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By
Kim Klaiman
SteadyOptions.com
Options Greeks:
The Delta
General
 The option's delta is the rate of change of the
price of the option with respect to its underlying
price.
 The delta of an option ranges in value from 0 to 1
for calls (0 to -1 for puts) and reflects the increase
or decrease in the price of the option in response
to a 1 point movement of the underlying asset
price.
 Far Out-of-The-Money options have delta values
close to 0 while Deep-In-The-Money options have
deltas that are close to 1.
Call Options
 Call options have positive deltas between 0 and 1.
 When the underlying stock increases in price, the
value of your call option will also increase by the call
options delta value.
 When the underlying market price decreases the
value of your call option will also decrease by the
amount of the delta.
 When the call option is deep in-the-money and has a
delta of 1, then the call will move point for point in the
same direction as movements in the underlying asset.
Put Options
 Put options have negative deltas between -1 and
0.
 When the underlying market price increases the value
of your put option will decreases by the amount of the
delta value.
 When the price of the underlying asset decreases, the
value of the put option will increase by the amount of
the delta value.
 When the put option is deep in-the-money and has a
delta of -1, then the put will move point for point in the
same direction as movements in the underlying asset.
Delta Sensitivity
 As a general rule, in-the-money options will move
more than out-of-the-money options, and short-term
options will react more than longer-term options to the
same price change in the stock.
 As expiration nears, the delta for in-the-money calls
will approach 1 and delta for out-of the-money calls
will approach 0.
 As expiration approaches, the delta for in-the-money
puts will approach -1 and delta for out-of-the-money
puts will approach 0.
Delta as Probability
 Delta can be viewed as a percentage probability an option
will wind up in-the-money at expiration. Therefore, at-the-
money option would have a .50 Delta or 50% chance of
being in-the-money at expiration.
 Delta of a far-out-of-the-money option is a good indication
of its likelihood of having value at expiration. An option with
less than a .10 Delta is not very likely to be in-the-money.
 The sum of absolute values of delta of a call and a put with
the same strike is one. You can be sure that one of them
will expire in the money and the other will expire out of the
money .
 Just for clarification, delta and probability of expiring in the
money are not the same thing. Delta is usually a close
enough approximation to the probability.
Example
 If the delta on a particular call option is .55, then, all
other things being equal, the price of the option will
rise $0.55 for every $1 rise in the price of the
underlying security. For every $1 decline in the price
of the underlying the option will lose $0.55.
 If the delta on a particular put option is -.45, then, all
other things being equal, the price of the option will
rise $0.45 for every $1 fall in the price of the
underlying security. As with call options the obverse
scenario is also true.
 Word of caution: it is important to remember that Delta
is constantly changing during market hours and will
typically not accurately predict the exact change in an
option’s premium.
List of delta positive strategies
 Long Call
 Short Put
 Call Debit Spread
 Put Credit Spread
 Covered Call Write
strategies
 Long Put
 Short Call
 Put Debit Spread
 Call Credit Spread
 Covered Put Write
List of delta neutral strategies
 Iron Condor
 Butterfly
 Short Straddle
 Short Strangle
 Long Straddle
 Long Strangle
 Long Calendar Spread
Summary
 Positions with positive delta increase in value if
the underlying goes up
 Positions with negative delta increase in value if
the underlying goes down
 An option contract with a delta of 0.50 is
theoretically equivalent to holding 50 shares of
stock
 100 shares of stock is theoretically equivalent to
an option contract with a 1.00 delta

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Options Greeks: The Delta

  • 2. General  The option's delta is the rate of change of the price of the option with respect to its underlying price.  The delta of an option ranges in value from 0 to 1 for calls (0 to -1 for puts) and reflects the increase or decrease in the price of the option in response to a 1 point movement of the underlying asset price.  Far Out-of-The-Money options have delta values close to 0 while Deep-In-The-Money options have deltas that are close to 1.
  • 3. Call Options  Call options have positive deltas between 0 and 1.  When the underlying stock increases in price, the value of your call option will also increase by the call options delta value.  When the underlying market price decreases the value of your call option will also decrease by the amount of the delta.  When the call option is deep in-the-money and has a delta of 1, then the call will move point for point in the same direction as movements in the underlying asset.
  • 4. Put Options  Put options have negative deltas between -1 and 0.  When the underlying market price increases the value of your put option will decreases by the amount of the delta value.  When the price of the underlying asset decreases, the value of the put option will increase by the amount of the delta value.  When the put option is deep in-the-money and has a delta of -1, then the put will move point for point in the same direction as movements in the underlying asset.
  • 5. Delta Sensitivity  As a general rule, in-the-money options will move more than out-of-the-money options, and short-term options will react more than longer-term options to the same price change in the stock.  As expiration nears, the delta for in-the-money calls will approach 1 and delta for out-of the-money calls will approach 0.  As expiration approaches, the delta for in-the-money puts will approach -1 and delta for out-of-the-money puts will approach 0.
  • 6. Delta as Probability  Delta can be viewed as a percentage probability an option will wind up in-the-money at expiration. Therefore, at-the- money option would have a .50 Delta or 50% chance of being in-the-money at expiration.  Delta of a far-out-of-the-money option is a good indication of its likelihood of having value at expiration. An option with less than a .10 Delta is not very likely to be in-the-money.  The sum of absolute values of delta of a call and a put with the same strike is one. You can be sure that one of them will expire in the money and the other will expire out of the money .  Just for clarification, delta and probability of expiring in the money are not the same thing. Delta is usually a close enough approximation to the probability.
  • 7. Example  If the delta on a particular call option is .55, then, all other things being equal, the price of the option will rise $0.55 for every $1 rise in the price of the underlying security. For every $1 decline in the price of the underlying the option will lose $0.55.  If the delta on a particular put option is -.45, then, all other things being equal, the price of the option will rise $0.45 for every $1 fall in the price of the underlying security. As with call options the obverse scenario is also true.  Word of caution: it is important to remember that Delta is constantly changing during market hours and will typically not accurately predict the exact change in an option’s premium.
  • 8. List of delta positive strategies  Long Call  Short Put  Call Debit Spread  Put Credit Spread  Covered Call Write
  • 9. strategies  Long Put  Short Call  Put Debit Spread  Call Credit Spread  Covered Put Write
  • 10. List of delta neutral strategies  Iron Condor  Butterfly  Short Straddle  Short Strangle  Long Straddle  Long Strangle  Long Calendar Spread
  • 11. Summary  Positions with positive delta increase in value if the underlying goes up  Positions with negative delta increase in value if the underlying goes down  An option contract with a delta of 0.50 is theoretically equivalent to holding 50 shares of stock  100 shares of stock is theoretically equivalent to an option contract with a 1.00 delta