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Gamma - Source: CFA EOC Reading 30 Q12

Q: If current share price is $67.79, the call option with the largest gamma would have a strike price of:

A) $55 (call delta = 4.7)
B) $67.50 (call delta = 16.5)
C) $80 (call delta = 35.8)

Originally I had A) $55. Correct answer is $67.50. Is it because the call option of $67.50 is in the money and call delta is > than the call option with strike price of $55 but a lower call delta?

Thanks.

Comments

  • Ha, I love derivatives questions. ;)

    The answer should be (B), gamma is highest when an option is at-the-money (ATM), i.e. when current underlying stock price is near strike price of the option. Let me explain and see if this helps.

    Remember to difference between the definition of delta and gamma.

    Delta measures the rate of change in the option value due to a change in underlying stock price, i.e. it measures the sensitivity of option prices due to changes in the underlying stock price.

    Gamma measures the rate of change in delta due to a change in the underlying stock price, i.e. it measures the sensitivity of delta due to changes in the underlying stock price.

    In fact, the call delta figures they gave you is irrelevant for your choice of answers above. If we are looking for the highest gamma, it means we are looking for the point where a small change in underlying stock price will have the largest impact on delta (following the definition above), i.e. small changes in stock price will have the most impact on option value when it is hovering around the ATM strike price.

    Why? Because if the option is ATM, the intrinsic value of the option is zero (for call options, it's Stock price - Strike price). If the option is ITM, even by 0.01, it has huge impact on delta as delta (i.e. option value) changes from near zero (when ATM), to positive (when ITM) or stay zero (when very OTM). So the delta is very sensitive to a tiny tiny change in underlying stock price when it's hovering around ATM strike price.

    Here's a chart of gamma of a call option which I hope helps. But don't hesitate to let me know what part of my explanation doesn't make sense. I'm happy to help explain it until you do!

    image
    Dr_Pain28Zee
  • It should be (B). Gamma is derivative of Delta. Gamma changes more when there is more change in delta. More change in delta observed when it is ATM. Because when options are in ITM or deep ITM delta does not change much.
    Zee
  • @Alta12, if possible please tag me in future questions.. since I am also reading almost in sync with you, it will help me too!
  • @Sophie, Derivatives is definetely lot better in this level than level-2. In level-2, it was a nightmare for me :D
    Alta12
  • No worries @RaviVooda, derivatives is a nightmare for most, according to our CFA Results Analysis. Hope studies are going well!
  • @sophie @ravivooda Thanks guys! Got it! Will tag you in future questions RaviVooda. I'm keen to get the first run of reading done in the next 2 weeks. Would have finished a bit earlier but too tired after work to do readings or questions. Putting in big weekends.
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