Using Options to Infer Implied Probabilities

Options say a lot about what the market thinks about the future.  You can directly discern the market’s opinion about the probability of future price changes through the prices of options. The difference between options prices directly correlates to the implied probability of events as express by the market. So for instance, consider if you sold an Apple call at $132 (expiring next week let’s say) and bought one at $133.  This means you’re liable for the $1 dollar difference per share.  If Apple trades above $133 per share in a week, you must pay the $1 difference.  If it trades below $132 next week, you pay nothing and keep the premium.  Between $132 and $133 you pay a linearly increasing amount.  This is called a selling a bearish call spread.


An options spread is an extremely structured way to take a market position in that it is explicit what one’s implied odds are.  It’s not open ended; there is a definite payoff or a definite loss within known bounds.  You know exactly the risks you are taking.

So, for example, if I sell an Apple call option at $132 for $2 and buy a call at $133 for $1.8, I get a net premium of $0.20 per share.  But my net liability is $1 per share.  If Apple shares trade at above $133, I am liable for the dollar difference.  I am hedged against further increases because I bought the $133 call.  But because I also received a $0.20 premium, my greatest potential loss is $0.8 per share. The bet has 4:1 odds. Thus the $0.20 price difference means that the market believes that the chance that Apple stock will exceed $132 is only 20%.

You can look at the difference between sets of options to calculate the implied probability all along the curve.  What is the probability that Apple will trade between exactly $129 and $129.5 by next week?  You can infer the market’s opinion on that directly from options spreads.  I am building a tool to do this at  It’s in a really primitive state now but… expect more soon.  See this example for the S&P500 ETF expiring on 12-31-2015.

Note that these probabilities have nothing to do with what will actually happen.  They are simply the implied odds from real market prices of various events.  If you have a strong opinion that contradicts these implied probabilities, you should take a position, in either direction.

Another fascinating aspect is that, in theory, the implied probabilities from puts and calls should be equivalent, because of put-call parity.  You can always construct a position mirrored in both calls or puts.  So any discrepancy should be arbitraged away at zero risk.  In practice, highly liquid options like SPY show close symmetry, whereas illiquid ones often diverge.

Finally, one of my favorite things about options spreads is that you can make money from a negative opinion.  You can simply state that something will not happen.  If you’re right, you can make a lot of money.  You know exactly what the risks are.  So you could say, for instance, that AAPL will not exceed 135 in the next 2 months, and make a return from that opinion.  Or you could even express opinions about pairs trading, such as ‘if SPY rises, AAPL will not also go down’.  Being able to profit from negative statements is a novel trading feature that’s hard to tap into by simply being long or short the underlying.


One thought on “Using Options to Infer Implied Probabilities”

  1. Implied volatilities are not unbiased though – they include a volatility premium, meaning that the implied volatilities will be higher than the realized volatility for the same period.

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