• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar

Epsilon Options

Options Trading Education

  • Home
  • How Options Work
    • Puts and Calls Explained
    • Learn Options Trading
    • LEAP Options Explained
    • Put Call Parity
    • Buy to Open vs Buy to Close
    • Volatility Skewness | IV Skew In Options
  • Options Greeks
    • Delta
    • Vega
    • Gamma
    • Theta
    • Rho
  • Options Spreads
    • Long Call
    • Bear Put Spread
    • Iron Condor
    • Bull Call Spread
    • Covered Calls
    • Calendar Spread
    • Backspread
    • Strangle
    • Butterfly
    • Protective Put
    • Straddle
  • Options Brokers Reviews
  • Blog
  • Show Search
Hide Search

Options Delta Explained: Sensitivity To Price

Options Delta is the measure of an option’s price sensitivity to the underlying stock or security’s market price. It is the expected change in options price with a 1c change in security price (positive if it rises/falls with a rise/fall in market price; negative otherwise).


Table of Contents

  • Options Delta Explained
    • Options Delta Math
  • How Does Options Delta Change Over Time?
    • In the money
    • Out of the money
    • At the money
  • How Does Options Delta Change With Implied Volatility?
    • In The Money
    • Out Of The Money
    • At the money
  • Effect Of Changes Of Price On Delta
  • Conclusion

Options Delta Explained

For example, should a stock option price increase in price by 0.5c with a 1c increase in the underlying stock price then the option has a delta of 0.5.

Another way of looking at delta is as the probability of the option expiring in the money.

Options Delta Math

It’s not necessary to understand the math behind delta (please feel free to go to the next section if you want), but for those interested delta is defined more formally as the partial derivative of options price with respect to underlying stock price.

The formula is below (some knowledge of the normal distribution is required to understand it).

Options Delta Equation
Source: iotafinance

Delta is superficially the most intuitive of the options greeks. Even the newest beginner would expect the price of an option, giving the right to buy or sell a particularly security, to change with the security’s price.

Let’s look at an example with call options on a stock with $120 stock price as it rises higher (by $10 to $130, say).

In the money options – those with a strike price less than $120 – would become even more in the money. Thus their value to the holder would increase – the probability of them remaining in the money would be higher – and hence, all other things being equal, the option price would rise.

Out of the money and at the money options – those with an exercise price of $120 or greater – would also rise in value. The probability of, say, a $140 option expiring in the money would be higher if the stock price was $130 compared to $120. Hence its value would be higher.

Similar arguments can be used with put options: their value rises/falls with the fall/rise of the underlying (the only difference being put options have negative delta versus call options, whose delta is positive).

But the extent of this sensitivity – ie delta – and how it relates to expiration length, price, and volatility is quite subtle. Let’s look at it in more detail.


How Does Options Delta Change Over Time?

The effect of time on delta depends on an option’s ‘moneyness’.

In the money

All other things being equal, long dated in the money options have a lower delta than shorter dated ones.

In the money options have both intrinsic (stock price less exercise price) and extrinsic value.

As time progresses the extrinsic reduces (due to theta) and the intrinsic value (which moves in line with stock price) becomes more dominant. And so the option moves more in line with the stock, and hence its delta rises towards 1 over time.

Out of the money

All other things being equal, short dated OTM/ATM options have a lower delta than longer dated ones.

A short dated out of the money option (especially one which is significantly OTM) is unlikely to expire in the money, a fact that is unlikely to change with a 1c change in price. Hence its delta is low.

Longer dated OTM options are more likely to expire in the money – there is a longer time for the option to move ITM – and hence their value do move with stock price. Hence their delta is higher.

At the money

There is no effect of time on the delta of an at the money option.


How Does Options Delta Change With Implied Volatility?

Again the effect of implied volatility changes on delta depends on moneyness.

In The Money

As we saw above in the money options’ value comprise both intrinsic and extrinsic amounts.

In general the higher the proportion of an option’s value that is intrinsic (which moves exactly in line with stock price) and extrinsic value (which doesn’t), the higher its delta.

Increases in IV increase the extrinsic value of an option and so, as intrinsic value isn’t affected by implied volatility, increases the percentage of the option’s value that is extrinsic. This resultant reduction in the intrinsic value as a proportion of the whole, reduces the option’s delta as above.

Out Of The Money

Out of the money options have only extrinsic value, which is driven by the probability of it expiring in the money.

