OM-W8

Greeks

The Greeks are important in understanding the behavior of options under various conditions. These notes focus on Delta, which measures the sensitivity of an option's price to changes in the underlying asset's price.

Call Options: Understanding Delta

  1. Scenario Analysis of Call Option

    • Given:

      • Strike Price: $70

      • Current Stock Price: $50

    • Question: Is the delta of this option closer to (i) 25, (ii) 50, or (iii) 75?

    • Answer:

      • The option is out-of-the-money (OTM) since the stock price ($50) is below the strike price ($70).

      • Therefore, the delta should be smaller, likely closer to 25 (option i).

      • For a put option with a high strike price being in-the-money (ITM), the delta would be high, thus closer to 75 (negative value).

  2. Comparing Two Call Options with Different Maturities

    • Scenario:

      • Both options have a strike price of $70 and the same stock price of $50.

      • Option A: Maturity of 1 month

      • Option B: Maturity of 1 year

    • Question: Which option has a higher delta?

    • Answer:

      • Both options are OTM. However, the 1-month option is more OTM compared to the 1-year option.

      • It is more difficult for the stock price to reach $70 from $50 within just 1 month than within 1 year.

      • Therefore, both options have low delta (lower than 50), but the 1-month option has a lower delta due to being more out-of-the-money.

      • Consequently, the 1-year option has a higher delta.

      • For put options:

      • The delta of the put options remains higher than 50.

      • The 1-month put option has a higher delta (in absolute terms) and is more ITM, while the 1-year put option is closer to 50 and lower in absolute magnitude.

  3. Impact of Increased Volatility on Delta

    • Scenario: Volatility doubles while the stock price remains at $50.

    • Question: Should the delta of the above options increase or decrease?

    • Answer:

      • Higher volatility increases the probability of reaching the strike price of $70.

      • Therefore, the delta should increase and get closer to 50.

      • In the case of the call options, the delta would consequently increase.

      • For put options:

      • The delta is greater than 50 due to being ITM.

      • As the probability of reaching the strike price decreases, the delta of the put option will decline in absolute magnitude as it moves closer to 50.

Summary of Changes with Put Options

  1. For the first question regarding delta - a put option would have a delta closer to 75 (negative).

  2. For the second question about which option has a higher delta - the relative delta comparison remains the same, with the month-to-month option being lower in absolute terms while for puts, the month option has a higher absolute delta.

  3. Increasing volatility results in a declining absolute delta for the put due to its increased ITM characteristic, moving closer to 50.

Overall, the behavior and delta changes illustrate the differences between call and put options under various market conditions and structures. Understanding these nuances is crucial for effective options trading strategies.