Class StochasticProcessPricer

Inheritance Relationships

Derived Types

Class Documentation

class StochasticProcessPricer

Abstract base class for pricing instruments under a stochastic process.

Subclassed by otyca::AutoStochasticProcessPricer, otyca::DirectIntegrationPricer, otyca::FourierTransformPricer

Public Types

enum StrikeType

Types of strike input.

Values:

enumerator LOG_STRIKE

Logarithmic strike.

enumerator STRIKE

Standard strike.

enumerator DELTA

Delta.

enumerator STDEV

Standard deviation.

enum YType

Output types.

Values:

enumerator PRICE

Price.

enumerator IV

Implied volatility.

enumerator PDF

Probability density function.

Public Functions

virtual ~StochasticProcessPricer()
virtual std::string name() = 0

Returns the name of the pricer.

Returns:

The name as a string.

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

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

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<std::vector<double>>> price_derivatives_finite_difference(const StochasticProcess *stochastic_process, const std::vector<double> &tenors, const std::vector<std::vector<double>> &strikes, StrikeType strike_type = LOG_STRIKE, double epsilon = 1e-6) const

Price derivatives using finite differences.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Vector of tenors.

  • strikes – 2D strike array.

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

  • epsilon – Finite difference step size.

Returns:

3D vector of approximated derivatives.

bool compare_price_derivatives(const StochasticProcess *stochastic_process, const std::vector<double> &tenors, const std::vector<std::vector<double>> &strikes, StrikeType strike_type = LOG_STRIKE, double epsilon = 1e-6, double tolerance = 1e-6)

Compares analytical and finite-difference derivatives.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Vector of tenors.

  • strikes – 2D strike array.

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

  • epsilon – FD step size.

  • tolerance – Acceptable error.

Returns:

true if all derivatives are within tolerance.

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

Prices for a single tenor and set of strikes.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenor – Single tenor value.

  • strikes – Strike vector.

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

Returns:

Vector of prices.

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

Prices a single option.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenor – Tenor value.

  • strike – Strike value.

  • strike_type – Strike type.

Returns:

Option price.

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.

void measure_stochastic_process(StochasticProcess *stochastic_process, const std::vector<double> &tenors, const std::vector<std::vector<double>> &strikes, const std::vector<std::vector<double>> &weights, const std::vector<double> &parameters, arma::colvec &result)

Measures model by weighting results over strikes and tenors.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Vector of tenors.

  • strikes – 2D strike array.

  • weights – 2D weights for each strike.

  • parameters – Model parameters.

  • result – Output column vector to fill.

inline const arma::colvec &get_u()

Gets the u values.

Returns:

Column vector of u values.

inline const arma::colvec &get_u2()

Gets the u^2 values.

Returns:

Column vector of u squared values.

inline const arma::cx_colvec &get_iu()

Gets the imaginary u values.

Returns:

Complex column vector of i*u values.

inline const arma::colvec &get_logu()

Gets the log(u) values.

Returns:

Column vector of log(u) values.

inline const arma::rowvec &get_t()

Gets the t values.

Returns:

Row vector of t values.

Protected Functions

void _pdf_transformation(const StochasticProcess *stochastic_process, const std::vector<double> &tenors, const std::vector<std::vector<double>> &strikes, StrikeType strike_type, std::vector<std::vector<double>> &pdfs) const

Computes PDF values for given parameters and stores in output.

Parameters:

  • stochastic_process – Pointer to stochastic process.

  • tenors – Tenor values.

  • strikes – Strike values.

  • strike_type – Strike interpretation.

  • pdfs – Output PDF values.

Protected Attributes

double _cut_off_vol
double _cut_off_price
double _cut_off_pdf
arma::colvec _u_col
arma::colvec _logu_col
arma::colvec _u2_col
arma::cx_colvec _iu_col
arma::rowvec _t_row