In addition, the option price is affected by the underlying price S, exercise price X, term T, risk-free interest rate R, volatility σ and other factors, so how to measure the impact of their changes on the option price? Generally speaking, the Greek letters Greeks——Delta, Gamma, Vega, Theta and Rho are used to indicate these changes.
Option price curve
The option line chart we usually see is the price of the option's expiration date, which only contains intrinsic value. However, in the actual trading process, the option price is mostly the price of the unexpired date, which is in the form of a curve, including intrinsic value and time value.
Time value comes from the asymmetry of rights and obligations of options. When the option has not expired, the fluctuation of the underlying asset price may bring benefits or implied value to the option holder. Therefore, the time value of option price is sometimes called fluctuating value.
Brief introduction of option sensitivity factors
Incremental value
Delta value is the partial derivative of option value to the underlying asset price, that is, the slope of option price curve, which is used to measure the risk of option price change caused by the underlying price change. Among them, the Delta value of the call option is positive, and the range is 0-1; The Delta value of put option is negative, and the range is-1-0; The incremental value of the plane option is approximately equal to 0.5. It should be pointed out that the symbol of risk indicators is considered from the perspective of call options. In the actual trading process, we should pay attention to the difference between option index and position index.
Delta values mainly have the following characteristics: first, Delta values can be added; Second, the position where the delta value is zero is called delta value neutrality; Thirdly, the Delta value varies with the underlying asset price, and the Delta value neutrality is a dynamic concept.
For example, in the option portfolio, the Delta value of position 1 is 0.5, the Delta value of position 2 is -0.4, and the total Delta value of the portfolio is 0.5-0.4=0. 1, which is equivalent to holding 0. 1 futures long position.
Gamma value
Gamma value is the second-order partial derivative of option value to the underlying asset price, and it is also the partial derivative of option Delta value to the underlying asset price, that is, the slope of Delta value curve, which is used to measure the risk of Delta value change caused by option price change.
The Gamma value of option bullish is positive and the Gamma value of option bearish is negative, that is, the Gamma value of call option and put option is positive and the Gamma value of call option and put option is negative.
Gamma value mainly has the following characteristics: first, only options have Gamma value; Second, when the Gamma value of the portfolio is zero, it is said to be in a neutral state of Gamma value; Thirdly, gamma value neutrality is to eliminate the error of delta value neutrality, which is also a dynamic concept.
Vega value
Vega value is the partial derivative of option value to the volatility of the underlying asset, which measures the sensitivity of option value to the volatility of the underlying asset. Among them, the Vega value of option buyer is positive, and the Vega value of option seller is negative; The Vega value of option contracts with different connotation values is also different, and the Vega value of plane options is greater than that of real options or imaginary options.
θ value
The θ value reflects the value lost by the option buyer in a period of time, and is used to measure the speed at which the theoretical value of the option declines with the approach of the expiration date. It is a time-varying risk measurement index. Whether it is a call option or a put option, the theoretical value of the option will accelerate to decline as the maturity approaches.
On the one hand, the θ value of the option buyer is negative, that is, the maturity period decreases, the option value decreases accordingly, and the θ value of the option seller is positive; On the other hand, the θ value of option contracts with different connotation values is also different, and the θ value of plane options is greater than that of real options or virtual options.
ρ value
ρ value is the ratio of option price change to interest rate change, which measures the sensitivity of option theoretical value to interest rate change.
Application of option sensitivity factor
Delta hedging
In the actual operation, considering the final exercise, it is only necessary to ensure that the underlying position corresponding to the option is equal to the position that investors need to hedge. If we only consider the hedging of options, futures and other positions in the price, we need to keep the Delta value neutral.
It should be noted that the option Delta value is nonlinear. In the process of Delta value neutral hedging operation, Delta value will change due to the change of option price, which will lead to the neutral failure of Delta value. Therefore, it is necessary to dynamically adjust the Delta value neutral strategy to keep the Delta value of the portfolio zero.
Gamma hedging
Because keeping the Gamma value neutral can only be achieved by adjusting the position of the option, the result of realizing the Gamma value neutrality is often that the Delta value is not neutral. Therefore, it is often necessary to use the underlying assets or future positions to adjust the portfolio to achieve both Delta value neutrality and Gamma value neutrality. Because the Gamma value of options is nonlinear, it is also a dynamic concept.
Comprehensive analysis, the biggest feature of option is nonlinear, the option price is nonlinear, and the option sensitivity factor is also nonlinear. Therefore, in practice, Delta value neutral hedging and Gamma value neutral hedging are both dynamic concepts, and positions need to be constantly adjusted to maintain a neutral state.