Practically Understanding Greeks Meaning for Option Value
We are going to examine the calculator output generated in our fully working option greek calculator of DeriBit transactions to practically explain each of the calculated option greeks. In the below example, the market participant sold one Call contract with a strike price of $28,000 and a maturity date of April 14, 2023 (9 days away as of time of writing). The participant stands to make a profit of $895 (minus commissions) if the Bitcoin (BTC) Index price is less than $28,000 at the time of expiration. The participant received the value ($$) upfront as premium because he sold the option contract.
Delta can be understood as the change in value of the option per $1 change in the underlying asset (BTC Index). Calculated delta of -0.50 means that for every $1 move higher (lower) in the change of the BTC Index, the option value loses (gains) $0.50c.
Gamma indicates the change in the "Delta" per $1 move in the BTC Index; The value of -0.000168 indicates that Delta will further decrease from -0.50 at the rate of gamma (-0.000168) for every $1 change in the BTC Index. As an additional, further example: if hypothetically, the BTC Index fell $100 from its current value; the option's delta will approximately change from -0.50 to -0.5168. Gamma more so refers to the anticipated Delta for each $1 change rather than the change in the option value itself.
The implied volatility of this option when executed was 0.5399 - The calculated vega value of -17.51 can be understood to mean that if implied volatility increases (decreases) 1% from .5399 to .5499, then the value of the underlying option will decrease (increase) by $17.51.
Theta is calculated as 54.17; which basically means that for a one day change closer to option maturity, the option value will increase by $54.17. Or you can think of it another way, assuming all other market factors stay the same: the market participant would receive an additional $54.17 in premium upfront (since they sold the option) if the days to maturity increased from 9 to 10.
No one ever talks about Rho because changes in underlying interest rates are historically less volatile and therefore has less effect on overall option value than the other greeks. For interpretation purposes: the change in the risk free rate from 4.62% to 5.62% (always understood for a 1% change), will decrease the value of the option by $35.75. Rho is generally more important of a consideration for longer term options.
Here is an example results/output from script
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