Greeks of a Covered Call Position

Summary

The document clarifies how to combine option Greeks for a covered call, consisting of long stock and a short call. Since the stock position contributes delta but has no gamma, theta, or vega in the framework described, the portfolio delta is the stock’s unit delta offset by the long call’s delta. The other three Greeks are the negatives of the long call’s corresponding values, reflecting the short option position.

This corrects the proposed approach of subtracting one from every Greek: that treatment is only appropriate in spirit for delta, where the underlying shares contribute. The explanation is a position-level accounting rule, not a calculation of the option Greeks themselves. It does not specify a pricing model, contract multiplier, or adjustments for dividends, financing, or other real-world exposures, so those details still matter in an applied valuation.

Key ideas

• A covered call combines long stock exposure with a short call position.
• The stock contributes delta, so covered-call delta equals the stock delta minus the long call delta.
• The stock contributes no gamma, theta, or vega in the stated framework.
• Covered-call gamma, theta, and vega are the negatives of the long call’s respective Greeks.
• Position-level Greek signs do not provide the option Greeks’ underlying pricing calculations.

Tags

# Calculating Greeks in Covered Calls?


# Calculating Greeks in Covered Calls?












Just want to confirm whether Delta, Gamma, Theta, Vega will be calculated in the following way? Since we own 100 shares of stock while selling a call we need to subtract greek value from one? right?

Covered Call Delta = 1 - "Long Call delta"

Covered Call Gamma = 1 - "Long Call gamma"

Covered Call Theta = 1 - "Long Call theta"

Covered Call Vega = 1 - "Long Call vega"

## Answer by CHP (score 4, accepted)

https://quant.stackexchange.com/a/9292

You are right for delta but wrong for other greeks.

Delta of stock is 1 so `Covered call Delta = 1 - "long call delta"` is correct

However a stock doesn't have `gamma` , `theta` or `vega`. So these greeks of your covered call positions will be just that of short call. i.e

```
Covered Call Gamma =  - "Long Call gamma"

Covered Call Theta =  - "Long Call theta"

Covered Call Vega =  - "Long Call vega"
```

## Answer by Chris Andy (score 1)

https://quant.stackexchange.com/a/25437

Check out this post: http://www.macroption.com/option-greeks-excel/

Let me know if it answers your query.

The Excel equations used to calculate Delta, Gamma, Theta and Vega are shown in the above link.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.