Class BlackScholesEuropeanOptionsFunctions

Set of static functions for Black-Scholes model calculations for european-style options.

Inheritance

System.Object

BlackScholesEuropeanOptionsFunctions

Namespace: QuantSharp

Assembly: QuantSharp.dll

Syntax

public static class BlackScholesEuropeanOptionsFunctions : Object

Methods

CallDelta(Double, Double, Double, Double, Double)

Delta of an european-style CALL option, i.e. the derivative of the option's price with respect to price of the underlying instrument.

Declaration

public static double CallDelta(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's delta

CallImpliedVolatility(Double, Double, Double, Double, Double)

Calculate the annual implied volatility of an european CALL option given its price. (Value is returned as fraction, e.g. 0.2 is 20% volatility.)

Declaration

public static double CallImpliedVolatility(double S, double K, double T, double r, double C)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)
System.Double	C	Price of the option

Returns

Type	Description
System.Double	Implied volatility of the option

Remarks

Solves numerically using Newton-Raphson method. Might fail if result would fall outside of 0-1000% range.

CallPrice(Double, Double, Double, Double, Double)

Price of an european-style CALL option.

Declaration

public static double CallPrice(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's price

CallRho(Double, Double, Double, Double, Double)

Rho of an european-style CALL option, i.e. the derivative of option price with respect to risk-free interest rate.

Declaration

public static double CallRho(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's rho. Important: The value returned is the raw value of the derivative of option price with respect to risk-free rate. To get Rho value per the conventional definition ("per 1% of rate change"), divide the result by 100.

CallTheta(Double, Double, Double, Double, Double)

Theta of an european-style CALL option, i.e. the derivative of the option's price with respect to passage of time.

Declaration

public static double CallTheta(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's theta. Important: The value is the raw value of the derivative of option price with respect to time. To get Theta value per the conventional definition ("decay per 1 day"), divide the result by 365. Additionally, the value will be positive for long positions because T decreases as time moves forward, therefore conventional understanding of Theta requires multiplication by -1.

Gamma(Double, Double, Double, Double, Double)

Gamma of an european-style option (same for CALL and PUT), i.e. the second derivative of the option's price with respect to price of the underlying instrument. It reflects the convexity of Delta.

Declaration

public static double Gamma(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's gamma

PutDelta(Double, Double, Double, Double, Double)

Delta of an european-style PUT option, i.e. the derivative of the option's price with respect to price of the underlying instrument.

Declaration

public static double PutDelta(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's delta

PutImpliedVolatility(Double, Double, Double, Double, Double)

Calculate the annual implied volatility of an european PUT option given its price. (Value is returned as fraction, e.g. 0.2 is 20% volatility.)

Declaration

public static double PutImpliedVolatility(double S, double K, double T, double r, double P)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)
System.Double	P	Price of the option

Returns

Type	Description
System.Double	Implied volatility of the option

Remarks

Solves numerically using Newton-Raphson method. Might fail if result would fall outside of 0-1000% range.

PutPrice(Double, Double, Double, Double, Double)

Price of an european-style PUT option.

Declaration

public static double PutPrice(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's price

PutRho(Double, Double, Double, Double, Double)

Rho of an european-style PUT option, i.e. the derivative of option price with respect to risk-free interest rate.

Declaration

public static double PutRho(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's rho. Important: The value returned is the raw value of the derivative of option price with respect to risk-free rate. To get Rho value per the conventional definition ("per 1% of rate change"), divide the result by 100.

PutTheta(Double, Double, Double, Double, Double)

Theta of an european-style PUT option, i.e. the derivative of the option's price with respect to passage of time.

Declaration

public static double PutTheta(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's theta. Important: The value is the raw value of the derivative of option price with respect to time. To get Theta value per the conventional definition ("decay per 1 day"), divide the result by 365. Additionally, the value will be positive for long positions because T decreases as time moves forward, therefore conventional understanding of Theta requires multiplication by -1.

Vega(Double, Double, Double, Double, Double)

Vega of an european-style option (same for CALL and PUT), i.e. the derivative of option price with respect to volatility.

Declaration

public static double Vega(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's vega. Important: The value is the raw value of the derivative of option price with respect to volatility. To get Vega value per the conventional definition ("per 1% of volatility change"), divide the result by 100.

Vomma(Double, Double, Double, Double, Double)

Vomma (also known as "Volga") of an european-style option (same for CALL and PUT), i.e. the second-order derivative of option price with respect to volatility. It reflects the convexity of Vega.

Declaration

public static double Vomma(double S, double K, double T, double sigma, double r)

Parameters

Type	Name	Description
System.Double	S	Price of the underlying instrument
System.Double	K	Strike price of the option
System.Double	T	Time to expiration (in years)
System.Double	sigma	Annual volatility of the underlying instrument (as fraction, e.g. 20% is 0.2)
System.Double	r	Risk-free interest rate (as fraction, e.g. 5% is 0.05)

Returns

Type	Description
System.Double	The option's Vomma. Important: The value is the raw value of the second-order derivative of option price with respect to volatility. To get Vomma value per the conventional definition ("per 1% of volatility change"), divide the result by 100.