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Delta

By: OTC Team, OTC Team

Delta

 

Formatting not supported in Market Intelligence html format. Contact kathryn.ziegler@stonex.com for PDF version

 

INTRODUCTION TO GREEKS

DEFINITION

Mathematically derived figures used to predict the change in option premium with relation to the change in futures price

Also called:

Risk measurements

Hedge parameters

Risk sensitivities

CHARACTERISTICS

Different than a two-dimensional futures contract that are affected only by the direction change in the market

Call options         Direct Relationship to futures

Move higher when futures go UP

Move lower when futures go DOWN

Put options          Inverse Relationship to futures

Move higher when futures go DOWN

Move lower when futures go UP

Option prices can change for four different reasons, and each Greek measures one of those specific risk characteristics.

FIVE MAIN GREEKS

Delta change in option premium with relation to directional movement

Gamma change in option premium with relation to directional movement

Theta change in option premium with relation to time decay

Vega change in option premium with relation to volatility of the futures market

Rho change in option premium with relation to changes in interest rates

 

DELTA

 

DEFINITION

Measures DIRECTIONAL RISK of the position

CHARACTERISTICS

             Measurement

                             Call        Amount between -1 and 1

                             Put         Amount between -1 and 1

              Relation

                             Positive Delta      Long Call

                                                          Short Put

                             Negative Delta     Short Call

                                                          Long Put

Delta is Largest ITM

Delta is Smallest OTM

THREE DELTA DESCRIPTIONS

Rate of Change

Speed at which the option premium changes per one unit move in the futures price

Hedge Ratio

Futures quantity needed to hedge away the directional risk of the options

Payoff Probability

Probability the option will expire In The Money

FORMULAS

Rate of Change

Delta * Futures Move = Option Premium Change

Hedge Ratio

Delta * Position Quantity = Hedge Quantity

Payoff Probability

Delta = Percent Chance the option will expire In The Money

EXAMPLES

Using 1000 Call Option with 0.50 Delta

Rate of Change

Futures 1000                                    Futures move 1.0 cent to 1001

Call Option Premium 45.0                Option Premium moves to 45.5

=0.50 delta * 1.0 cent futures move = +0.5 cent option premium change

Hedge Ratio of Position

Long 100 SX 1000c 50

0.50 * 100 = 50 Long

To hedge positional risk

Sell 50 SX Futures

New Delta = 0

 

Payoff Probability of being In The Money at Expiration

0.50 Delta = 50% Probability

 

EXERCISE

Long 50 Call Options with a 0.20 Delta, Option Premium 40 and futures at 1000, solve for the following:

  1. What is the option premium at 1005
  2. What trade will hedge this position

ANSWERS:  1) 41         2) Sell 10 futures    

                 

 

 

 

 

DISCLAIMER

Trading over-the-counter and exchange-traded derivatives is not suitable for all investors and involves substantial risk.  StoneX Markets, LLC (“SXM”), a subsidiary of StoneX Group Inc., is a member of the National Futures Association and provisionally registered with the U.S. Commodity Futures Trading Commission (“CFTC”) as a swap dealer. SXM’s products are designed only for individuals or firms who qualify under CFTC rules as an ‘Eligible Contract Participant’ (“ECP”) and who have been accepted as customers of SXM.  Any recipient of this material who wishes to express an interest in trading with SXM must first prequalify as an ECP, independently determine that derivatives are suitable for them and be accepted as a customer of SXM.  Trading over-the-counter (“OTC”) products or “swaps” involves substantial risk of loss.

This is not an offer to buy or sell any derivative. This material does not constitute investment research and does not take into account the particular investment objectives, financial situations, or needs of individual clients or recipients of this material.  You are directed to seek independent investment and tax advice in connection with derivatives trading.

2024 StoneX Group Inc. All rights reserved.

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