Smile.Representations.SmileRepresentationConverter

Classes

MoneynessSmileRepresentation(atm_vol: float, ...)	” Container Class that describes a smile as a vector of deltas for moneyness, the atm volatility, and the shifts in
SmileRepresentationConverter	Class that permits to convert a smile representation from Strike-> Vol(Strike) to Moneyness -> Vol(Moneyness)
StrikeSmileRepresentation(atm_vol: float, ...)	Container class that describes a smile as a vector of strikes, the atm volatility, and the shifts in order to recover non-atm vols.

class Smile.Representations.SmileRepresentationConverter.SmileRepresentationConverter

Class that permits to convert a smile representation from Strike-> Vol(Strike) to Moneyness -> Vol(Moneyness) and vice-versa

Methods

moneyness_representation(...)	Compute the smile parametrized in deltas equivalent to a given smile parametrized in strikes.
moneyness_to_strike(...)	Compute the strike associated to a given moneyness expressed in delta.
strike_representation(...)	Compute the smile parametrized in strike equivalent to a given smile parametrized in deltas.
strike_to_moneyness(...)	Compute the moneyness expressed in delta associated to a given strike.

static moneyness_representation(strike_representation: Smile.Representations.StrikeSmileRepresentation.StrikeSmileRepresentation, underlying_level: float, duration: float) → Smile.Representations.MoneynessSmileRepresentation.MoneynessSmileRepresentation

Compute the smile parametrized in deltas equivalent to a given smile parametrized in strikes.

Parameters:

strike_representation : StrikeSmileRepresentation

The representation of the volatility smile in terms of strikes.

underlying_level : float

The market value of the option underlying.

duration : float

The duration of the option for which the strike was provided

Returns:

moneyness_representation : MoneynessSmileRepresentation

The representation of the volatility smile in terms of deltas.

Examples

>>> from Smile.Representations.SmileRepresentationConverter import SmileRepresentationConverter
>>> from Smile.Representations.StrikeSmileRepresentation import StrikeSmileRepresentation
>>> import numpy as np
>>> underlying_level = 100.0
>>> duration = 2.5
>>> atm_vol = 0.15
>>> strikes = np.array([65.108,84.538,100.000,116.786,142.618])
>>> vol_shifts = np.array([0.10, 0.05, 0, -0.03, -0.09])
>>> strike_representation = StrikeSmileRepresentation(atm_vol, strikes, vol_shifts)
>>> moneyness_representation = SmileRepresentationConverter.moneyness_representation(strike_representation,underlying_level, duration)
>>> print(moneyness_representation)
Moneyness |0.087|0.267|0.500|0.767|0.977|
Vols      |0.165|0.158|0.150|0.145|0.137|
Skew      |0.100|0.050|0.000|-0.030|-0.090|

static moneyness_to_strike(underlying_level: float, moneyness: float, volatility: float, duration: float) → float

Compute the strike associated to a given moneyness expressed in delta.

Parameters:

underlying_level : float

The market value of the option underlying.

moneyness : float

The moneyness expressed in terms of delta.

volatility : float

The volatility associated to the inputted moneyness.

duration : float

The duration of the option for which the moneyness was provided

Returns:

strike : float

The strike associated to the given moneyness.

Examples

>>> from Smile.Representations.SmileRepresentationConverter import SmileRepresentationConverter
>>> underlying_level = 100.0
>>> moneyness = 0.45
>>> volatility = 0.15
>>> duration = 2.5
>>> SmileRepresentationConverter.moneyness_to_strike(underlying_level, moneyness, volatility, duration)
103.02517658563964

static strike_representation(moneyness_representation: Smile.Representations.MoneynessSmileRepresentation.MoneynessSmileRepresentation, underlying_level: float, duration: float) → Smile.Representations.StrikeSmileRepresentation.StrikeSmileRepresentation

Compute the smile parametrized in strike equivalent to a given smile parametrized in deltas.

Parameters:

moneyness_representation : MoneynessSmileRepresentation

The representation of the volatility smile in terms of deltas.

underlying_level : float

The market value of the option underlying.

duration : float

The duration of the option for which the strike was provided

Returns:

strike_smile_representation : StrikeSmileRepresentation

The representation of the volatility smile in terms of strikes.

Examples

>>> from Smile.Representations.SmileRepresentationConverter import SmileRepresentationConverter
>>> from Smile.Representations.MoneynessSmileRepresentation import MoneynessSmileRepresentation
>>> import numpy as np
>>> underlying_level = 100.0
>>> duration = 2.5
>>> atm_vol = 0.15
>>> moneyness = np.array([0.05,0.25,0.5,0.75,0.95])
>>> vol_shifts = np.array([0.10, 0.05, 0, -0.03, -0.09])
>>> moneyness_representation = MoneynessSmileRepresentation(atm_vol, moneyness, vol_shifts)
>>> strike_representation = SmileRepresentationConverter.strike_representation(moneyness_representation,underlying_level, duration)
>>> print(strike_representation)
Strikes   |65.108|84.538|100.000|116.786|142.618|
Vols      |0.165|0.158|0.150|0.145|0.137|
Skew      |0.100|0.050|0.000|-0.030|-0.090|

static strike_to_moneyness(underlying_level: float, strike: float, volatility: float, duration: float) → float

Compute the moneyness expressed in delta associated to a given strike.

Parameters:

underlying_level : float

The market value of the option underlying.

strike : float

The strike of the option.

volatility : float

The volatility associated to the inputted strike.

duration : float

The duration of the option for which the strike was provided

Returns:

moneyness : float

The moneyness associated to the given strike.

Examples

>>> from Smile.Representations.SmileRepresentationConverter import SmileRepresentationConverter
>>> underlying_level = 100.0
>>> strike = 103.0251
>>> volatility = 0.15
>>> duration = 2.5
>>> SmileRepresentationConverter.strike_to_moneyness(underlying_level, strike, volatility, duration)
0.45000124057807839