Black-Scholes Valuations

Assumptions

Like all economic models, the Black-Scholes model has a number of assumptions.

The Black-Scholes assumptions are:

• the stock pays no dividends during the option's life
• European exercise terms are used
• markets are efficient
• no commissions are charged
• interest rates remain constant and known and
• returns are normally distributed

Let’s take a closer look…

The stock pays no dividends during the option's life.

Some companies pay dividends to their shareholders. This might appear to seriously limit the model since higher dividend yields elicit lower call premiums.

But there’s a common way of adjusting the model for this situation:

Subtract the discounted value of a future dividend from the stock price.

European exercise terms are used.

American options are more valuable than European options because American options are more flexible. Let’s take a look…

But this limitation is not a major concern since few calls are ever exercised before their last few days of life. Why? When you exercise a call early, you forfeit the remaining time value on the call and collect the intrinsic value.

For the purposes of the analyses in this course, employee stock options are like European-style options until the vesting date, because they may not be exercised until then. However, after the vesting date, they more closely resemble American options, as they can be exercised at any time.

Markets are efficient

This assumption suggests that people cannot consistently predict the direction of the market or an individual stock since both are stochastic.

No commissions are charged.

Market participants usually have to pay a commission to buy or sell options. Even floor traders pay some kind of fee, although it’s usually small. Individual investors usually pay more substantial fees. These fees can distort the output of the model.

Interest rates remain constant and known.

The Black-Scholes model uses the risk-free rate to represent this constant and known rate.

There’s really no such thing as the risk-free rate, but the discount rate on U.S. government Treasury Bills with 30 days left until maturity is usually used to represent it. During periods of rapidly changing interest rates, these 30-day rates are often subject to change, thereby violating one of the assumptions of the model.

Returns are normally distributed.

This assumption suggests that returns on the underlying stock are normally distributed. This is reasonable for most assets that offer options.