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Generalized Black Scholes

Variants of Black scholes can be used to price: stocks with dividends, futures, and currencies. The generalized Black Scholes formulation unifies these three. variants into a single formula.

Instead of taking a dividend yield, or foreign currency rate, the formula takes a cost of carry (typically represented by b), where:

  • b=r for European options on non-dividend paying stock.
  • b=r−q for European options and indices on dividend paying stock.
  • b=0 for pricing European futures options.
  • b=r−rf for pricing European currency options.

The cost of carry methodology is not restricted to the Black Scholes, and is used in many of the formula in this package.

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Using pandas