quant::bs Namespace Reference

Analytic Black–Scholes European option pricing and Greeks. More...

Classes
struct	Params

Functions
double	call_price (const Params &p)
double	call_price (double S, double K, double r, double q, double sigma, double T)
	Price a European call option under Black–Scholes (present value).
double	d1 (double S, double K, double r, double q, double sigma, double T)
double	d2 (double d1_value, double sigma, double T)
double	delta_call (double S, double K, double r, double q, double sigma, double T)
double	delta_put (double S, double K, double r, double q, double sigma, double T)
double	gamma (double S, double K, double r, double q, double sigma, double T)
double	implied_vol_call (double S, double K, double r, double q, double T, double price)
double	implied_vol_put (double S, double K, double r, double q, double T, double price)
double	normal_cdf (double x)
double	normal_pdf (double x)
double	put_price (const Params &p)
double	put_price (double S, double K, double r, double q, double sigma, double T)
	Price a European put option under Black–Scholes (present value).
double	reiner_rubinstein_price (OptionType opt, const BarrierSpec &barrier, double S, double K, double r, double q, double sigma, double T)
double	rho_call (double S, double K, double r, double q, double sigma, double T)
double	rho_put (double S, double K, double r, double q, double sigma, double T)
double	theta_call (double S, double K, double r, double q, double sigma, double T)
double	theta_put (double S, double K, double r, double q, double sigma, double T)
double	vega (double S, double K, double r, double q, double sigma, double T)

Detailed Description

Analytic Black–Scholes European option pricing and Greeks.

Reiner–Rubinstein closed-form barrier option pricer.

Function Documentation

call_price() [1/2]

double quant::bs::call_price ( const Params &  p )

inline

call_price() [2/2]

double quant::bs::call_price	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

Price a European call option under Black–Scholes (present value).

Parameters

S	spot price
K	strike
r	risk-free rate (cont.)
q	dividend yield (cont.)
sigma	volatility (per annum)
T	time to expiry (years)

Returns

call option price

d1()

double quant::bs::d1 ( double  S, double  K, double  r, double  q, double  sigma, double  T  )

inline

Helper: d1.

Parameters

S	spot price
K	strike
r	risk-free rate (cont.)
q	dividend yield (cont.)
sigma	volatility (per annum)
T	time to expiry (years)

d2()

double quant::bs::d2 ( double  d1_value, double  sigma, double  T  )

inline

Helper: d2 = d1 - sigma * sqrt(T).

Parameters

d1_value	the value of d1
sigma	volatility (per annum)
T	time to expiry (years)

delta_call()

double quant::bs::delta_call	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

Greeks (per 1.0 change in inputs; vega per 1.0 vol unit). All Greeks returned are present-value sensitivities.

delta_put()

double quant::bs::delta_put	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

gamma()

double quant::bs::gamma	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

implied_vol_call()

double quant::bs::implied_vol_call	(	double	S,
		double	K,
		double	r,
		double	q,
		double	T,
		double	price
	)

Implied volatility from price using a robust bracketed solver. Returns NaN if no solution is found within [1e-6, 5.0].

implied_vol_put()

double quant::bs::implied_vol_put	(	double	S,
		double	K,
		double	r,
		double	q,
		double	T,
		double	price
	)

normal_cdf()

double quant::bs::normal_cdf ( double  x )

inline

Standard normal CDF (via erfc for tail stability).

Parameters

x	input real value

Returns

.

normal_pdf()

double quant::bs::normal_pdf ( double  x )

inline

Standard normal PDF.

Parameters

x	input real value

Returns

.

put_price() [1/2]

double quant::bs::put_price ( const Params &  p )

inline

put_price() [2/2]

double quant::bs::put_price	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

Price a European put option under Black–Scholes (present value).

Parameters

S	spot price
K	strike
r	risk-free rate (cont.)
q	dividend yield (cont.)
sigma	volatility (per annum)
T	time to expiry (years)

Returns

put option price

reiner_rubinstein_price()

double quant::bs::reiner_rubinstein_price	(	OptionType	opt,
		const BarrierSpec &	barrier,
		double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

rho_call()

double quant::bs::rho_call	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

rho_put()

double quant::bs::rho_put	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

theta_call()

double quant::bs::theta_call	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

theta_put()

double quant::bs::theta_put	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)

vega()

double quant::bs::vega	(	double	S,
		double	K,
		double	r,
		double	q,
		double	sigma,
		double	T
	)