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:
The Black-Scholes value can be calculated using a spreadsheet model or from websites like this.
Here’s a practical example: Let’s say that you think Burlington Northern (BNI) is worth $90-110. The Graham-Olson model values the $80 January 2011 calls at $8.3-$19.5. Time to expiration is 1.75 years and the Black-Scholes model uses volatility of 25%, risk free rate of 3% and current price of $68.
The graph to the right represents both valuation models of the BNI options with an IV of $100. The x-axis is the time to expiration in years.
The formula isn’t very precise, but then again, neither is value investing. The Intrinsic Value input is obviously very subjective (that’s why I’d probably use a “range” of valuations like in the example above).
The numbers 3 and 5 in the exponent adjust the”shape” of the graph so that on average, a stock should reach its intrinsic value in around 4 years. As you can see from the graph above, the equation puts BNI at approximately intrinsic value in 3 years. These numbers can be adjusted based on how long you think the average stock takes to reach fair value.
I think that most value investors who purchase options already intuitively use the above method when making a purchase. But the Graham-Olson model can be used to check your assumptions using a variety of different inputs.
If a stock is overvalued, it shows that the Black-Scholes formula can overprice even very short-term options. There are also many occasions when an option reaches its value even though the underlying stock hasn’t — in this scenario the Graham-Olson model could be a useful guide of when to sell.
If you have any suggestions or criticisms please feel free to comment below.
* In reality, IV should be the present value of your estimate of IV at the time of expiration.