FinancePy

FinancePy API Reference

Option Implied Dbn

financepy.models.option_implied_dbn

Functions

option_implied_dbn

option_implied_dbn(s: float, t: float, r: float, q: float, strikes: Sequence[float], sigmas: Sequence[float]) -> numpy.ndarray
Calculate the option smile/skew-implied risk-neutral distribution. Uses the Breeden-Litzenberger result f(K) = exp(rT) * d²C/dK² and returns f(K) * dK at each strike, rather than the raw probability density f(K). Parameters ---------- s : float Current underlying spot price. t : float Time to expiry in years. r : float Continuously compounded risk-free rate. q : float Continuously compounded dividend yield. strikes : Sequence[float] Increasing, equally spaced strike grid. sigmas : Sequence[float] Black-Scholes implied volatility corresponding to each strike. Returns ------- np.ndarray Probability mass f(K) * dK associated with each strike-grid point. The first and last values are zero because a central finite difference cannot be calculated there.
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