# Factors that Influence Option Value + The Black-Scholes Model

An integral part of understanding option trading basics, is mastering the components that influence option value. Many option traders will look to make money as a result of a discrepancy between an option’s current market value and its theoretical value. In other words, is the option overpriced or undervalued? If, for example, an option is calculated to be underpriced an investor will purchase it and look to sell it when market forces return it to the higher, more appropriate value. An analogy would be if you found a real estate property on sale for \$100k in an area where similar homes were selling for \$120k…buy low and sell high. In order to utilize this approach, we would first need to determine the theoretical value (a mathematically derived estimate of the value of the contract) of the option to determine if it is priced fairly.

The most well known of these option pricing models is the Black-Scholes Model introduced by Fischer Black and Myron Scholes in 1973. The following option and underlying characteristics need to be known for the calculations:

#### Parameters used for the Black-Scholes Model:

• The option’s exercise price
• The current price of the underlying
• The risk-free interest rate over the life of the option
• The amount of time remaining until expiration
• The volatility of the underlying

These parameters are entered into the formula developed by Black and Scholes and a theoretical value for the option is calculated and then compared to the current market value. There have been several variations of the Black-Scholes Model developed since 1973 but the original remains the most popular amongst traders. There are several assumptions made by this model some of which have come under criticism:

#### A discussion of the Assumptions of the Black-Scholes Model:

1)  The stock pays no dividends during the option’s life

Many companies do in fact distribute dividends which may impact call premiums. One way to adjust the model for this would be to subtract the discounted value of a future dividend from the stock price. Even though the original Black-Scholes model does not take dividends into consideration, an extension of the Black-Scholes Model proposed by Merton in 1973 alters the Black-Scholes model in order to take annual dividend yield into consideration. This model is not as widely used as the original Black-Scholes Model.

2) European exercise terms are used

The model assumes that the option can only be exercised on the expiration date. We, in fact, use American style options which allow the option to be exercised at any time during the life of the option, making American options more valuable due to their greater flexibility. This limitation is not a major concern because very few calls are ever exercised before the last few days of their life. This is true because when you exercise a call early, you lose the remaining time value on the call and collect only the intrinsic value.

3) Markets are efficient

This assumption suggests that people cannot consistently predict the direction of the market or an individual stock. The Black-Scholes model assumes stocks move in a manner referred to as a random walk. Random walk means that at any given moment in time, the price of the underlying stock can go up or down with the same probability. The price of a stock in time t+1 is independent from the price in time t.

4) No commissions are charged

Usually market participants do have to pay a commission to buy or sell options. Even floor traders pay some kind of fee, but it is usually very small. The fees that individual investor’s pay is more substantial and can often distort the output of the model.

5) Interest rates remain constant and known

U.S. Government Treasury Bills 30-day rate can be used since the U. S. government is deemed to be credible enough. However, these treasury rates can change in times of increased volatility.

6) Liquidity

The Black-Scholes model assumes that markets are perfectly liquid and it is possible to purchase or sell any amount of stock or options at any given time.

7) Returns are lognormally distributed (normal distribution of the log of the returns)

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

#### Effect of changing market conditions on an options theoretical value:

1) As the stock price rises, the call value rises and the put value falls and vice versa.

2) As volatility rises, call and put value rise and vice versa.

3) As we approach expiration Friday (time passes), call and put value fall.

4) Rising interest rates will cause calls to increase in value and puts to fall in value and vice versa. When interest rates are high it costs more to buy the stocks (cost of carry) and therefore calls become more desirable.

5) As dividends increase, call value declines and put value increases.

