A Primer For Valuing Options

||A Primer For Valuing Options

A Primer For Valuing Options

January 2013

Option contracts existed as early as ancient Greece.  Aristotle wrote in his Politics how Thales made a fortune in option contracts for olive presses. Thales, who previously was poor, forecasted that the olive harvest would be exceptionally good the next fall season. Being confident in his predictions, he offered a deal to olive-press owners.  Thales offered to pay the press owners what little money he had in exchange for exclusive use of their olive presses when the harvest time came. Thales successfully negotiated low prices because the harvest was in the future and no one knew whether the season would be abundant or scarce.  However, Thales was not obligated to exercise the options.  If the olive harvest did not occur as he predicted, Thales could let the options expire and limit his loss to the amount he paid for the option contracts.  But, as Thales predicted, the harvest was plentiful and he exercised the options.  Thales then made enormous profits by reselling the use of the olive presses.

When used with financial instruments, options are a contract between two parties in which one party has the right, but not the obligation, to do something.  Usually, the option involves buying or selling an underlying asset.  Having rights without obligations has financial value, so option holders must purchase these rights at a price, called a premium. Options derive their value from the underlying asset, which is why they are called derivative instruments.

Call options are contracts giving the option holder the right to buy something.  Put options give the option holder the right (not the obligation) to sell something.

At the option’s expiration, the call option is worth the greater of zero (negative values cannot occur because exercise of the call is not required) and the difference between the underlying asset value (such as a stock price) and the amount that must be paid when the option is exercised (called the strike price).  The excess of the stock price over the strike price is called option’s intrinsic value.

Here is an illustration.  Assume a call option has an initial cost (called a premium) of $1.  The option gives the right to purchase an asset (in this case a share of stock) for a $10 strike price.  The option expires in a year. The stock’s current price is $6. The option purchaser is betting that the underlying asset price will go up in the future, so he waits. Now, fast-forward to when the option expires. The stock price is now $15. The option holder buys the stock from the option writer for the $10 strike price and sells the stock in the market at $15 making $5 profit.  This $5 is the option’s intrinsic value.  But the option holder paid $1 to purchase the call, so the profit drops to $4 (ignoring considerations for the time value of money).

Alternatively, if the price of the stock were $8 at the time of the option’s expiration, the option holder would not exercise the option, and let it expire as worthless.  In this case, the option holder’s loss is limited to the amount paid ($1) to purchase the call option.

Now, let’s go back to the time when the call was first bought. The stock price is currently at $6, which is below the strike price. Even though the option is not in the money (i.e., it has no intrinsic value at that moment), the option still has market value because no one knows what will happen to the stock value before the option expires. That uncertainty is an added value of the option.  In the example we have been using, that option premium was assumed to be $1.

In real life, we do not get to assume values.  That’s where the option valuation models come in.   Although there are several mathematical models available, options are most commonly appraised through a mathematical model called the Black-Scholes option pricing model.  The model’s name comes from Fischer Black and Myron Scholes, who published their option pricing model in 1973 (and who won a Nobel Prize for their creation).

The Black-Scholes model has two parts.  The first part calculates the expected benefit from selling the underlying stock when the call option is exercised. This portion of the model makes a projection of future prices.  The model’s second part is the present value of paying the strike price on the expiration day. The fair market value of the call option is the difference between these two parts.

Since its origination, others have improved the Black-Scholes model to account for complexities that the original authors ignored (or assumed away).  The most important of these improvements are:

  1. A modification for the impact of dividends – The original model ignores dividends.  Options which have not been exercised do not earn dividends. This impacts the decision of whether to exercise an option early, and lessens an option’s value for a stock that pays dividends.
  2. A modification for the dilutive effect of issuing additional shares – The original model assumes that options have no dilutive effect.  This assumption is satisfactory when valuing (i) exchange traded options, and (ii) covered options.  (Covered options, also called synthetic warrants or third-party warrants, are a stock, basket, or index warrant issued by a party other than the issuer of the underlying stock.)

In contrast, warrants and employee stock options have a dilution effect because new shares are issued when those warrants or stock options are exercised.  When additional shares are issued, all shares have a lesser ownership interest, so options causing dilution are worth less than if no dilution occurred.

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