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What are the Greeks?
In quantitative finance, "the Greeks" refers to a set of measures used to assess the sensitivity of options and other derivatives to various factors. These factors are typically related to the underlying asset, time, volatility, and interest rates. The Greeks are named after letters from the Greek alphabet, such as Delta, Gamma, Theta, Vega, and Rho. They play a crucial role in understanding and managing the risks associated with options and other derivative positions.
Below are the key Greeks and their interpretations:
Delta (Δ): Delta measures the sensitivity of an option's price to changes in the price of the underlying asset. It represents the change in the option price for a one-unit change in the underlying asset price. Delta ranges between 0 and 1 for call options (0 to -1 for put options), indicating the percentage change in the option price relative to a change in the underlying asset price.
Gamma (Γ): Gamma measures the rate of change of an option's delta in response to changes in the price of the underlying asset. It quantifies the convexity of an option's delta and indicates how much the delta itself will change given a one-unit change in the underlying asset price.
Theta (Θ): Theta measures the rate of change of an option's price with respect to the passage of time. It quantifies the erosion of the option's value due to the diminishing time to expiration. Theta is typically negative, indicating that options lose value over time.
Vega (V): Vega measures the sensitivity of an option's price to changes in the implied volatility of the underlying asset. It quantifies the impact of changes in market expectations of future volatility on the option price. Vega is typically positive, suggesting that an increase in implied volatility will lead to a higher option price and vice versa.
Rho (ρ): Rho measures the sensitivity of an option's price to changes in the risk-free interest rate. It quantifies the impact of interest rate changes on the option price. Rho is typically positive for call options (negative for put options), indicating that higher interest rates generally increase the value of call options and decrease the value of put options.
These Greeks provide valuable insights into the risk exposures and behavior of options and other derivatives. They help traders, portfolio managers, and risk analysts assess and manage risks related to changes in asset prices, time decay, volatility fluctuations, and interest rate movements. It's important to note that the Greeks are not standalone measures but are interconnected and should be considered collectively to fully understand the risk profile of a derivative position. Additionally, the Greeks are based on various assumptions and simplifications, so their accuracy may be influenced by market conditions and modeling assumptions.
The Greeks are covered in more detail in module 3 of the CQF program.