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Michael C. Thomsett is a widely published options author. His "Getting Started in Options" (Wiley, 9th edition) has sold over 300,000 copies. He also is author of "Options Trading for the Conservative Investor" and "The Options Trading Body of Knowledge" (both FT Press); and "Options for... More
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  • Problems with Black-Scholes 5 comments
    Mar 1, 2012 11:31 AM

    The most popular option pricing model -- Black-Scholes -- is outdated and unreliable, for several reasons:

    1. First, it was first published in 1973, when the public trading of options was in its primitive stages. Calls were available on only a handful of listed companies, and puts were not traded publicly at all. With this in mind, the model was a theory only and not based on any market statistics.

    2. The model assumes European style expiration (positions can be exercised only on the last trading day). However, options on listed stocks are traded American style, meaning they can be exercised at any time. This changes the assumptions underlying the Black-Scholes model.

    3. The model assumes no dividend yield. Options traders know that dividends play a major role in total return and cannot be ignored.

    4. The model further assumes that valuation and income have to be compared to an assumed rate of risk-free interest. Under today's odd money market, is this even valid any more?

    5. With online trading and Internet access to information, the world of 1973 is practically prehistoric in terms of information flow, transaction speed, and costs.

    Although subsequent papers have tried to modify Black-Scholes to make it more in line with market realities,the basic theory has little to do with modern options pricing. An alternative method may split premium into three parts, two of which are specific and easily identified in advance. First is intrinsic value, the in-the-money point spread between current price and strike. This is an exact dollar value. Second is time value, which is also predictable and precise. It can be modeled and isolated so that the rat of time decay is known well in advance -- and it should be unaffected by proximity between strike and current value.

    The final leg of value is implied volatility, also called extrinsic value. This is where all of the variables are found. These include the complex interaction between proximity of strike to value, and time to expiration. The calculation of implied volatility is further complicated by historic volatility of the underlined as well as current fundamental and technical volatility of the stock. This may be based on company-specific news or events, or on market-wide perceptions, right or wrong. To get a handle on the complexities of implied volatility in a quick and easy way, check
    volatility edge

    In other words, it is time for a different and more realistic pricing model. I intend to begin studying this issue and trying to arrive at some guidelines. Any suggestions or feedback about ideas for option pricing will be greatly appreciated. Please send to me at - thank you.

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Comments (5)
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  • Thomsett
    , contributor
    Comments (104) | Send Message
    Author’s reply » I truly think this model is outdated.
    1 Mar 2012, 12:10 PM Reply Like
  • atulkapadia
    , contributor
    Comment (1) | Send Message
    I agree Black Scholes does not apply now.
    1 Mar 2012, 09:24 PM Reply Like
  • Thomsett
    , contributor
    Comments (104) | Send Message
    Author’s reply » Thank you for confirming my suspicions - the market has changed so drastically and the variables are also outdated. -- Michael
    9 Mar 2012, 01:27 PM Reply Like
  • crconlan0205
    , contributor
    Comments (2) | Send Message
    I think outdated is the wrong word. The model's theoretical basis sheds a lot of light on options prices when its outputs are compared to market-quoted prices.


    Points 1 and 5 argue for a more empirical study of options prices that accounts for statistical tendencies and transaction costs respectively. These are important, but are not the aim of the model. The model serves as a benchmark that allows us to examine statistical tendencies in implied volatility. Transaction costs are user-dependent and not hard to determine and model, therefore are not in the scope of a valuation model.


    Point 4 argues that a volatile money market cannot support the risk-free assumption. The model allows us to set boundary conditions by barring arbitrage and eliminating market inefficiencies. Even if the interest rates violently fluctuate over the life of the option, the risk-free assumption needed as to not return "impossible" prices (especially in this information super-highway that is our modern market environment, see point 5).


    The lack of dividend yields (#3) in the model was accounted for less than a year after the original publication of the model. It is a smooth transition considering, in the long-run, stocks will depreciate (in a continuously compounded fashion, so goes the model) by their quarterly/yearly dividend yield.


    As for point 2: I agree, that pisses me off.
    20 Jun 2013, 03:28 AM Reply Like
  • Thomsett
    , contributor
    Comments (104) | Send Message
    Author’s reply » Thanks for your insights. I think a benchmark should accurately reflect what it measures, and that's where I have a problem with Black Scholes. You make some very good points.
    20 Jun 2013, 08:52 AM Reply Like
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