OPTION GREEKS

• Delta (Δ): Description: Delta measures the sensitivity of the option's price to changes in the price of the underlying asset. It ranges from -1 to 1 for put and call options, respectively. A Delta of 0.5 means the option's price is expected to change by 50% of the change in the underlying asset's price.
• Example: Suppose a call option on a stock has a Delta of 0.5. If the stock price increases by $2, the price of the call option will increase by $2 * 0.5 = $1. Conversely, if the stock price decreases by $2, the option's price will decrease by $1. If the option initially costs $4, it will increase to $5 with the stock price rise and decrease to $3 with the stock price fall.
• Gamma (Γ): Description: Gamma measures the rate of change of Delta with respect to changes in the underlying asset's price. It helps assess how Delta will change as the underlying asset's price moves. Gamma is highest when the option is at-the-money and decreases as the option moves in- or out-of-the-money.
• Example: Suppose an option has a Gamma of 0.1. If the underlying stock price increases by $2, the Delta will change by 0.1 * $2 = 0.2. If the initial Delta was 0.5, the new Delta would be 0.5 + 0.2 = 0.7. Therefore, further changes in the stock price will have a larger impact on the option's price.
• Theta (Θ): Description: Theta measures the sensitivity of the option's price to the passage of time, also known as time decay. It indicates how much the option's price will decrease per day as it approaches expiration. Theta is usually negative for long positions (options bought) because options lose value over time.
• Example: Suppose an option has a Theta of -0.05, meaning it loses $0.05 in value each day. If the option's current price is $3.00, after one day, the price will be $3.00 - $0.05 = $2.95. After two days, it will be $2.95 - $0.05 = $2.90, and so on.
• Vega (ν): Description: Vega measures the sensitivity of the option's price to changes in the volatility of the underlying asset. It shows how much the option's price will change with a 1% change in volatility. Higher Vega values indicate greater sensitivity to volatility changes.
• Example: Suppose an option has a Vega of 0.2. If the volatility of the underlying stock increases by 5%, the option's price will change by 0.2 * 5 = $1.00. If the option's initial price was $4.00, the new price would be $4.00 + $1.00 = $5.00. Conversely, if volatility decreases by 5%, the option's price would drop to $4.00 - $1.00 = $3.00.
• Rho (ρ): Description: Rho measures the sensitivity of the option's price to changes in the risk-free interest rate. It indicates how much the option's price will change with a 1% change in interest rates. Rho is positive for call options and negative for put options, meaning an increase in interest rates generally increases the value of call options and decreases the value of put options.
• Example: Suppose an option has a Rho of 0.1. If the risk-free interest rate increases by 1%, the option's price will increase by 0.1 * 1 = $0.10. If the option's initial price was $5.00, the new price would be $5.00 + $0.10 = $5.10. Conversely, if the interest rate decreases by 1%, the option's price would decrease to $5.00 - $0.10 = $4.90.

MCQs

These MCQs effectively test your understanding of Option Greeks, assessing your grasp of key concepts like Delta, Gamma, Theta, Vega, and Rho in options trading.

What does Delta (Δ) measure in options trading?

a) Sensitivity of the option's price to changes in volatility

b) Sensitivity of the option's price to changes in the underlying asset's price

c) Sensitivity of the option's price to changes in the risk-free interest rate

d) Sensitivity of the option's price to time decay

If a call option has a Delta of 0.5 and the underlying stock price increases by $3, by how much will the option's price increase?

a) $1.50

b) $3.00

c) $0.50

d) $2.00

Gamma (Γ) is a measure of:

a) The rate of change of Vega with respect to changes in volatility

b) The rate of change of Theta with respect to the passage of time

c) The rate of change of Delta with respect to changes in the underlying asset's price

d) The sensitivity of the option's price to changes in interest rates

An option has a Gamma of 0.2, and the underlying stock price increases by $1. If the initial Delta was 0.4, what will the new Delta be?

a) 0.6

b) 0.8

c) 0.2

d) 0.5

Theta (Θ) primarily indicates:

a) The rate of change of Delta with respect to the underlying asset's price

b) The sensitivity of the option's price to changes in volatility

c) The sensitivity of the option's price to time decay

d) The sensitivity of the option's price to changes in interest rates

If an option has a Theta of -0.05, what will be its price after two days if its current price is $4.00?

a) $3.90

b) $3.95

c) $3.85

d) $3.80

Which Greek measures the sensitivity of an option's price to changes in the volatility of the underlying asset?

a) Delta

b) Gamma

c) Theta

d) Vega

An option with a Vega of 0.25 will change by how much if the volatility increases by 4%?

a) $0.50

b) $1.00

c) $0.10

d) $2.00

Rho (ρ) is used to measure the sensitivity of an option's price to changes in:

a) The underlying asset's price

b) Volatility

c) Interest rates

d) Time decay

If a call option has a Rho of 0.15 and the risk-free interest rate increases by 2%, how much will the option's price increase?

a) $0.30

b) $0.15

c) $0.45

d) $0.10

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