Calculate the theoretical price of a call or put option and its Greeks in real time. European Black-Scholes model.
Volatility (σ) is the only input you cannot read directly from a quote. It comes from the options chain on your platform. In ProRealTime v13, open the options chain for your underlying: the IV column (or Implied Volatility) shows the implied volatility for each contract. Use the value for the strike and expiry you are analysing.
Useful benchmarks: European indices themselves (e.g. the Euro Stoxx 50, tracked by the VSTOXX) sit around 15–20% under normal conditions. Individual stocks are more volatile: often 20–30% for a large cap, 35–50% for a tech name. During a stress spike (earnings release, macro shock), volatility can double within hours.
Delta: if you buy an option on a stock at €100 with a Delta of 0.5, you have the equivalent exposure of €50 in the stock. It is also your hedge ratio: short 0.5 of the stock to neutralise directional risk.
Theta: on a call at €5.35 with a Theta of −0.031, every night costs you 3.1 cents at first, even if the market does not move. Theta accelerates as expiry approaches: over the next 30 days the option loses a little over €1 — more than a simple multiplication suggests. It is the time decay you pay when you buy an option.
Vega: before an earnings release, implied volatility inflates, then drops sharply once the announcement is out. With a Vega of 0.20, each volatility point is worth €0.20: +5 points earn the buyer €1, −5 points cost just as much. That is why buying right before earnings is risky — and why some traders sell at that point: they sell volatility at a premium, before it falls back.
ProRealTime v13’s options pricer uses Black-Scholes by default, with Bjerksund-Stensland for American options. You enter the same six parameters as this calculator and get the theoretical price directly on the platform, with the ability to analyse up to 10 scenarios in parallel.
The key difference from this calculator: ProRealTime reads implied volatility in real time from market data. No need to look it up manually in the options chain.
Black-Scholes has three important limitations to know.
It assumes implied volatility is constant across all strikes. That is never true in practice: OTM options, especially puts, have higher implied volatility than ATM options. That is the volatility smile, and it makes Black-Scholes imprecise on strikes far from the money.
It does not model price jumps. A 10% overnight gap on an earnings announcement: Black-Scholes does not account for it. That is why options on earnings events often appear underpriced by the model.
It is designed for European options. American options are worth more because they can be exercised before expiry, and the model does not capture that premium.
In ProRealTime v13, open the options chain for your underlying. The IV column shows implied volatility for each contract. You can also use this calculator in reverse: adjust σ until the displayed price matches the observed market price. The resulting σ is the implied volatility.
The option has time value because the market can still move before expiry. That value decays each day. Theta measures what one night costs. It is highest for ATM options close to expiry.
Historical volatility looks backwards and measures past price changes. Implied volatility is read from the options market: it is the value of σ that corresponds to the quoted price. This calculator uses implied volatility. Find it in the options chain of your platform.
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