A higher volatility suggests there is a greater chance of the option expiring ITM (as the stock is expected to move around more) and hence delta increases.

At the money

ATM options have a delta of approx. 0.5, which is unchanged as volatility changes.


Effect Of Changes Of Price On Delta

One of the other subtleties of delta is that it in itself changes value as the underlying security’s price changes.

The extent to which this occurs is another of the options greeks: gamma. This is the change in delta resulting in in a 1c change in stock price.

Gamma for long options holders is positive whereas it is negative for short positions, meaning it helps the former and penalises the latter. It is also at its highest absolute value near expiration. (See here for more discussion on gamma).


Conclusion

Delta is an important greek as it reflects an option holder’s exposure to one of the main variables: the price of the underlying security.

Whilst one of the easiest option concepts to understand, its behaviour resulting from changes to other variables such as time, IV and underlying price is more complex.

It is vital for an options trader to understand these concepts.


Further Reading On Options Trading...

How Options Work: Trading Put And Call Options

Learning how options work is a key skill for any trader or investor wanting to add this to their arsenal of trading weapons. It’s really not possible to trade options ...
Read More

Options Rho: Sensitivity To Interest Rates

Rho is the sensitivity of an options's price to changes in interest rates. It is usually only worth considering for long dated options such as LEAPS. Rho is the least ...
Read More

Options Spreads: Put & Call Combination Strategies

Options Combinations Explained Options spreads involve the purchase or sale of two or more options covering the same underlying stock or security (ref). These options can be puts or calls ...
Read More

Protective Put: This Defensive Put Option Strategy Explained

How Can The Protective Put Strategy Help A Trader? Introduction To Protective Puts The protective put (sometimes called a married put) strategy is one of the simplest, but most, popular, ...
Read More

Straddle Spread: Learn This Options Trading Strategy

Options Trading Strategy: Straddle Spread Introduction The straddle spread is a relatively simple options strategy that can be used under different market scenarios. However its most normal use is a ...
Read More

Out Of The Money (OTM) Options Explained

Out of the money (OTM) options: where the exercise price for a call is more than the current underlying security’s price (or less for a put). This is an example ...
Read More

Calendar Spread

The Calendar Spreads Options Strategy What is a Calendar Spread? Intro Calendar Spreads are one of the key non-directional strategies used by options traders to make money in any market ...
Read More

Options Trading Strategies: Call And Put Backspreads

Backspreads: Extreme Bullish Or Bearish Options Trading Strategies What Are Backspreads? A backspread is very bullish or very bearish strategy used to trade direction; ie a trader is betting that ...
Read More

Options Trading Strategy: Long Call

A long call option strategy is the purchase of a call option in the expectation of the underlying stock rising. It is delta and theta positive. Introduction Options can provide ...
Read More

Options Theta Explained: Price Sensitivity To Time

Options theta measures option price sensitivity to time. Time Decay & Options Theta All things being equal options lose value over time - so called 'time decay' - and theta ...
Read More

Options Brokers Reviews

How To Choose The Best Options Broker There are several things an option trader needs to look for in an options broker. However, whilst most traders will need most, if ...
Read More

Options Trading Strategy: Bear Put Spread

Introduction Options can be an extremely useful tool for short-term traders as well as long-term investors. Options can provide investors with a vehicle to bet on market direction or volatility, ...
Read More

Zero Cost (Costless) Collar Explained

What Is A Zero Cost Collar? A costless, or zero cost, collar is an options spread involving the purchase of a protective put on an existing stock position, funded by ...
Read More

Options Trading Education

Options trading is a potential lucrative sideline for those willing to put in the effort. Epsilon Options is here to help you learn the skills you’ll need to become a ...
Read More

Volatility Skewness | IV Skew In Options

Volatility skewness, or just skew, describes the difference between observed implied volatility with in-the-money, out-of-the-money, and at-the-money options with the same expiry date and underlying. It occurs due to market ...
Read More

Primary Sidebar

Featured Posts:

Options Spreads: Put & Call Combination Strategies

Protective Put: This Defensive Put Option Strategy Explained

Options Greeks: Theta, Gamma, Delta, Vega And Rho

How To Learn Stock Options Trading: Stock Options For ‘Dummies’

LEAP Options Explained: What Are They And How Do They Work?

Options Trading Strategy: Butterfly Spread

Copyright © 2021 · Monochrome Pro on Genesis Framework · WordPress · Log in

  • Facebook
  • Twitter
  • Pinterest
  • Privacy Policy