In the risk-neutral world, the forward maturity value discounted at the risk-free interest rate is equal to the present value, that is, under the risk-neutral condition, the forward discount value is a martingale. The value of long-term bulls is S0-kexp (-RT), taking the first derivative of the underlying asset S, and the delta is 1 ..

Extended data

I. Introduction of Delta Value

1, Delta, also known as hedging value: it is a measure of the range of option price change when the underlying asset price changes. Expressed by the formula: Delta= option price change/spot price change of the underlying asset. The Delta value of call option is positive (ranging from 0 to+1), and the Delta value of put option is negative (ranging from-1 to 0).

2. The Delta value of the call option is positive (ranging from 0 to+1), because when the stock price rises, the price of the call option will also rise. The Delta value of put option is negative (the range is-1 and 0), because when the stock price rises, the price of put option will fall. The Delta value of the equivalent call option will be close to 0.5, while the Delta value of the equivalent put option will be close to -0.5.

3. For the Delta value, you can refer to the following three formulas:

1. option Delta weighted part = market value of the underlying asset of the option × option Delta value;

2. Delta weighted position of option × market risk coefficient of each target =Delta risk equivalent;

3.Delta weighted position value = option delta weighted position value+spot hedging position value.

Second, the law of gamma value

Unlike delta, the gamma values of call options and put options are positive for bulls:

With the rise of futures prices, the long delta value of call options moves from 0 to 1, and the long delta value of put options moves from-1 to 0, that is, the delta value of options changes from small to large, and the gamma value is positive.

When the futures price falls, the long Delta value of the call option moves from 1 to 0, and the long delta value of the put option moves from 0 to-1, that is, the delta value of the option changes from large to small, and the Gamma value is negative.

For the option part, whether it is a call option or a put option, the Gamma value of this part is positive as long as it is a call option, and it is negative if it is a put option.

The Gamma value of the flat option is the largest, and the Gamma value of the deep real value or deep imaginary value option approaches 0. As the expiration date approaches, the Gamma value of flat options will increase sharply.

Option traders must pay attention to the influence of the change of option Gamma value on position risk. When the price of the underlying asset changes by one unit, the new delta value is equal to the original delta value plus or minus the Gamma value. Therefore, the greater the Gamma value, the faster the Delta value changes. Delta neutral hedging, the greater the absolute value of Gamma, the higher the risk, because the frequency of neutral hedging needs to be adjusted; On the contrary, the smaller the absolute value of γ, the lower the risk.