The Black-Scholes model does an admirable job at valuing short-term options. If an option expires in a few weeks, the current price of the underlying stock and its recent volatility have a good deal of influence on the outcome of the option investment. A simple Black-Scholes calculation has a lot of flaws (none of which I’ll go over), but in my opinion it does alright on the short-term options. However, the further away the expiration date, the worse it gets.
Value investors know that the historic volatility of a stock has nothing to do with its long-term value, and therefore should never be used when making a purchase. However, when purchasing equities, value investors have the luxury of waiting however long they need until price eventually reaches fair value.
If a stock is worth $30, that doesn’t mean a call option with a strike of $20 is worth $10. The option value must also depend on the duration of the option: the further out the expiration, the greater the underlying valuation should affect the option price (and the less volatility should matter). A lot of value investors purchase LEAPs, or options a year or more out, for this very reason.
The Graham-Olson Option Valuation Model
In honor of Benjamin Graham, I put forth the following equation as the value of a call option: