Class FourierTransformPricer

Inheritance Relationships

Base Type

Derived Types

Class Documentation

class FourierTransformPricer : public otyca::StochasticProcessPricer

Option pricer using Fourier Transform.

This class implements a numerically efficient option pricing technique based on Fourier transform, as introduced by Peter Carr and Dilip B. Madan (1999) in “Option Valuation Using the Fast Fourier Transform.”

It computes option prices, derivatives, implied volatilities, and PDFs using the characteristic function of a given stochastic process.

Subclassed by otyca::FFTPricer, otyca::FRFTPricer

Public Functions

FourierTransformPricer(unsigned int, double, double)
virtual ~FourierTransformPricer()
virtual std::vector<std::vector<double>> price(const StochasticProcess*, const std::vector<double>&, const std::vector<std::vector<double>>&, StrikeType = LOG_STRIKE) const override

Prices for multiple tenors and strike sets.

Parameters:

  • stochastic_process – Pointer to the stochastic process model.

  • tenors – Vector of tenors.

  • strikes – 2D vector of strikes (per tenor).

  • strike_type – Type of strike to use. See StrikeType for available options.

Returns:

2D vector of prices.

virtual std::vector<std::vector<std::vector<double>>> price_derivatives(const StochasticProcess*, const std::vector<double>&, const std::vector<std::vector<double>>&, StrikeType = LOG_STRIKE) const override

Analytical price derivatives for each input.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Vector of tenors.

  • strikes – 2D strike array.

  • strike_type – Strike type to interpret. See StrikeType for available options.

Returns:

3D vector of derivatives.

virtual std::vector<std::vector<double>> implied_volatility(const StochasticProcess*, const std::vector<double>&, const std::vector<std::vector<double>>&, StrikeType = LOG_STRIKE, double tolerance = 1e-4) const override

Implied volatilities for multiple tenors and strike sets.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Tenor vector.

  • strikes – 2D strike array.

  • strike_type – Strike type. See StrikeType for available options.

  • tolerance – Root-finding tolerance.

Returns:

2D vector of implied volatilities.

virtual std::vector<std::vector<double>> pdf(const StochasticProcess*, const std::vector<double>&, const std::vector<std::vector<double>>&, StrikeType = LOG_STRIKE) const override

Returns PDFs for multiple tenors and strikes.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Vector of tenors.

  • strikes – 2D vector of strikes.

  • strike_type – Strike type. See StrikeType for available options.

Returns:

2D vector of PDF values.

inline void set_fourier_transform(std::shared_ptr<FourierTransform> v)
inline void get_u(arma::cx_colvec &u, arma::cx_colvec &iu, arma::cx_colvec &u2) const
double implied_volatility(const StochasticProcess *stochastic_process, double tenor, double strike, StrikeType strike_type = LOG_STRIKE, double tolerance = 1e-4) const

Calculates implied volatility for one option.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenor – Tenor.

  • strike – Strike.

  • strike_type – Strike type. See StrikeType for available options.

  • tolerance – Root-finding tolerance.

Returns:

Implied volatility.

std::vector<double> implied_volatility(const StochasticProcess *stochastic_process, double tenor, const std::vector<double> &strikes, StrikeType strike_type = LOG_STRIKE, double tolerance = 1e-4) const

Implied volatilities for a vector of strikes at a given tenor.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenor – Tenor.

  • strikes – Strike vector.

  • strike_type – Strike type. See StrikeType for available options.

  • tolerance – Root-finding tolerance.

Returns:

Vector of implied volatilities.

virtual std::vector<std::vector<double>> implied_volatility(const StochasticProcess *stochastic_process, const std::vector<double> &tenors, const std::vector<std::vector<double>> &strikes, StrikeType strike_type = LOG_STRIKE, double tolerance = 1e-4) const = 0

Implied volatilities for multiple tenors and strike sets.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Tenor vector.

  • strikes – 2D strike array.

  • strike_type – Strike type. See StrikeType for available options.

  • tolerance – Root-finding tolerance.

Returns:

2D vector of implied volatilities.

double pdf(const StochasticProcess *stochastic_process, double tenor, double strike, StrikeType strike_type = LOG_STRIKE) const

Returns PDF value at a given tenor and strike.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenor – Tenor.

  • strike – Strike.

  • strike_type – Strike type. See StrikeType for available options.

Returns:

PDF value.

std::vector<double> pdf(const StochasticProcess *stochastic_process, double tenor, const std::vector<double> &strikes, StrikeType strike_type = LOG_STRIKE) const

Returns PDF values for a vector of strikes.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenor – Tenor.

  • strikes – Strike vector.

  • strike_type – Strike type. See StrikeType for available options.

Returns:

Vector of PDF values.

virtual std::vector<std::vector<double>> pdf(const StochasticProcess *stochastic_process, const std::vector<double> &tenors, const std::vector<std::vector<double>> &strikes, StrikeType strike_type = LOG_STRIKE) const = 0

Returns PDFs for multiple tenors and strikes.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Vector of tenors.

  • strikes – 2D vector of strikes.

  • strike_type – Strike type. See StrikeType for available options.

Returns:

2D vector of PDF values.

Protected Functions

virtual void _price_kernal(const StochasticProcess*, const arma::rowvec &expirations) const = 0
virtual std::vector<arma::mat> _price_derivatives_kernal(const StochasticProcess*, const arma::rowvec &tenors) const = 0
virtual void _pdf_kernal(const StochasticProcess*, const arma::rowvec &expirations) const = 0
void _interpolate(const StochasticProcess*, const std::vector<double>&, const std::vector<std::vector<double>>&, std::vector<std::vector<double>>&, StrikeType, YType) const
void _interpolate(const arma::colvec *xs, const arma::mat *ys, const std::vector<std::vector<double>> &strikes, std::vector<std::vector<double>> &values) const
void _calls_to_vols(const StochasticProcess*, double tolerance = 1e-4) const
void _cn_to_calls(const StochasticProcess *process) const

Protected Attributes

unsigned int _n
double _lambda
double _eta
arma::cx_colvec _scaler
arma::cx_colvec _um
arma::cx_colvec _iu
arma::cx_colvec _u2
double *_x
double *_y
double *_u
double *_ya
arma::colvec _kj
arma::colvec _kn
mutable arma::rowvec _expirations
mutable arma::mat _vn
mutable arma::mat _cn
mutable arma::mat _calls
mutable arma::mat _pdf
std::shared_ptr<FourierTransform> _ft
arma::colvec _dampen_factor