期权Greeks（一）：基于Delta、Gamma、Theta精细化管理方向性期权策略

Report Industry Investment Rating No relevant content provided. Core Viewpoints of the Report In recent years, the Chinese commodity options market has witnessed explosive growth, with continuous enrichment of trading varieties and a significant increase in trading volume. The market participant structure shows a significant institutionalization trend, and investment strategies vary among different participants. Market volatility characteristics have also changed profoundly, posing challenges to traditional options strategies. Therefore, it is necessary to optimize options strategies. This report focuses on Delta, Gamma, and Theta among the option Greeks, elaborating on their meanings, characteristics, and how to optimize directional options strategies based on them from four dimensions: opening positions, adjusting positions, taking profits, and setting stop - losses [1][12][16][21]. Summary According to the Directory 1. Necessity of Optimizing Options Strategies - The Chinese commodity options market has achieved explosive growth. From a product layout perspective, it has formed a complete product system covering 55 varieties, with a target coverage rate exceeding 70%. In terms of market scale, the annual compound growth rate of on - exchange commodity options trading volume from 2017 - 2023 was as high as 117%, and the off - exchange market also maintained an average annual growth rate of 77.68% in the past five years [12]. - The options market participant structure shows significant institutionalization. In the Shanghai Stock Exchange options market, the proportion of individual investors has been decreasing year by year, and in 2024, institutional investors accounted for 68.29%. Individual and institutional investors have different investment strategies, with individuals preferring to buy to open positions for directional gains and institutions mainly selling to open positions [16]. - Market volatility characteristics have changed. Major macro - events have led to an increase in the volatility center, and the popularity of algorithmic trading has made the market microstructure more complex. Traditional options strategies relying solely on directional judgments or fixed parameters may not adapt to the new environment [16][21]. 2. Meanings and Characteristics of Delta, Gamma, and Theta 2.1 Delta: Current Earning Speed - Delta measures the first - order sensitivity of the option price to the underlying price. It is affected by the moneyness (S/K), time to maturity (T), and volatility (σ). In the Black - Scholes framework, the Delta of a call option can be regarded as the risk - neutral probability of the underlying asset being in - the - money at maturity, while the absolute value of the Delta of a put option corresponds to the probability of the underlying being below the strike price at maturity [24]. - The moneyness has a core impact on Delta. The Delta of a call option increases monotonically from 0 to 1 as the underlying asset price rises, while that of a put option increases monotonically from - 1 to 0, showing an S - shaped curve [25]. - The impact of time to maturity on Delta is non - linear. For in - the - money and out - of - the - money options, the Delta of deep in - the - money options converges to 1 as time decreases, and that of deep out - of - the - money options decays to 0. For at - the - money options, the Delta becomes more sensitive to underlying price changes as the expiration date approaches [28]. - The impact of implied volatility on Delta is dynamic and non - monotonic. For in - the - money and out - of - the - money options, the impact is asymmetric. For at - the - money options, an increase in implied volatility causes the Delta to converge to 0.5 [30]. 2.2 Gamma: Future Earning Acceleration - Gamma measures the second - order sensitivity of the option price to the underlying price, indicating the change rate of Delta. It is affected by the moneyness (S/K), time to maturity (T), and volatility (σ) [34]. - The moneyness has a significant impact on Gamma. Gamma shows a bell - shaped curve distribution. The Gamma values of deep in - the - money and deep out - of - the - money options are close to zero, while the Gamma of at - the - money options reaches its peak [35]. - The impact of time to maturity on Gamma is non - linear. For at - the - money options, Gamma increases rapidly as the expiration date approaches, especially in the last 1 - 5 trading days. For deep in - the - money or out - of - the - money options, Gamma remains close to zero and is less affected by the remaining term [42]. - The impact of implied volatility on Gamma is significant for at - the - money options, showing a negative correlation. High implied volatility weakens the timeliness requirement of Gamma hedging, while low implied volatility increases the urgency of Gamma hedging [45]. 2.3 Theta: Cost for Option Buyers - Theta measures the first - order sensitivity of the option price to time, representing the decay rate of the option's time value. It is usually negative and is affected by the time to maturity, moneyness, and implied volatility [49]. - The impact of time to maturity on Theta is non - linear. For at - the - money options, Theta shows an "acceleration effect", with the time value decaying non - linearly faster as the expiration date approaches. For deep in - the - money or out - of - the - money options, Theta is less sensitive to the change in the remaining time [51]. - The moneyness has a significant impact on Theta. The absolute value of Theta shows an inverted U - shaped distribution, with the at - the - money options having the largest absolute value of Theta [54]. - The impact of implied volatility on Theta is non - linear. An increase in implied volatility leads to an increase in the absolute value of Theta for at - the - money options, while the impact on out - of - the - money and deep in - the - money options is relatively small [57]. 3. Optimizing Directional Options Strategies Based on Delta, Gamma, and Theta 3.1 Opening Positions - When constructing an option buyer strategy, the choice of strike price is crucial. Different moneyness options have different risk - return characteristics. Investors should choose according to the expected trend of the underlying asset. For short - term sharp rises, at - the - money or slightly out - of - the - money options may be better; for long - term steady upward trends, in - the - money options may be more advantageous [61]. - When evaluating the cost - effectiveness of strike price selection, the historical percentile of implied volatility should be considered. In a high implied volatility environment, out - of - the - money options show better cost - effectiveness [62]. - The remaining time to maturity also affects the option value. For short - term trading, options with a remaining maturity of less than 1 month are suitable; for medium - and long - term layouts, in - the - money options can better control time value decay [68]. - The current on - exchange commodity options market in China has a single contract term structure. The launch of short - term options provides more strategy options, such as the calendar spread strategy [69][71]. 3.2 Adjusting Positions - "Chasing to buy": When implementing a call option buying strategy, as the underlying price rises, the option position moves from out - of - the - money to in - the - money. By adjusting the position to out - of - the - money options, it can balance the locking of profits and risk control [76]. - "Chasing to sell": When implementing a put option selling strategy, as the underlying price rises, the option becomes more out - of - the - money. By adjusting the position from deep out - of - the - money to slightly out - of - the - money options, it can increase the profit space, but it also requires strict risk management [77]. 3.3 Taking Profits - For put option selling, the core of taking profits is to balance the realized time value gain and potential risk. Time value decay take - profit is a basic strategy, and the implied volatility should also be considered [84]. - For call option buying, taking profits based on the target price of the underlying and technical analysis is a basic strategy. The implied volatility should also be monitored, especially in event - driven trading [88]. 3.4 Setting Stop - Losses - For call option buying, the key to risk management is to control the scale of the premium at the beginning, as the maximum loss is limited to the premium paid. - For put option selling, pre - investment and in - investment risk control and stop - loss strategies are crucial. This includes position size management, contract screening, dynamic management of Greek letters, and sensitivity analysis and stress testing. In the investment process, a dynamic protection system should be established, including price trigger mechanisms, implied volatility monitoring, and dynamic hedging of Greek letter risks [92]. 4. Characteristics of Greek Letters of Common Options Combinations Option combination strategy investors should manage the multi - factor risk exposure of their positions before opening positions and during the holding period, as some Greek letters of option combination strategies may be overlooked [4].