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What are the Option Greeks?

Understanding Options Greeks

What are the Option Greeks? : Today, we will learn about the option greeks. Options Greeks are metrics that help traders assess the sensitivity of an option’s price to various factors, such as changes in the underlying asset’s price, volatility, and time. Here’s a detailed explanation of the major Greeks:

1. Delta (Δ): Price Sensitivity

  • Definition: Measures the rate of change in the option’s price (premium) for a $1 change in the price of the underlying asset.
  • Range: Between -1 and +1 for options.
    • Call Option Delta: Positive (0 to +1).
    • Put Option Delta: Negative (0 to -1).
  • Interpretation:
    • A delta of 0.5 means the option’s price will increase by 5 Rs for every 10 Rs increase in the underlying asset’s price.
    • At-the-money (ATM) options have deltas around 0.5, while in-the-money (ITM) options have deltas closer to 1 for calls or -1 for puts.
  • Hedge Use: Helps calculate the number of options needed to hedge a stock position.
  • Example:
    • You own a call option on Stock A with a delta of 0.5.
    • If Stock A increases by 1 Rs, the option’s price is expected to increase by 0.50 paisa.
  • Hedging Application:
    • Suppose you own 100 shares of Stock A. To hedge this position, you can sell call options with a delta of 0.5.
    • Calculate the hedge: Hedge Ratio=Shares Owned Delta of Option=1000.5=200 call options.\text{Hedge Ratio} = \frac{\text{Shares Owned}}{\text{Delta of Option}} = \frac{100}{0.5} = 200 \text{ call options}.

2. Gamma (Γ): Delta Sensitivity

  • Definition: Measures the rate of change of delta for a $1 change in the price of the underlying asset.
  • Importance: Indicates how stable the delta is. High gamma implies that delta changes rapidly with the underlying price movement.
  • Range: Always positive for both call and put options.
  • Interpretation:
    • Options near expiry or ATM tend to have higher gamma.
    • High gamma implies a higher risk of large changes in delta.
  • Example:
    • You own a call option with a delta of 0.5 and a gamma of 0.1.
    • If the underlying stock increases by 1, delta will increase by 0.1, making the new delta 0.6.
  • Risk Management Application:
    • High gamma near expiration means rapid changes in delta. You might adjust your position more frequently to maintain your hedge, especially during volatile times.

3. Vega (ν): Volatility Sensitivity

  • Definition: Measures the change in the option’s price for a 1% change in implied volatility of the underlying asset.
  • Interpretation:
    • Higher vega implies greater sensitivity to changes in volatility.
    • Long options (both calls and puts) have positive vega, benefiting from an increase in volatility.
    • Short options have negative vega, losing value when volatility rises.

 

Example:

      • You own a call option with a price of 5 and a vega of 0.25. If implied volatility increases by 1%, the option’s price will increase by 0.25 paisa
    • Volatility Trading Application:
      • Suppose implied volatility is historically low. You could buy options expecting a volatility spike (e.g., before earnings or news releases).
      • If volatility rises, the option’s price will increase regardless of the stock’s movement.

4. Theta (Θ): Time Decay

  • Definition: Measures the rate at which an option’s price decreases as it approaches expiration (assuming all other factors remain constant).
  • Range: Negative for long options (both calls and puts) because time decay erodes their value.
  • Interpretation:
    • Theta is larger for ATM options and increases as expiration nears.
    • Sellers (writers) of options benefit from time decay (positive theta).
    • Time Decay Strategy:
      • Option Buyers:
        • Time decay works against you, so buy options with sufficient time to expiration.
      • Option Sellers:
        • Selling ATM options can benefit from rapid theta decay, especially in the last 30 days before expiration.

5. Rho (ρ): Interest Rate Sensitivity

  • Definition: Measures the change in the option’s price for a 1% change in interest rates.
  • Interpretation:
    • Call options have positive rho: their value increases with rising interest rates.
    • Put options have negative rho: their value decreases with rising interest rates.
  • Practical Use: Less impactful in low-interest-rate environments but can matter in high-rate settings.

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Categories: Option Trading