Smile.Interpolation.TensionSplineImpliedVolatilityInterpolator

Classes

IImpliedVolatilityInterpolator	General interface to interpolate the implied volatility smile in strike.
List	Methods
MoneynessSmileRepresentation(atm_vol: float, ...)	” Container Class that describes a smile as a vector of deltas for moneyness, the atm volatility, and the shifts in
TensionSpline(calldeltavec, volvec, F, T, ...)	Attributes
TensionSplineImpliedVolatilityInterpolator(...)	Class to interpolate the volatility smile in strikes using a tension spline.

class Smile.Interpolation.TensionSplineImpliedVolatilityInterpolator.TensionSplineImpliedVolatilityInterpolator(moneyness_smile_representation: Smile.Representations.MoneynessSmileRepresentation.MoneynessSmileRepresentation, underlying_level: float, duration: float, weightvec: typing.List[float], sm: float, smtol: float)

Class to interpolate the volatility smile in strikes using a tension spline.

Parameters:

moneyness_smile_representation : MoneynessSmileRepresentation

The volatility smile represented in terms of deltas.

underlying_level : float

The market value of the option underlying.

duration : float

The maturity of the option for which the smile is computed.

weightvec : List[float]

Vector of length N containing positive weights associated with the data values. The recommend- ed value of W(I) is 1/DY^2, where DY is the standard deviation associated with Y(I). If nothing is known about the errors in Y, a constant (estimated value) should be used for DY. If PER = TRUE, it is assumed that W(N) = W(1).

sm : float

Positive parameter specifying an upper bound on Q2(YS), where Q2(YS) is the weighted sum of squares of deviations from the data (differences between YS and Y). H(x) is linear (and Q2 is minimized) if SM is sufficiently large that the constraint is not active. It is recommended that SM satisfy N-SQRT(2N) <= SM <= N+SQRT(2N) and SM = N is reasonable if W(I) = 1/DY^2.

smtol : float

Parameter in the range (0,1) specifying the relative error allowed in satisfying the constraint: the constraint is assumed to be satisfied if SM*(1-SMTOL) <= Q2 <= SM*(1+SMTOL). A reasonable value for SMTOL is SQRT(2/N) for N > 2.

Methods

slope_at_strike((strike: float) -> float)	Compute the implied volatility slope or skew for a given strike.
vol_at_strike((strike: float) -> float)	Compute the implied volatility for a given strike.

slope_at_strike(strike: float) → float

Compute the implied volatility slope or skew for a given strike.

Parameters:

strike : float

The strike for which the implied volatility slope will be calculated.

Returns:

implied_volatility_slope : float

The implied volatility slope for the provided strike.

vol_at_strike(strike: float) → float

Compute the implied volatility for a given strike.

Parameters:

strike : float

The strike for which the implied volatility will be calculated.

Returns:

implied_volatility : float

The implied volatility for the provided strike.