**Scenarios**

- Investors hold a large number of options and want to avoid the impact of the underlying asset's volatility on the option's value
- Investors hold the underlying asset and expect significant fluctuations in the underlying price but do not know whether it will rise or fall
- The current market's implied volatility is too high and expected to decrease. Investors want to short volatility

Delta hedging can ensure that the option price is not affected by changes in the underlying asset price.

## Description

Delta is a sensitivity indicator of options, representing the degree of impact of changes in the underlying asset price on the option price. When Delta is 0, the option combination is not sensitive to changes in the underlying asset price, and the risk of the option combination is hedged.

Options investors need to pay attention to the delta of their holding positions in the investment portfolio to make further delta hedging adjustments. When investors are long delta, it means they are bullish on the future market; when investors are short delta, it means they are bearish on the future market.

Underlying Asset Type |
Portfolio Holding Positions |
Delta of Holding Positions |
Delta Trading Nature |

Spot/Contract | Buy Underlying | Positive | Long Delta |

Spot/Contract | Short Underlying | Negative | Short Delta |

Option | Buy Call Option | Positive | Long Delta |

Option | Sell Call Option | Negative | Short Delta |

Option | Buy Put Option | Negative | Short Delta |

Option | Sell Put Option | Positive | Long Delta |

Delta neutral hedging means that investors increase or decrease the position of the underlying asset while holding the option position to make the delta of the entire portfolio equal to 0 or approximately equal to 0. For example, the following four two-legged hedging methods:

**Buy Call Option (Long Delta) + Short Underlying (Short Delta)**

**Sell Call Option (Short Delta) + Buy Underlying (Long Delta)**

**Buy Put Option (Short Delta) + Buy Underlying (Long Delta)**

**Sell Put Option (Long Delta) + Short Underlying (Short Delta)**

Of course, in addition to using the two different positions mentioned above for delta hedging, we can also use three or more different positions, that is, multi-leg delta hedging.

**Delta hedging is usually divided into static hedging and dynamic hedging.**

Delta static hedging means that no position adjustments are made from establishing the strategy to closing it. This is the method commonly used by most ordinary option investors. For institutional users or market makers, because of the large amount of capital involved, once the underlying price changes, the delta value will change, so dynamic adjustments need to be made when the portfolio deviates from delta neutrality to maintain a delta of 0, that is, delta dynamic hedging.

## Example

Let's take the example of delta hedging with two positions.

Assume the current BTC price is $28,000 and we sold a BTC-28APR23-30000-C call option on Coincall with a delta value of 0.4 and received a premium of $1,000. How do we achieve a delta-neutral portfolio?

Since this is a short call option, which means a short delta, we need to buy BTC to hedge. Let's assume we buy X BTC. The calculations are as follows:

Position |
Price |
Quantity |
Delta |
Total Delta |

Call Option | 1,000 | -1 | 0.4 | 0.4*(-1)= -0.4 |

BTC | 28,000 | X | 1 | 1*X = X |

Since the portfolio delta is zero, we can calculate X by adding the total delta of the call option (-0.4) and the total delta of BTC (X) and setting it equal to 0. Therefore, X = 0.4.

Next, let's calculate the hedging profit/loss. The opening and closing operations of the portfolio are as follows:

**Opening Portfolio = Sell 1 Call Option + Buy 0.4 BTC**

**Closing Portfolio = Buy 1 Call Option + Sell 0.4 BTC**

Assume that the BTC price rises to $30,000, and the call option price rises to $1,800 = (1,000 + 0.4*(30,000 - 28,000)).

Assume that the BTC price falls to $26,000, and the call option price falls to $200 = (1,000 - 0.4*(28,000 - 26,000)).

Transaction |
Option P/L |
BTC P/L |
Portfolio Value Change |

Opening | +1,000 | -11,200 | -10,200 |

Closing (BTC up to $30,000) | -1,800 | +12,000 | +10,200 |

Closing (BTC down to $26,000) | -200 | +10,400 | +10,200 |

As shown in the table, by using delta hedging, the total portfolio value at the opening and closing positions always sums up to **Zero**, regardless of whether the BTC price rises or falls. Therefore, the portfolio value is not affected by changes in the underlying asset price.

If the delta remains the same during the period, the total profit and loss of the hedged portfolio are approximately zero (ignoring actual trading costs).

## Advantages

For investors, delta hedging can reduce market risk and increase the success rate of trading. By achieving a delta value of zero, investors can profit from different market conditions, such as long or short volatility, or earn time value, without incurring losses due to changes in market prices.

Delta hedging can also be used to construct complex combination strategies and is widely used in various option combination strategies and hedging operations to reduce risk and maximize returns.

Learning to use delta hedging strategies flexibly can help options traders construct more practical combination strategies and enable traders to truly understand the importance of risk control in options trading, thereby using options as a hedging tool for trading and investment.

## Extended

From the previous examples, we can see that in the process of opening to closing a position, the total profit and loss are always equal to zero because the delta of the option remains constant. However, in actual trading, the delta is constantly changing as the underlying asset price and options market price fluctuate. Therefore, as professional investment institutions (such as market makers), they need to constantly adjust the delta-hedging positions to maintain delta neutrality, and this is called delta dynamic hedging.

The principle of delta dynamic hedging is the same as that of static hedging, but the operation is more complex. The difference is that in the process of opening and closing positions, dynamic hedging needs to dynamically adjust the position to continuously maintain the delta of the combination strategy at 0. There are two commonly used ways of dynamic position adjustment, including threshold deviation adjustment and fixed time interval adjustment, such as adjusting the position when the delta value deviates by 10%, or adjusting the position once a day. Delta dynamic hedging has a certain level of operational difficulty. We recommend that investors start with static hedging of two positions in trading and gradually increase the frequency of position adjustment and the number of positions.

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