How Are Theoretical Values and Greeks Calculated?

City API and City Trader make available live theoretical values and greeks and implied volatilities on all options. These values are provided as a convenience and details of how these are calculated are subject to change.

Currently, however, here are some details regarding these calculations:

  • The Black-Scholes Model is used.
  • A carry cost of zero is assumed for all options with a future underlying.
  • Values are provided not just per instrument, but per market (buy, sell, last, etc.) by the API. The underlying used as the input depends on the market:
    • Last underlying price for last option data.
    • Buy underlying price for sell put markets and buy call markets.
    • Sell underlying price for buy put markets and sell call markets.
    • Client applications may have a precedence rule to select the values to display, or they may display an average.
  • Implied volatilities are calculated per strike and are cached for up to 10 minutes before being recalculated with live market data. Only bid/ask out-of-the-money option markets are used to calculate implied volatiles. Bid and ask results are then averaged. If a one-sided market is present, that market is used to calculate the implied volatility.