What are the assumptions behind this POP estimate?

The model assumes prices are lognormally distributed, that implied volatility stays constant until expiry, zero drift (risk-neutral, no dividends), and that returns have no skew or fat tails. Real markets violate these, so treat POP as a directional guide, not a precise figure.

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Q: What is probability of profit (POP)?

Probability of profit is the estimated chance that the underlying price finishes the trade beyond your breakeven at expiry. It is derived from a lognormal model of price using the implied volatility, the time to expiry and the current spot — not a guarantee, but a statistical estimate.

Q: How is POP calculated from implied volatility?

We compute the standard deviation of the log return, sigma = IV/100 × sqrt(days/365). Then z = ln(breakeven / spot) / sigma. The probability the spot ends above an upside breakeven is 1 − N(z), where N is the standard normal cumulative distribution function.

Estimate the chance the spot ends beyond your breakeven at expiry — from IV, days to expiry and spot — using a lognormal model.

Your trade

Spot price (₹)

₹

Breakeven price (₹)

₹

Days to expiry

Implied volatility (% annualised)

Result

Probability spot ends beyond breakeven

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Enter values and press Calculate

1-σ move (₹)—

σ of log return—

z-score—

Prob. ends below breakeven—

How it's calculated

This tool models the underlying price at expiry as lognormally distributed — the standard assumption behind Black-Scholes. The steps are:

Standard deviation of the log return: σ = (IV ÷ 100) × √(days ÷ 365). This scales the annualised implied volatility down to the time horizon of your trade.
z-score of the breakeven: z = ln(breakeven ÷ spot) ÷ σ. This expresses how many standard deviations the breakeven sits away from today's spot, on a log scale.
Probability beyond an upside breakeven: POP = 1 − N(z), where N is the standard normal cumulative distribution function (CDF). When the breakeven is below the spot, z is negative and 1 − N(z) is above 50%, correctly showing a high chance of finishing above it.

For a breakeven above the spot (a typical long-call target) this returns the probability the index rallies past it. For a breakeven below the spot it returns the probability the index stays above that level. The "probability ends below breakeven" row is simply N(z).

Assumptions & caveats: the estimate assumes zero drift (risk-neutral, no dividend yield), constant implied volatility to expiry, and a symmetric lognormal distribution with no skew or fat tails. Real index returns are skewed and fat-tailed, so treat the number as a directional guide, not a precise odds quote. See the IV explainer for how implied volatility itself is read.

FAQ

What is probability of profit (POP)?

POP is the estimated chance the underlying finishes the trade beyond your breakeven at expiry, derived from a lognormal model using IV, time and spot. It is a statistical estimate, not a guarantee.

How is POP calculated from implied volatility?

We compute σ = IV/100 × √(days/365), then z = ln(breakeven/spot) ÷ σ, then the probability of finishing above an upside breakeven as 1 − N(z), where N is the normal CDF.

What are the assumptions?

Lognormal prices, constant IV to expiry, zero drift, and no skew or fat tails. Markets violate these, so use POP as a guide alongside live Greeks and the option chain.

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