Price movements and what's at risk

Lesson in Course: Derivatives and options (advanced, 6min)

I understand the difference between in-the-money and out-of-the-money options. How do I know which option contract is for me?


What it's about: Actionable ways to use the Greek delta.

Why it's important: Delta gives us an estimate for the chance to make money and sets expectations for gains and losses. 

Key takeaway: Adding delta to or subtracting delta from the current option price helps predict the future price of the option if the underlying increases or decreases in value.

Most professional poker players and gamblers in Vegas spend a lot of time understanding each play to determine the amount of money at risk and the percent chance they have to win it big. The ones that are good at it go on to build profitable careers and avoid the pitfalls of losing everything on a bad bet. If we are to speculate with options, we should do the same.

What does delta tell us about risk?

Let's review the basics of delta and some helpful ways we can use delta.

Delta review
  • Delta is often provided in decimal format but is referred to as a percent (e.g. Delta of 0.40 is referred to as Delta 40)
  • Delta of an option cannot be above 100% or 1 in decimal format
  • Delta for call options are positive
  • Delta for put options are negative

Delta as an indicator for price

Delta provides an estimate for future price

Let's start with how delta provides an indication of the price sensitivity of our options to changes in the underlying stock price with a working example.

Percent change in value

 Below, we can see the Greeks and relevant info regarding a $394 strike call option. The current share price of the underlying stock is $395.86, while the price for the option is $1.86 per share.

For the option, we have a delta of 0.42 (rounded up from 0.4171). A 42-delta (slang) means that for every $1 increase in value for the stock price, the options contract increases by $0.42. Assuming the stock price rises by a dollar to $396.86, we can expect the price of the option to be ($1.86+$0.42) or $2.28 per share — a 23% increase. Likewise, if the stock price drops by a dollar to $394.86, we can expect the price for the option to be ($1.86-$0.42) or $1.44 per share — a 23% decrease.

Putting it all together, we can expect to pay $186 ($1.86 x 100 shares per contract) for each of these in-the-money call options. As a rule of thumb, we can expect to lose around $42 ($0.42 x 100 shares per contract) for every $1 per share the stock decreases without factoring in gamma.

An example including gamma

Delta, in practice, is similar to an option's price and will continue to change when the underlying stock price changes. Gamma is the greek that describes the rate of change in delta per $1 change in the price of the underlying. In the call option example above, a gamma of 0.06 (rounded up from 0.0630) means that delta would be on a steady decline from 0.42 to 0.36 over the $1 drop decrease in the underlying.

For a $1 drop in the underlying, delta alone tells us that we should expect the option's price to drop by $0.42 per share or $42 for a single option contract. Gamma tells us that the option price should drop by $0.36 ($0.42 - $0.06) or $36 for a single option contract. In this example, the value of the options price is in between the two price drops. We'll cover gamma in detail in future lessons. For now, we can just use an average of the two values to use gamma in estimating our price change.

Underlying stock -$1 value of option contract = -($42 + ($42 - $6)) / 2 = -$39
Underlying stock -$2, value of option contract = -$39 - ($36 + ($36 - 6)) / 2 = -$72
Underlying stock -$3, value of option contract = -$39 - $33 - ($30 + ($30 - $6)) / 2 = -$99

If our stock price drops to $392.86 per share, we can lose 53% of our money on these contracts.

Here's another example of a delta 42; gamma 6 positive price movement:

Underlying stock +$1, value of option contract = +($42 + ($42 + $6)) / 2 = + $45
Underlying stock +$2, value of option contract = +$45 + ($48 + ($48 +$6)) / 2  = +$96


Delta as a chance of success

Delta also gives us an estimate for the chance of the option maturing in-the-money.

What if we knew our chances of hitting jackpot?

A 42-delta means buyers and sellers of the call option are collectively guessing that the option has a 42% chance to finish in-the-money at maturity. It's important to know that this percentage is just an estimate and not a guarantee. The percentage can be based on a bunch of factors including market sentiment, interest rate risk, dividends, or supply and demand for the options contracts. The market can change anytime, and the odds can swing quickly in or against our favor.

Things to look out for

At the time of the screenshot above, the delta is actually telling us something fishy might be happening with this specific call option. The options are currently in-the-money, but the delta is suggesting a below 50% chance to stay in-the-money. While we don't have enough additional information to understand the specific cause, we should be wary of buying these options as the chance of success is not in our favor for the risk taken.

Actionable ideas

Delta is a very versatile tool for us to get a peek at what's behind the scene for options. We've just started to cover delta on a beginner level and it's important for us to make sure we've understood delta. We need to understand how to apply our knowledge when looking at different options contracts. Advanced strategies covered in future lessons require mastery over delta and other Greeks.