Option Premium

1. Definition

The Option Premium is the current market price of an option contract. * It is the income received by the seller (writer) and the cost paid by the buyer.

2. The Formula

The premium is the sum of two components:

$$Premium = Intrinsic\ Value + Extrinsic\ Value\ (Time\ Value)$$

2.1. Intrinsic Value

• The tangible value of the option if it were exercised today.
• Call Option: $Current\ Price - Strike\ Price$ (if positive).
• Put Option: $Strike\ Price - Current\ Price$ (if positive).
• If the option is OTM (Out-of-the-Money), Intrinsic Value is Zero.

2.2. Extrinsic Value (Time Value)

• The premium amount over and above the intrinsic value.
• It represents the "risk premium" or the probability that the option will increase in value before expiration.
• Drivers: Time to expiration (Theta) and Implied Volatility (Vega).
• Decay: Extrinsic value wastes away as expiration approaches, eventually hitting zero at expiration.

3. Example

• Scenario: Stock at \$50. You buy a \$45 Call for \$7.
• Breakdown:
  • Intrinsic Value: \$5 (\$50 - \$45). This is real profit.
  • Extrinsic Value: \$2 (\$7 Premium - \$5 Intrinsic). This is the price you pay for the remaining time and potential upside.

4. Key Takeaway

• OTM (Out-of-the-Money) options consist 100% of Extrinsic Value.
• This is why buying OTM options is risky: if the stock doesn't move significantly, the entire premium evaporates due to time decay.