Explanation on the Option Greeks

The values of the Greeks are an important risk indicator for options trading. To facilitate users’ management of risk exposure of options positions, Huobi Options adopts Greeks to measure the risk situations of options positions in a certain dimension and carries out corresponding risk hedging.

1. Options Mark Price
Due to the violent fluctuations of options market price, Huobi Options uses the options mark price, which is calculated based on the options implied volatility as reference price. The mark price is calculated by using the Black-Scholes model.

2. Implied Volatility (IV):

The volatility implied by the market price of an option is calculated according to the option pricing formula.
The implied volatility of an option is calculated and determined by the whole options market (determined by the buy 1 and sell 1 of the option and the nearby option). The process of deriving the implied volatility from the average price, buy 1 and sell 1 is to combine the option pricing formula and use the dichotomy to continuously calculate and approximate the average price until the calculated price reaches the set accuracy. Then use the implied volatility to calculate the marked price and the Greek value of the corresponding option.

Initial default parameters:

 (1) Listing price: a reference value can be used for the initial volatility, such as IV=0.8;

(2) Maximum IV = 500%

(3) Minimum IV =0

3. Greeks Value Algorithm

The algorithm of options Greeks value and the specific risk value measurement of Greeks are as following:

  • Delta is a measure of change in an option's price (that is, the premium of an option) resulting from the change in the underlying asset.

Delta = ∂c/∂S

Example: Delta = 0.121 When the index price changes 1 USDT, the corresponding changes of the options price is 0.121 * 1=0.121 USDT

  • Gamma measures the rate of change in the Delta for each one-point change in the underlying asset. 

Gamma =∂Delta/∂S

Example: gamma=0.021 when the index price changes 1 USDT, the corresponding changes of options delta is 0.021*1=0.021

  • Theta measures the rate of time decay of an option or its premium, the asset amount an option will lose each day due to the passage of time.

Theta =∂c/∂T

Note: In above formula, the theta value obtained is in the unit of year, while the Theta value shown on the trading page and pushed by the API is in the unit of day; hence the theta on the trading page=Theta/365

The Theta value obtained from the above calculation formula is in the unit of year, while the Theta value shown on trading page and pushed by API are in the unit of day, hence the theta value shown on the trading page = Theta/365 (theta = Theta/365)

Example: Theta=-4.2, the Theta value of the option in the unit of day is -4.2/365=-0.011507, meaning that every day closer to the expiration date, the corresponding change in the option price is 1*-0.011507 = -0.011507 USDT

  • Vega measures the risk of changes in implied volatility or the forward-looking expected volatility of the underlying asset price.

Vega =∂c/∂σ

Note:The Vega value obtained from the above calculation formula corresponds to the annualized volatility with a change unit 1 (100%), while the vega value shown on the front-end and API push corresponds to a vega with a change unit of 1%, hence the value of vega shown on the front-end is Vega/100 (vega = Vega/100)

Example: Vega =12.1 When IV increases (or decreases) 1%, the options price will increase (or decrease) 12.1*1%=0.121 USDT correspondingly.

 

 

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