How Option Premium Is Calculated
The premium of a covered call option is determined by a complex interplay of mathematical and market forces. The Black-Scholes model provides the theoretical framework, but real-world premiums also reflect supply and demand, market maker positioning, and trader sentiment. Understanding the formula helps you identify when premiums are rich (favorable to sell) or cheap (unfavorable to sell).
Option premium has two components: intrinsic value (the in-the-money amount) and extrinsic value (everything else, driven primarily by time and volatility). For covered call sellers, the extrinsic value is the true income component because it decays to zero by expiration.
The Black-Scholes Premium Formula
- 1T = 30/365 = 0.0822 years
- 2d1 = [ln(100/105) + (0.05-0.015+0.045)*0.0822] / (0.30*sqrt(0.0822))
- 3d1 ≈ -0.505, d2 ≈ -0.591
- 4N(d1) = 0.307, N(d2) = 0.277
- 5C = 100 * e^(-0.001) * 0.307 - 105 * e^(-0.004) * 0.277
- 6Theoretical premium ≈ $1.45 per share
Factors in the Premium Formula
| Input | Increase | Decrease | Relative Impact |
|---|---|---|---|
| Implied Volatility (sigma) | Premium UP significantly | Premium DOWN | Highest impact |
| Time to Expiration (T) | Premium UP | Premium DOWN (theta decay) | High impact |
| Stock Price (S) | Premium UP for calls | Premium DOWN | High impact |
| Strike Price (K) | Premium DOWN for calls | Premium UP | High impact |
| Risk-Free Rate (r) | Premium UP slightly | Premium DOWN slightly | Low impact |
| Dividend Yield (q) | Premium DOWN for calls | Premium UP | Moderate impact |
For ATM options, premium is approximately 0.4 x Stock Price x IV x sqrt(DTE/365). For a $100 stock with 30% IV and 30 DTE: 0.4 x $100 x 0.30 x sqrt(30/365) = $3.44. This quick estimate works well for ATM options and degrades for deep ITM or OTM options.