Class implements Black Scholes model. More...

#include <BlackScholesModel.hpp>

Inheritance diagram for julian::BlackScholesModel:

Public Member Functions
	BlackScholesModel ()
	Default Constructor. More...

	BlackScholesModel (const Date &date, const double &asset_prize, const SmartPointer< ir::Curve > &discounting_curve, const SmartPointer< ir::Curve > &dividend_curve, const SmartPointer< Volatility > &volatility)
	Constructor. More...

virtual Date	getDate () const override
	returns the date on which market data are actual More...

virtual double	getAssetPrize () const override
	returns the prize of asset More...

virtual SmartPointer< ir::Curve >	getDiscountingCurve () const override
	returns discounting curve More...

virtual SmartPointer< ir::Curve >	getDividendCurve () const override
	returns dividend curve More...

virtual void	setDate (Date &) override
	sets the market date More...

virtual void	setAssetPrize (double) override
	sets asset prize More...

virtual void	bumpAssetPrize (double) override
	bump asset prize additively More...

virtual void	bumpVolatility (double) override
	bump volatility additively More...

double	prizeAnalytically (const EuropeanOpt &) const override
	method calculates the prize of European vanilla option More...

Public Member Functions inherited from julian::DeeplyCopyableMarketModel< BlackScholesModel >
virtual MarketModel *	clone () const
	virtual copy constructor More...

Public Member Functions inherited from julian::MarketModel
virtual	~MarketModel ()
	destructor More...

Private Member Functions
double	calculateDrift (Date) const
	basing on discounting and dividend curve exponential drift is calculated More...

Private Attributes
Date	date_
	Market date. More...

double	asset_prize_
	Underlying asset prize. More...

SmartPointer< ir::Curve >	discounting_curve_
	Curve used to discount CFs. More...

SmartPointer< ir::Curve >	dividend_curve_
	Curve used to estimate continuous dividend. More...

SmartPointer< Volatility >	volatility_
	Volatility of the asset prize. More...

Detailed Description

Class implements Black Scholes model.

PDE

${\frac {\partial V}{\partial t}}+{\frac {1}{2}}\sigma ^{2}S^{2}{\frac {\partial ^{2}V}{\partial S^{2}}}+rS{\frac {\partial V}{\partial S}}-rV=0$

SDE

$dS_t = (r-q) S_t dt + \sigma S_t dW_t^Q$

For more information see: [14] [15] [20] [18]

and links

Examples:: optionPricingExample.cpp.

Constructor & Destructor Documentation

julian::BlackScholesModel::BlackScholesModel ( )

inline

Default Constructor.

julian::BlackScholesModel::BlackScholesModel	(	const Date &	date,
		const double &	asset_prize,
		const SmartPointer< ir::Curve > &	discounting_curve,
		const SmartPointer< ir::Curve > &	dividend_curve,
		const SmartPointer< Volatility > &	volatility
	)

inline

Constructor.

Member Function Documentation

void julian::BlackScholesModel::bumpAssetPrize ( double h )

overridevirtual

bump asset prize additively

Parameters

h bump size

Implements julian::MarketModel.

void julian::BlackScholesModel::bumpVolatility ( double h )

overridevirtual

bump volatility additively

Parameters

h bump size

Note: Depending on the implementation of volatility bumping may have different mechanism

Implements julian::MarketModel.

double julian::BlackScholesModel::calculateDrift ( Date date ) const

private

basing on discounting and dividend curve exponential drift is calculated

double julian::BlackScholesModel::getAssetPrize ( ) const

overridevirtual

returns the prize of asset

Implements julian::MarketModel.

Date julian::BlackScholesModel::getDate ( ) const

overridevirtual

returns the date on which market data are actual

Implements julian::MarketModel.

SmartPointer< ir::Curve > julian::BlackScholesModel::getDiscountingCurve ( ) const

overridevirtual

returns discounting curve

Implements julian::MarketModel.

SmartPointer< ir::Curve > julian::BlackScholesModel::getDividendCurve ( ) const

overridevirtual

returns dividend curve

Implements julian::MarketModel.

double julian::BlackScholesModel::prizeAnalytically ( const EuropeanOpt & opt ) const

overridevirtual

method calculates the prize of European vanilla option

$\begin{aligned} C & = i_{cp} (S e^{-q T_{today,maturity} }N(i_{cp} d_{1}) - K e^{-r T_{today,maturity}} N(i_{cp}d_{2})) \\ d_{1} & = \frac{ln(\frac{S}{K}) + (r - q) T_{today,maturity} + \frac{var}{2} }{\sqrt{var}} \\ d_{2} & = \frac{ln(\frac{S}{K}) + (r - q) T_{today,maturity} - \frac{var}{2} }{\sqrt{var}} \\ var & = \sigma^2(K, expiry) T_{today, expiry} \end{aligned}$