SteadyOptions is an options trading forum where you can find solutions from top options traders. TRY IT FREE!

We’ve all been there… researching options strategies and unable to find the answers we’re looking for. SteadyOptions has your solution.

Pricing Models and Volatility Problems


Most traders are aware of the volatility-related problem with the best-known option pricing model, Black-Scholes. The assumption under this model is that volatility remains constant over the entire remaining life of the option.

Of course, this makes no sense. Volatility changes constantly, ands this points out the problem with any model. It must assume that volatility remains unchanged for the math to work out. Even so, the assumption is so flawed that it makes the model unreliable. Making matter worse, the BSM has many other flaws as well. In math, one flaw is bad enough; but when you face at least 8 flaws (as BSM dies), it means there is zero reliability. [1]


But it gets worse.


Volatility is unpredictable. Even with the high number of flaws that create unaccounted for variables, the volatility problem is more severe. With fixed volatility, the degree of standard deviation is predictable, but this is not how things work in the real world. Price movement is chaotic, meaning that volatility is also chaotic and unpredictable. High and low volatility occur when price behavior is narrow and, on the other extreme, when it is broad. But how can this be predicted? It cannot. Volatility never remains unchanged, and it never changes in a predictable manner, or in a straight line.


Volatility does not anticipate direction or degree of price change. Even though the BSM assumes volatility remains unchanged, another problem must be recognized. Even if the degree of today’s volatility remained unchanged, which direction will price take? Will it rise, fall,  or remain unchanged? High daily volatility can occur within a range of price, but from day to day exhibit no significant movement. This is a factor never anticipated in BSM or, for that matter, in any pricing model. The flaws about volatility are more complex than the initial assumption that volatility does not change. Beyond direction of price movement, even fixed volatility does not reveal the degree of price movement in the underlying. A 5% move in a stock selling for $30 per share implies a 1½ point change. But if the price per share is $90, the same 1½ point movement is 4½ points. The assumed degree of volatility is not fixed but varies based on the underlying price range.


The timing of price changes also affects volatility. Does the underlying advance and then decline, or does it move in the opposite direction? Are there extended periods of consolidation? Every underlying behaves different, causing great variability in how volatility reacts. The option contract changes based on underlying price movement, and a correlation between the timing of price trends, and the volatility of the option, cannot be overlooked. The time required and the sequence of movement are further affected by moneyness and time to expiration.


Moneyness also affects volatility. The BSM assumption is normally applied to any option, regardless of its proximity to the strike. This is also unrealistic. ATM options have the highest gamma levels, so there are obvious differences between ATM, OTM and ITM contracts. And the greater the distance to strike, the greater the effect on volatility. It cannot be assumed in any situation that the option is ATM and will remain there. If it would, then no pricing model is needed. Nothing moves. But in practice, as an option moves ITM or OTM, gamma will change as well. Volatility changes as the distance grows.


Time to expiration also affects volatility. A shorter-term option is likely to exhibit higher gamma than longer-term options, and the time span affects volatility directly. As expiration approaches, gamma should increase as well (assuming offsetting movement in moneyness does not change the calculation). In applying a price model, it is unrealistic to base assumptions on an option remaining ATM because, as movement occurs (and as expiration nears), the entire matter of gamma changes drastically. As expiration nears, volatility behavior also changes. Even if a trader could know the volatility level near expiration, a pricing model is likely to undervalue an ATM option as volatility rises, and to overvalue the ATM option as volatility declines.


Type of option trade distorts volatility assumptions. Is the trade a long contract or a short contract? Is it a spread or a straddle? The nature and attributes of trades matter and volatility is going to vary based on the trade itself. A related issue is the historic volatility of the underlying. A highly volatile underlying price will directly affect option premium and its implied volatility. When this point is expanded to different types of trades, the overall problem also becomes clearer. Not all trades are the same, so BSM assumptions about volatility are more complex for some trades and combinations, than for others.


Adjusting for stochastic volatility (SV) creates yet another variable. Under the BSM model, volatility is assumed to remain constant. Applying Stochastic volatility, the assumption is added that volatility varies as time passes. This does not make the calculation more reliable; it only adds one more random variable. This may allow for analysis of a range of possible pricing outcomes, but it remains a guess to matter how many variations of the model are used.

The problem remains: No pricing model can accurately forecast option prices in the future.  Those few theorists who swear by BSM must ignore the facts, but any model contains flaws and imperfections. The solution is not to develop better methods for calculating volatility, because it is entirely unpredictable. The solution is to identify strategies and risk limiting methods to survive in an uncertain world.

