Derivatives: Exploring Delta and Gamma in Options Trading

  1. Trading for professionals: Options trading
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    3. What Is Call Option and How to Use It With Example
    4. Options Terminology The Master List of Options Trading Terminology
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    7. How to Calculate Profit on Call Option
    8. Selling Call Option What is Writing/Sell Call Options in Share Market?
    9. Call Option Payoff Exploring the Seller’s Perspective
    10. American vs European Options What is the Difference?
    11. Put Option A Guide for Traders
    12. put option example: Analysis of Bank Nifty and the Bearish Outlook
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    14. Put Option Selling strategies and Techniques for Profitable Trading
    15. Call and put option Summary Guide
    16. Option premium Understanding Fluctuations and Profit Potential in Options Trading
    17. Option Contract moneyness What It Is and How It Works
    18. option moneyness Understanding itm and otm
    19. option delta in option trading strategies
    20. delta in call and put Option Trading Strategies
    21. Option Greeks Delta vs spot price
    22. Delta Acceleration in option trading strategies
    23. Secrets of Option Greeks Delta in option trading strategies
    24. Delta as a Probability Tool: Assessing Option Profitability
    25. Gamma in option trading What Is Gamma in Investing and How Is It Used
    26. Derivatives: Exploring Delta and Gamma in Options Trading
    27. Option Gamma in options Greek
    28. Managing Risk in Options Trading: Exploring Delta, Gamma, and Position Sizing
    29. Understanding Gamma in Options Trading: Reactivity to Underlying Shifts and Strike Prices
    30. Mastering Option Greeks
    31. Time decay in options: Observing the Effect of Theta
    32. Put Option Selling: Strategies and Techniques for Profitable Trading
    33. How To Calculate Volatility on Excel
    34. Normal distribution in share market
    35. Volatility for practical trading applications
    36. Types of Volatility
    37. Vega in Option Greeks: The 4th Factors to Measure Risk
    38. Options Trading Greek Interactions
    39. Mastering Options Trading with the Greek Calculator
    40. Call and Put Option Guide
    41. Option Trading Strategies with example
    42. Physical Settlement in Option Trading
    43. Mark to Market (MTM) and Profit/Loss Calculation
Marketopedia / Trading for professionals: Options trading / Derivatives: Exploring Delta and Gamma in Options Trading

Drawing Parallels

Throughout the last several sections, we’ve comprehended how Delta of a choice functions. As we know, Delta exemplifies the alteration in premium for any switch in the underlying cost.

If the Nifty spot value is 8000, then it’s evident that the 8200 CE option is out-of-the-money (OTM), which means its delta could range anywhere from 0 to 0.5. To continue this conversation, let us fix this value at 0.2.

If Nifty spot experiences a surge of 300 points, it would no longer be OTM for the 8200 CE option. It would instead become slightly ITM and as such its delta value would alter from 0.2 to around 0.5 to 1.0; let’s approximate this at 0.8.

This alteration in the root cause means that Delta’s value is no longer static; instead, it evolves in accordance with alterations to the underlying and the premium. Just like velocity alters according to time and distance travelled, so too does Delta shift its value.

An option’s Gamma tells us the response of its delta to a shift in the underlying. It is the answer to how much the delta of an option will be affected by a change in the underlying.

Let’s now make a comparison between velocity and acceleration, on one hand, and Delta and Gamma, on the other.

1st order Derivative

  • Change in position over time is captured by velocity, which is the 1st order derivative.
  • The change in premium corresponding to alteration of the underlying is measured by delta, thus it is referred to as the first derivative of the premium.

2nd order Derivative

  • Acceleration, which represents the change in velocity over time, is captured as the second-order derivative of position.
  • Delta captures the effect of a change in the underlying value on the option premium, and Gamma is thus referred to as the second derivative of the premium.

As you can imagine, computing Delta and Gamma values (and all other Option Greeks) necessitates a hefty amount of number crunching and advanced calculus (like differential equations and stochastic calculus).

Do you know why derivatives are called derivatives? The reason is that their value depends on the underlying asset that it represents.

The value that the derivatives contracts take from their related underlying is gauged by using the mathematical concept of “Derivatives”, thus why Futures & Options are known as ‘Derivatives’.

If you’re curious, there is an alternate world where traders utilise derivative calculus to discover trading possibilities continually. Generally known as ‘Quants’, these investors have a quite distinguished name. Quantitative trading is the reality behind the ‘Markets’ mountain.


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