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Summary

1. Delta (Δ) – Measures Price Sensitivity

What it tells you:

  • Delta shows how much the option price changes when the underlying asset (stock or currency) moves by ₹1.
  • It ranges from 0 to 1 for calls and -1 to 0 for puts.

Stock Options (Without Dividends)

  • Call Options: Delta is positive (between 0 and 1). As the stock price increases, the call option value rises.
  • Put Options: Delta is negative (between -1 and 0). As the stock price increases, the put option loses value.

Stock Options (With Dividends)

  • Call Delta is slightly lower because dividends make the stock less valuable for option holders.
  • Put Delta is slightly higher because dividends increase the appeal of put options.

Currency Options

  • Call Delta is lower because the foreign currency earns interest, reducing the impact of price movements.
  • Put Delta is slightly higher for the same reason.

2. Theta (Θ) – Measures Time Decay

What it tells you:

  • Theta shows how much value an option loses per day as time passes, assuming everything else stays constant.
  • It is always negative because options lose value over time.

Stock Options (Without Dividends)

  • As expiration approaches, Theta increases in magnitude (more time decay).
  • At-the-money (ATM) options lose value the fastest.

Stock Options (With Dividends)

  • Call options lose value faster than non-dividend cases, as dividends lower the stock’s effective value.
  • Put options have slightly lower time decay because puts benefit from dividends reducing stock value.

Currency Options

  • Call options lose value slower than stock options due to foreign interest rates.
  • Put options decay a little faster than non-currency puts due to the same effect.

3. Gamma (Γ) – Measures Delta Sensitivity

What it tells you:

  • Gamma shows how much Delta changes when the underlying price moves by ₹1.
  • High Gamma means Delta changes quickly, making the option more sensitive to price swings.

Stock Options (Without Dividends)

  • Gamma is highest for ATM options and low for deep ITM/OTM options.
  • As expiration nears, Gamma spikes because small price changes drastically affect Delta.

Stock Options (With Dividends)

  • Call and put options have slightly lower Gamma than the no-dividend case because dividends reduce the underlying stock’s value.

Currency Options

  • Currency options have a similar Gamma profile to stocks but are slightly adjusted for foreign interest rates.

4. Vega (ν) – Measures Sensitivity to Volatility

What it tells you:

  • Vega shows how much an option’s price changes when volatility increases by 1%.
  • Higher Vega means the option price is more sensitive to changes in market uncertainty.

Stock Options (Without Dividends)

  • ATM options have the highest Vega because they are most sensitive to changes in volatility.
  • As expiration nears, Vega drops, making options less reactive to volatility.

Stock Options (With Dividends)

  • Call and put Vega values are slightly lower than in the non-dividend case because dividends dampen volatility’s impact.

Currency Options

  • Currency options have lower Vega than stock options since exchange rate volatility is typically lower than stock volatility.

5. Rho (ρ) – Measures Sensitivity to Interest Rates

What it tells you:

  • Rho shows how much an option’s price changes when interest rates move by 1%.
  • It is most relevant for long-term options since short-term options are less affected by interest rates.

Stock Options (Without Dividends)

  • Call options: Rho is positive, meaning rising interest rates increase the call option’s value.
  • Put options: Rho is negative, meaning rising interest rates decrease put option value.

Stock Options (With Dividends)

  • Dividend-paying stocks reduce the impact of interest rates, making Rho slightly lower for both calls and puts.

Currency Options

  • Rho is adjusted for both domestic and foreign interest rates.
  • If foreign interest rates rise, call options become less valuable, and put options become more valuable.

Summary Table of Greeks Across Different Options

Greek Meaning Stock Options (No Dividend) Stock Options (With Dividend) Currency Options
Delta Sensitivity to price changes 0 to 1 (Calls), -1 to 0 (Puts) Calls lower, Puts higher Adjusted for foreign rates
Theta Time decay Negative, strongest for ATM Calls decay faster Slightly different due to foreign rates
Gamma Sensitivity of Delta Highest for ATM, rises near expiration Slightly lower than no-dividend case Similar to stocks but adjusted
Vega Sensitivity to volatility Highest for ATM, drops near expiration Slightly lower than no-dividend case Lower than stock options
Rho Sensitivity to interest rates Calls increase, Puts decrease Less affected due to dividends Adjusted for domestic & foreign rates

Final Thoughts

  • Stock options without dividends follow standard Black-Scholes behavior.
  • Dividends lower Call Delta and Vega, but increase Put Delta slightly.
  • Currency options adjust for foreign interest rates, making their Greeks slightly different.
  • All options lose value over time (Theta is negative).
  • ATM options are the most sensitive to Gamma and Vega.
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