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 Impl. Vol.) shows the implied volatility for each contract. Use the value for the strike and expiry you are analysing.
Useful benchmarks: large-cap European stocks typically run between 15% and 25% under normal conditions. Tech stocks reach 35–50%. During a stress spike (earnings release, macro shock), volatility can double within hours.
Delta: if you buy 1 options contract 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 €5.60 with a Theta of −0.034, every night costs you 3.4 cents, even if the market does not move. Over 30 days, that is just over €1. It is the time decay you pay when you buy an option.
Vega: if you buy an option before an earnings release, implied vol can rise sharply before the announcement and collapse after. With a Vega of 0.20, a 5-point vol increase earns you €1. That is why traders sometimes sell options just before an announcement: they are selling expensive vol.
ProRealTime v13’s options pricer uses Black-Scholes by default, with Bjerksund-Stensland for American options. You enter the same five parameters as this calculator and get the theoretical price directly in 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 is a starting point, not an oracle.
It assumes implied volatility is constant across all strikes. That is never true in practice: OTM options generally have higher vol than ATM options. That is the volatility smile, and it makes Black-Scholes imprecise on the wings.
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 vol for each contract. You can also use the inverse of this calculator: enter the observed market price and adjust σ until you match that price. That is implied vol by inversion.
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 vol looks backwards and measures past price changes. Implied vol is read from the options market: it is the value of σ that corresponds to the quoted price. This calculator uses implied vol. Find it in the options chain of your platform.