 

[1] The 8 most serious flaws of BSM are: (1) Volatility remains constant (2) there is no restriction on buying or selling the underlying; (3) no tax consequences apply to profits; (4) interest rates are fixed and available to all; (5) no transaction costs are in effect; (6) trading is continuous without any gaps in price movement; (7) volatility is independent from underlying price; and (8) price changes are normally distributed.


Michael C. Thomsett is a widely published author with over 80 business and investing books, including the best-selling Getting Started in Options, coming out in its 10th edition later this year. He also wrote the recently released The Mathematics of Options. Thomsett is a frequent speaker at trade shows and blogs on his website at Thomsett Publishing as well as on Seeking Alpha, LinkedIn, Twitter and Facebook.

What Is SteadyOptions?

Full Trading Plan

Complete Portfolio Approach

Diversified Options Strategies

Exclusive Community Forum

Steady And Consistent Gains

High Quality Education

Risk Management, Portfolio Size

Performance based on real fills

Try It Free

Non-directional Options Strategies

10-15 trade Ideas Per Month

Targets 5-7% Monthly Net Return

Visit our Education Center

Recent Articles

Articles

  • Signs that you Are Ready to Start Investing

    If you want to build your wealth, you have to make sure that you invest your money. If you put money into a savings account and don’t earn any interest from it, this won’t work for you in the long term. Your money will lose value because of inflation, and this is the last thing that you need. So when do you invest?

    By Kim,

    • 0 comments
    • 31 views
  • One Year of Diversified leveraged Anchor

    I almost hate to keep saying it, but the Diversified Leveraged Anchor strategy keeps exceeding expectations and performing as designed. To remind our readers, Diversified Leveraged Anchor was created in April 2020 attempting to further increase performance, reduce risk, and to reduce volatility. 

    By cwelsh,

    • 3 comments
    • 428 views
  • Should I Pay Off My Mortgage Early Or Invest?

    Paying off a home mortgage early is a popular financial goal. Most people feel a level financial peace when their home is paid off that is beneficial in many ways. The most common approach to paying off the mortgage early is directly making additional principal payments to the lender on a regular basis.

    By Jesse,

    • 0 comments
    • 120 views
  • Option Order Execution Tips

    As a community of option traders, we all can relate to the occasional challenges of order execution. Best practices for avoiding errors as well as techniques for better potential execution will be the focus of this article.  Like countless others in the Steady Options community, I personally have traded thousands of option contracts over the last decade.

    By Jesse,

    • 10 comments
    • 909 views
  • What Trading Can Offer To A Newcomer

    For any first-time investor, one of the most important questions to ask is “why are you doing this?”. Getting into investment can be thrilling and open up new worlds for you, but it can also be draining both physically and emotionally, with long days and sudden market moves always a genuine risk.

    By Kim,

    • 0 comments
    • 207 views
  • Updated: The Performance Gap Between Large Growth and Small Value Stocks

    Eight months ago on July 21st 2020 I posted an article, The Performance Gap Between Large Growth and Small Value Stocks. Over the long-term small cap value stocks have outperformed large cap growth stocks, although not over more recent history.

    By Jesse,

    • 0 comments
    • 398 views
  • 6 Ways to Invest Your Money That Aren't Cash Savings

    It’s always a good idea to keep some of your money in cash so if there is an emergency and you need money in a hurry, you can access it without having to worry. However, cash savings are not your only option if you have money left over at the end of the month, and there are a lot of other options that could bring greater returns.

    By Kim,

    • 0 comments
    • 418 views
  • Jade Lizard Options

    The jade lizard is one of those bullish spreads with limited maximum profit, and no risk on the upside. It is a combination of a short put with a short call spread . The credit this creates is higher than the span of the spread. To set this up, two actions are required:

    By Michael C. Thomsett,

    • 0 comments
    • 709 views
  • Are Your Emotions Trying To Tell You Something?

    As a trader, you may find yourself frequently trying to ignore or rationalize emotions.  You may have even created your own “solutions” to manage them. You exit early to lock up profit and avoid a potential blow-up if the trade turns against you.

    By Jared Tendler,

    • 0 comments
    • 444 views
  • Stock Trading Basics: 5 Rules for Successful Stock Trading

    You might be a stock trader, or just interested in learning more about how to trade and make the most out of your stock investment. Regardless, successful stock trading is not that easy. You must first have the financial capital to start and a very great endurance for risks.

    By Kim,

    • 2 comments
    • 623 views

  Report Article

We want to hear from you!


There are no comments to display.



Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account. It's easy and free!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now

Options Trading Blogs Expertido