I often see blog posts and content on option basics, and strategies such as covered calls, or protective puts. However, very little of that content actually covers what the “Fair Value” of an option should be.
The easiest way for me to understand it after learning through the years is to first think about expected payoffs, followed by asset price simulations.
The expected payoff is the product of my probability of profit and my actual profit. Let’s take a call option as an example, a call option is the right to buy the underlying at a specific strike price. Say we’re at maturity, and the strike of the option is at $10.
If the underlying stock was worth $11, then my option value is worth $1 (11-10). If the underlying stock was worth $15, then my option value is worth $5 (15-10). If the underlying stock was worth $9, then my option is worthless $0.
What’s the probability of my underlying stock being greater than the strike of $10? If there’s an 20% chance that the underlying stock will be $15, and a 30% chance it’ll be worth $11, and a 50% chance it’ll be worth 0... then the expected value is 0.20*$5+0.30*$1+0.50*0 = $1.30.