# An Option Model for Value Investors

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:

*Where*:

IV = Intrinsic value of underlying stock (In reality, IV should be the present value of your estimate of IV at the time of expiration.)

SP = Strike price of option

BS = Black-Scholes valuation of option

x = Time to expiration (in years)

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 above 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.

## Conclusion

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.