What does nonlinear derivatives mean?

Nonlinear derivatives mean that in the financial market, the relationship between its price and the price of the underlying asset is not a simple linear relationship, but exhibits nonlinear characteristics. Such derivatives usually include options, futures options, etc. Their value changes are not only affected by the price of the underlying asset, but also by other factors (such as time decay, volatility changes, etc.), causing their profit and loss curves to behave under different market scenarios. It is a non-linear form.

Nonlinear properties of options:

In financial markets, options have nonlinear characteristics. The linear relationship refers to the relationship between the changes of two quantities in a fixed proportion. It can be expressed by a function whose first derivative is a constant, and the expression is ?. It shows that the relationship between two quantities is a straight line. For example, the relationship between profit and loss and price of stocks, futures, etc. usually shows a linear relationship.

On the contrary, a nonlinear relationship means that the changes in the two quantities do not have a fixed proportional relationship, that is, the first derivative is not a constant. There is a typical non-linear relationship between option profit and loss and price. It means that the value changes of options at different price levels may not be a simple proportional relationship, but may appear as broken lines, curves and other graphics.

The relationship between price changes and profit and loss of linear investments such as futures and stocks is relatively linear, that is, if the price rises or falls by the same unit, the changes in profit and loss are relatively even. As a non-linear investment type, options have more complex changes in their profit and loss relationship at different price points.

The nonlinearity of options comes from the separation of rights and obligations. One party to the option has the right to decide whether to execute the contract, which means that the profit and loss curve of the option takes on different shapes under different market conditions. This unequal rights structure makes options flexible in combination and strategy construction. Investors can flexibly adjust the return and risk characteristics of the investment portfolio through different option combinations, providing more choices for their asset allocation and risk management.

In terms of the non-linear application of options, investors often use options for risk hedging. For example, for investors holding spot stocks, put options can be purchased as a hedging tool. When the market price drops sharply, the profit from the put option can make up for the spot loss; while when the market price rises sharply, only the premium is lost and the rising profit can be retained.

Compared with traditional futures risk hedging methods, although options require payment of premium, they are more flexible and can retain more rising profits.