Estimating Options Expiration Probabilities from Delta and Straddle Prices
Summary
The document considers how to estimate the chance that an underlying asset will finish between breakeven levels of an options strategy when historical price data is unavailable but an analytical implied volatility curve is available. Its proposed method is to calculate the delta of a hypothetical option at each breakeven, interpret each delta as an approximate probability of finishing above that level, and take differences between those probabilities to estimate the chances of landing in each interval.
The response endorses delta as a quick estimate, provided the option expiration matches the time horizon of interest. It also describes using the premium of an at-the-money straddle to estimate an expected move and an approximate one-standard-deviation range, with tail probabilities given as rough complements. These are rules of thumb, not a fitted physical distribution or precise forecast. The document does not discuss risk-neutral versus real-world probabilities, volatility skew effects, or how rates and dividends affect the estimates, so the method’s assumptions and calibration limits remain unresolved.
Key ideas
- Use options with an expiration aligned to the horizon whose probability you want to estimate.
- Treat delta at a breakeven as an approximate probability of finishing above that level.
- Estimate the probability of a price interval by subtracting the probabilities at its boundaries.
- An at-the-money straddle premium can serve as a rough estimate of the expected move.
- The proposed probabilities are approximations rather than a fitted forecast distribution.
Tags
Full text
# Options strategy expiration probability # Options strategy expiration probability #### Big picture For any options strategy, for any segment between zero profit (breakeven) points, I want to calculate probabilities of the underlying instrument price will be within a segment at expiration. On the illustration, I want to know probabilities for segments 1,2 and 3. #### My environment - No time series of the underlying instrument price available. So I don't consider approaches where I have to fit real distribution with something like Student. - Analitical form of a volatility curve is available. #### The approach that is on my mind - For each breakeven point calculate a delta of a virtual option with a strike at this point. Can do this since I have analitycal IV curve. - Each of these deltas can be interpreted as a probability of underlying price is higher then corresponding breakeven point at expiration - Having array of these probabilities, I can calculate probabilities for segments. #### My questions - Is my approach generaly acceptable? - What are another approaches you might advise? ## Answer by Dr. Michael J. Stefano (score 1) https://quant.stackexchange.com/a/85340 to use delta as an estimate you would have to decide on a time frame and choose an expiration at or near that time frame. It seems like your approach is the easiest and fastest way to do it as option delta is generally considered as an acceptable estimate of probability. another way that is generally accepted as an estimate of a 1 standard deviation range is as follows. take the sum of the premium values of an ATM straddle, again for an option expiration period of your choosing. that is the expected move up and down. the range between the upper and lower prices will be your 1 standard dev range which is about a 68% range, meaning you would have a 16% prob above the upper price and vice versa on the bottom.
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