or expiring in the money if an option has a low delta or close to zero it has a small probability of becoming shares and will behave less like them or be less sensitive to changes in the stock price conversely if an option has a high delta meaning it is close to positive or negative one It has a high probability of becoming shares at expiration and therefore it will trade much more like shares of stock experiencing a one dollar change in the option price for a one dollar change in the stock price.

So if we interpret delta as the estimated probability of an option expiring in the money which it sometimes is used as that proxy then we can understand gamma as the change in the options probability of expiring in the money as the stock price changes. So for example, if we have a call with a delta of 0.5 and a gamma of 0.05, this tells us that if the stock price goes up by $1, the delta is going to increase to 0.55, indicating a higher chance of expiring in the money at expiration. This makes sense because if the stock price is increasing towards that call option strike price or even above it, that means that the probability of the stock price being above that call's strike price is 0.55.

at expiration is increasing and so therefore the delta increases making the option more sensitive to changes in the stock price since it has a higher probability of becoming shares of stock at expiration. The third option Greek to understand is called theta. Theta predicts the expected decrease in an option's price over time assuming no change in the stock price or expected volatility. So consider this option price simulation with a 90-day call option and a $200 strike price analysis. and a volatility of 20%.

If we keep the stock price and expected volatility constant, the call's price diminishes from $8 to $0 over the 90-day period. Theta gauges the estimated daily depreciation of an option's price if the stock price and expected volatility remain unchanged. Option prices are essentially a function of how likely they are to be valuable at the time of expiration.

Generally speaking, option prices will fall as they get closer to expiration because with less and less time before those options expire, we have a smaller probability of seeing big stock price movements. And with a smaller probability of big stock price movements comes a smaller probability of big option price movements. And therefore, the options price will get smaller and smaller as expiration approaches.

The fourth option Greek to understand is called vega, and vega indicates the expected changes in an option's price. corresponding to a 1% shift in implied volatility. Implied volatility reflects the anticipated fluctuations in a stock's price over a specific period as implied from option prices.

For instance, consider two $100 stocks and we're looking at 30-day call options with the same strike price on each of these stocks. Let's say the first stock has a call priced at $5 and the other stock has the same call priced at $10. The second scenario results in higher implied volatility because the elevated option price suggests that the market is anticipating more stock volatility over the next month in that second scenario as opposed to the first stock scenario. Vega is the option Greek that informs us how an options price is expected to change given a change in implied volatility. So look at this 60-day Tesla call option with a Vega of 0.31.

This suggests that if the implied volatility increases by 1%, the options price is expected to rise by 31 cents. If the implied volatility decreases by 1%, the options price is anticipated to fall by 31 cents. Earlier, I mentioned that option prices is are essentially a function of how likely they are to be valuable at the time of expiration.

And so an increase in expected stock volatility will inflate all option prices because with larger anticipated stock price movements comes larger potential option price movements as well. And on the other hand, if the expected stock volatility decreases, that means there is smaller potential option price changes and therefore a decrease in expected stock volatility will deflate all option prices. So using an option pricing simulator, let's look at a 200 strike call option on a $200 stock, and let's plot the prices of these two different call options, assuming different levels of expected volatility.

Assuming the stock price remains constant and no time passes, if you bought the call when implied volatility was 20% and it immediately rose to 30%, you'd profit from the increase in option prices. However, if you bought the call when IV was 30% and it dropped to 20%, you would lose money due to the deflation in option prices as the market factors in lower expected stock price volatility. Of course, volatility changes will coincide with some passage of time and sometimes significant stock price changes, but this simulation shows us just how the option price is expected to change given changes in volatility expectations.

So far, we've talked about the individual option Greeks, meaning the expected price changes of an option as related to various factors. But now I want to look at position level Greeks which tells us how much we can expect an entire option position to make or lose given a change in the stock price, the passage of time, or a change in volatility. So for instance this position here has a delta of plus 175, gamma of plus 7, theta of negative 2.8, and vega of plus 81. This translates to a potential gain of $175 if the stock price goes up by $1 and a $175 loss if the stock price falls by $1. The gamma of plus 7 indicates that if the stock price goes up by $1, the position delta will increase by 7 points. And if the stock price goes down by $1, the position delta will decrease by 7 points.

The theta of negative 2.8... tells us that if the stock price and volatility remain the same, then this overall position should lose $2.80 with the passage of one day. Finally, the vega of plus 81 suggests that if implied volatility goes up by 1%, this position should make $81.

And if implied volatility falls by 1%, this position should lose $81. Now this might be a little confusing to you because earlier I mentioned that call deltas can only range from zero to positive one and put deltas can only range from zero to negative one. So how do we get a delta of plus 175?

The answer is that we have to account for the option contract multiplier. What I mean by that is if we have an option that is worth two dollars and fifty cents, we actually have to buy that option with $250 because we have to multiply that listed price by 100 since each option corresponds to 100 shares of stock. And a 50 cent change in an option price is actually a $50 profit or loss when you have a position in that option.

So if you buy a call option for $2.50 and its price increases to $3, that represents an actual $50 profit on that option position. So the position delta in that case would be positive 50. Another example, if an options trader buys five call options and that call option has a delta. of 0.5, that means they will make or lose $50 for a $1 change in the stock price.

And therefore, their delta or position delta would be a positive 250. Because if the stock price goes up by $1, they will have a $50 gain per option times five contracts, which gives them a $250 gain if the stock price goes up by $1 and a $250 loss if the stock price goes down by $1. The next thing I want to do is to go a little bit deeper. on theta and vega because the greek's theta and vega only affect the option's extrinsic value, not its intrinsic value.

So time decay or the loss of an option's value over time only impacts extrinsic value, not intrinsic value. The intrinsic value of an option or the amount that it is in the money remains unaffected by the passage of time. This means if we have a call strike of $135 and the stock price is at $150, this call option will have intrinsic value of $15 since it has the ability to purchase shares of stock for $15 less than the current market price of the shares and the value of that will never change no matter how much time passes or no matter how much volatility changes. Changes in implied volatility also only relate to extrinsic value, not intrinsic value. I really hope you enjoyed this option Greeks for beginners tutorial.

My name is Chris from Project Finance, and I will see you in the next video.

Transcript for:Understanding Option Greeks for Trading

Transcript for:
Understanding Option Greeks for Trading