Volatility used in the Black-Scholes Model:

The historical volatility is the volatility of a series of stock prices where we look back over the historical price path of the particular stock. To enable us to compare volatilities for different interval lengths we usually express volatility in annual terms.Volatility is simply the standard deviation (will occur 68% of the time) of the sampled series (over how many intervals). If, for example a \$60 stock has a historical volatility of 20%, it will fall in the range of \$48 – \$72, 68% of the time (one standard deviation) in one year. See the red area in the standard deviation chart below:

Standard deviation chart

One standard deviation away from the mean in either direction on the horizontal axis (the red area on the above graph) accounts for somewhere around 68 percent of the potential price range. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the price potential. And three standard deviations (the red, green and blue areas) account for about 99 percent of the potential prices.

Conclusion:

The method used by most options traders to determine the theoretical value of an option is the Black-Scholes Model. Certain parameters are fed into the equation and several assumptions are made to calculate the figure. It is important to understand the strengths and weaknesses of this model as we apply it to our investment strategies. For covered call writers it is more important to understand the relationship of the parameters to option and stock value rather than actually calculate theoretical value which is of more value to the traditional options trader.

Market tone:

With the election thankfully over attention has turned to the “fiscal cliff” which requires congressional agreement (an odd concept!) on tax policy and national debt. This understandably has negatively impacted our markets as has continued concerns over the European debt crisis. This week’s economic reports:

• Consumer credit increased \$11.4 billion in September, better tha analysts’ expectations. This may be the result of over 300,000 jobs created the past two months.
• The trade deficit narrowed to \$41.5 billion in September, the lowest level in 2 years
• The ISM’s services index declined in October, despite an increase in hiring. The index, however, remains solidly in expansion mode
• Initial jobless claims for the week ending 11-3-12 came in @ a better-than-expected 355,000

For the week, the S&P 500 declined 2.4% for a year-to-date return of 11.8%.

Summary:

IBD: Market in correction

BCI: This site is taking a conservative and cautious approach as we wait for the debate over the fiscal cliff. We are using in-the-money strikes, low beta stocks and ETFs. Those new to investing with stock options may want to keep some cash on the sidelines.

Wishing you the best in investing,

Alan ([email protected])

www.thebluecollarinvestor.com

Alan Ellman loves options trading so much he has written four top selling books on the topic of selling covered calls, one about put-selling and a sixth book about long-term investing. Alan is a national speaker for The Money Show, The Stock Traders Expo and the American Association of Individual Investors. He also writes financial columns for both US and International publications along with his own award-winning blog.. He is a retired dentist, a personal fitness trainer, successful real estate investor, but he is known mostly for his practical and successful stock option strategies.

### 5 Responses to “Factors that Influence Option Value + The Black-Scholes Model”

1. Barry B November 10, 2012 11:27 pm #

Also, be sure to check out the latest BCI Training Videos and “Ask Alan” segments. You can view them at The Blue Collar YouTube Channel. For your convenience, the BCI YouTube Channel link is:

Since Earnings Season is in full swing right now, be sure to read Alan’s article, “Constructing Your Covered Call Portfolio During Earnings Season”. You can access it at:
https://www.thebluecollarinvestor.com/constructing-your-covered-call-portfolio-during-earnings-season/

On a separate note, Alan presented to the Chicago Area AAII, one of the largest AAII chapters in the country. Early reports were that his presentation was “sensational” and The BCI Team made a lot of new friends in the Chicago area.

Best,

Barry and The BCI Team

2. Gene Montavon November 11, 2012 11:29 am #

Alan great article. There is also a great article imbedded in the home page of ivolatility.com called “Putting volatility to work” which is very good and touches in more detail on what is included here. The article includes a discussion specific just to covered call writing.

Thanks for all your great work.

Gene

3. Jerry November 12, 2012 4:29 pm #

Alan,

In your system do you look up any of the “Greek” statistics before using an option? I have read that the greeks are important as they relate to option trading. Thanks for everything.

Jerry

• Alan Ellman November 13, 2012 7:00 pm #

Jerry,

It is NOT necessary to look up “Greek” stats for covered call writing. However, it is critical to understand the relationship between share value, time decay and volatility as they relate to option premium and risk degree when using this great strategy.

Alan

4. Alan Ellman November 15, 2012 7:06 am #