How Options Verdict calculates
Updated October 18, 2026
Every number in Options Verdict comes from published formulas, and the app shows each one with your own numbers in its "Check the math" sheet. This page explains the method and its assumptions.
1. Two volatilities, two jobs
Implied volatility prices things; realized volatility forecasts outcomes. Option prices, estimated credits, Greeks and marks during simulated exits use implied volatility (with skew). Expected value, profit chance and position size use realized volatility: how much the stock has actually been moving. Keeping the two apart is the core of the method: if outcomes were priced with implied volatility, every fair trade would show zero edge by construction.
2. Time
Implied volatility runs on calendar hours: v = IV × √(hours ÷ 8,760). Realized volatility runs on trading sessions: v = RV × √(sessions ÷ 252), skipping weekends and NYSE holidays. So Friday to Monday counts as one session of movement, not three days.
3. Pricing
Black-Scholes with zero interest and dividends: d₁ = [ln(S/K) + v²/2] ÷ v, d₂ = d₁ − v; call = S·N(d₁) − K·N(d₂), put = K·N(−d₂) − S·N(−d₁). The normal distribution function uses an approximation with small relative error, so far-out-of-the-money prices stay accurate.
4. Skew
Each strike gets its own implied volatility from a skew curve measured in standard deviations from the price: puts get more volatility the further below the price they are, calls slightly less. Presets (low, normal, steep) or your own readings from the chain set the shape.
5. The outcome distribution
The stock's price at expiration is modeled as lognormal and driftless at realized volatility, with the market's skew shape stretched to that width. Using the same shape means skew alone never counts as free profit: with implied equal to realized, a fairly priced trade has an expected value of minus fees.
6. Expected value and profit chance
Because an options payoff at expiration is a set of straight lines between strikes, the app integrates it against the distribution exactly, piece by piece, rather than sampling. That gives profit chance, loss chance, average win and average loss. Expected value = premium − fees + the expected payoff of every leg, and it must equal p × average win − q × average loss; the tests check both.
7. Position size
Kelly: f = p − q ÷ b, with b = average win ÷ average loss. Risk per trade = the smaller of f × your Kelly fraction (an eighth by default) and your max risk rule, halved when the volatility edge is thin. Contracts = round down(account × risk ÷ max loss per contract including fees). For trades with no fixed max loss, a stress loss replaces max loss: the worst result across a 3-standard-deviation move, or at least ±3%.
8. Exit plans
Exit rules (profit targets, stops, time exits and more) are tested on simulated price paths. Each path ends at a price drawn from the outcome distribution and gets there by a Brownian bridge at realized volatility; positions are marked with implied volatility and skew along the way. Every simulation uses a fixed random seed, so the same inputs always give the same numbers, and a statistical technique called a control variate removes most of the sampling noise. The optimizer picks a plan on one set of paths and reports it on a fresh set, so results aren't cherry-picked.
9. Assumptions
- Realized volatility is the forecast, and it's the biggest assumption. Markets change.
- No drift, interest rates or dividends (worth tens of dollars per contract on 30-day spreads).
- Fills at the price you enter; no early assignment.
- Skew is sticky by strike, with no volatility jump in sell-offs, so stop-loss results may be optimistic.
- For calendars and diagonals, the back month's implied volatility holds when the front expires.
- For uncapped trades, a move bigger than the stress move loses more.
10. Testing
The math has its own automated test suite, including Monte Carlo cross-checks of every closed-form result, and browser tests that fail if any screen ever shows an invalid number. The free calculators on this site use the same pricing and probability code as the app, without skew or exits.
What it isn't
Options Verdict is an educational calculator. It works on trades and numbers you supply, doesn't recommend trades, and isn't a broker or an investment adviser. Options involve substantial risk.