When are options too cheap (mispriced)?

This post is for educational purposes only. I do not trade options. Options are generally easier to trade than futures, but are harder to trade than ETFs.
Options are priced based on a set of standard mathematical formulas. These formulas are ridden with assumptions, and sometimes these assumptions are wrong. Options become too cheap when these assumptions are wrong. These extremely cheap options are golden opportunities for savvy traders.
Here are a few common situations in which options are mispriced (too cheap).

Options are too cheap when recent market volatility was very low

Volatility is one of the components that go into standard options pricing formulas. This “volatility” is recent past volatility. So if the market has been trending very calmly recently, then options will be priced too cheaply. A savvy trader will buy options in anticipation of an increase in volatility.
In reality, low volatility over the past few months is usually a sign that volatility will increase in the future! Hence, being long options is a very cheap and good trade when volatility has been low for quite a while.
This is why long term options trading is generally more profitable than short term options trading. The longer the term frame, the more likely it is for volatility to explode. All sorts of exogenous events can occur.

Options are too cheap because volatility should not be based on the square root of time.

Standard pricing formulas assume that volatility scales with the square root of time.
Here’s what the graph looks like. X = time, Y = volatility.

This means that long dated options tend to be too cheap compared to short dated options. When recent volatility has been low, the further out in the future you go the more likely it is for volatility to explode!
In other words, when recent volatility is low, future volatility should scale EXPONENTIALLY to time (and not to the square root of time).

Option prices assume a normal distribution

Standard options pricing formulas state that future prices near current prices are most likely, and that future prices far away from current prices are unlikely.
This is a probability distribution curve.

This assumption is plainly wrong under certain scenarios.
E.g. When the stock market has been swinging in a sideways range for a long time, the market’s direction over the next few months does not fit on a normal distribution curve. Under a normal probability distribution, the stock market will most likely continue to trend side ways. In reality, the outcome is bimodal. Either

  1. The stock market breaks below the range and makes a significant correction (which our Medium-Long Term model is used to predict), or…
  2. The stock market breaks out on the upside and rallies vigorously (in the event that our Medium-Long Term Model does not predict a significant correction.)

Hence, this flawed assumption makes both long and put options too cheap.

Another problem with the normal distribution assumption

By assuming a normal distribution with regards to the market’s future direction, options assume that outcomes in either direction (i.e. the market moving up or down) are equally likely. This is simply not true.
For example, the U.S. stock market and economy move together in the long run. But many of the stock market’s 6%+ “small corrections” have nothing to do with the economy’s fundamentals. They occur purely for technical reasons. So if the stock market corrects but the economy continues to improve, then it is much more likely for the stock market to go up than down. Hence, call options are cheaper than put options (when adjusted for the real distribution of probabilities).

5 comments add yours

  1. Troy, further dated options are usually higher in premium paid the further out u go. I will never trade options because 1) u could be right but 2) your timing could be off and u risk losing the time deprecated premium u paid. Options is wealth destruction as it erodes your investment capital with time depreciation if the underlying stock price does not move in your favor. They say that over 50% of options expire worthless and you lose your premium. I will never ever trade options again! I recently bought wynn 175 call options in the beginning of February right after wynn went from $200 down to $160. 3 weeks out that expired this past Friday, I gave them 3 weeks to work. My belief in getting into them was that sexual allegations has nothing to do with overall corporate profits and wynn falling from $200 to $160 on the news was a discount to the recent high the stock was trading at prior to wynns allegations making the stock fall to $160. I lost $3800. Even though I truly believe wynn stock to be a great value to the long term direction of the company. I will never ever buy options again!

  2. How can we profit this mispriced options? Buying long date options and selling short date options and same strike?. And, at what level of VIX could we considered “very low volatility”?
    Thank you in advance.

      • But you said at your Medium-long term model that we are right now at 2/3 of bull markets. Are we still at a good moment to buy LEAPS? Thanks in advance.
        Mi first idea was try to profit the mispriced between short tem options and long term ones. Posibly selling short term options (more expensive) and buying LEAPS (cheaper). I am trying to find something like an arbitrage strategy (minimizing risks) but I don´t know how to execute it.
        Thank you for all your work, Troy

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