com.opengamma.strata.pricer.impl.option

Class BlackScholesFormulaRepository

java.lang.Object

com.opengamma.strata.pricer.impl.option.BlackScholesFormulaRepository

public final class BlackScholesFormulaRepository
extends Object

The primary repository for Black-Scholes formulas, including the price and greeks.

When the formula involves ambiguous quantities, a reference value (rather than NaN) is returned Note that the formulas are expressed in terms of interest rate (r) and cost of carry (b), then d_1 and d_2 are d_{1,2} = \frac{\ln(S/X) + (b \pm \sigma^2 ) T}{\sigma \sqrt{T}}.

Method Summary

Modifier and Type	Method and Description
static double	carryRho(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the carry rho.
static double	charm(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the charm.
static double	crossGamma(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the cross gamma.
static double	delta(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the spot delta.
static double	dualCharm(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the dual charm.
static double	dualDelta(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the dual delta.
static double	dualGamma(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the dual gamma.
static double	dualVanna(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the dual vanna.
static double	gamma(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the spot gamma.
static double	price(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the spot price.
static double	rho(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the rho.
static double	strikeForDelta(double spot, double spotDelta, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the strike for the delta.
static double	theta(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry, boolean isCall) Computes the theta.
static double	vanna(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the vanna.
static double	vega(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the spot vega.
static double	vegaBleed(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the vega bleed.
static double	vomma(double spot, double strike, double timeToExpiry, double lognormalVol, double interestRate, double costOfCarry) Computes the vomma (aka volga).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

price

public static double price(double spot,
                           double strike,
                           double timeToExpiry,
                           double lognormalVol,
                           double interestRate,
                           double costOfCarry,
                           boolean isCall)

Computes the spot price.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

isCall - true for call, false for put

Returns:

the spot price

delta

public static double delta(double spot,
                           double strike,
                           double timeToExpiry,
                           double lognormalVol,
                           double interestRate,
                           double costOfCarry,
                           boolean isCall)

Computes the spot delta.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

isCall - true for call, false for put

Returns:

the spot delta

strikeForDelta

public static double strikeForDelta(double spot,
                                    double spotDelta,
                                    double timeToExpiry,
                                    double lognormalVol,
                                    double interestRate,
                                    double costOfCarry,
                                    boolean isCall)

Computes the strike for the delta.

Note that the parameter range is more restricted for this method because the strike is undetermined for infinite/zero valued parameters.

Parameters:

spot - the spot value of the underlying

spotDelta - The spot delta

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

isCall - true for call, false for put

Returns:

the strike

dualDelta

public static double dualDelta(double spot,
                               double strike,
                               double timeToExpiry,
                               double lognormalVol,
                               double interestRate,
                               double costOfCarry,
                               boolean isCall)

Computes the dual delta.

This is the first derivative of option price with respect to strike.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

isCall - true for call, false for put

Returns:

the dual delta

gamma

public static double gamma(double spot,
                           double strike,
                           double timeToExpiry,
                           double lognormalVol,
                           double interestRate,
                           double costOfCarry)

Computes the spot gamma.

This is the second order sensitivity of the spot option value to the spot.

$\frac{\partial^2 FV}{\partial^2 f}$.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the spot gamma

dualGamma

public static double dualGamma(double spot,
                               double strike,
                               double timeToExpiry,
                               double lognormalVol,
                               double interestRate,
                               double costOfCarry)

Computes the dual gamma.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the dual gamma

crossGamma

public static double crossGamma(double spot,
                                double strike,
                                double timeToExpiry,
                                double lognormalVol,
                                double interestRate,
                                double costOfCarry)

Computes the cross gamma.

This is the sensitivity of the delta to the strike.

$\frac{\partial^2 V}{\partial f \partial K}$.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the cross gamma

theta

public static double theta(double spot,
                           double strike,
                           double timeToExpiry,
                           double lognormalVol,
                           double interestRate,
                           double costOfCarry,
                           boolean isCall)

Computes the theta.

This is the sensitivity of the present value to a change in time to maturity.

$\-frac{\partial V}{\partial T}$.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

isCall - true for call, false for put

Returns:

theta

charm

public static double charm(double spot,
                           double strike,
                           double timeToExpiry,
                           double lognormalVol,
                           double interestRate,
                           double costOfCarry,
                           boolean isCall)

Computes the charm.

This is the minus of second order derivative of option value, once spot and once time to maturity.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - The interest rate

costOfCarry - The cost of carry

isCall - true for call, false for put

Returns:

the charm

dualCharm

public static double dualCharm(double spot,
                               double strike,
                               double timeToExpiry,
                               double lognormalVol,
                               double interestRate,
                               double costOfCarry,
                               boolean isCall)

Computes the dual charm.

This is the minus of second order derivative of option value, once strike and once time to maturity.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost of carry

isCall - true for call, false for put

Returns:

the dual charm

vega

public static double vega(double spot,
                          double strike,
                          double timeToExpiry,
                          double lognormalVol,
                          double interestRate,
                          double costOfCarry)

Computes the spot vega.

This is the sensitivity of the option's spot price wrt the implied volatility (which is just the spot vega divided by the numeraire).

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the spot vega

vanna

public static double vanna(double spot,
                           double strike,
                           double timeToExpiry,
                           double lognormalVol,
                           double interestRate,
                           double costOfCarry)

Computes the vanna.

This is the second order derivative of the option value, once to the underlying spot and once to volatility.

$\frac{\partial^2 FV}{\partial f \partial \sigma}$.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the spot vanna

dualVanna

public static double dualVanna(double spot,
                               double strike,
                               double timeToExpiry,
                               double lognormalVol,
                               double interestRate,
                               double costOfCarry)

Computes the dual vanna.

This is the second order derivative of the option value, once to the strike and once to volatility.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the spot dual vanna

vomma

public static double vomma(double spot,
                           double strike,
                           double timeToExpiry,
                           double lognormalVol,
                           double interestRate,
                           double costOfCarry)

Computes the vomma (aka volga).

This is the second order derivative of the option spot price with respect to the implied volatility.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the spot vomma

vegaBleed

public static double vegaBleed(double spot,
                               double strike,
                               double timeToExpiry,
                               double lognormalVol,
                               double interestRate,
                               double costOfCarry)

Computes the vega bleed.

This is the second order derivative of the option spot price, once to the volatility and once to the time.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - the interest rate

costOfCarry - the cost-of-carry rate

Returns:

the spot vomma

rho

public static double rho(double spot,
                         double strike,
                         double timeToExpiry,
                         double lognormalVol,
                         double interestRate,
                         double costOfCarry,
                         boolean isCall)

Computes the rho.

This is the derivative of the option value with respect to the risk free interest rate . Note that costOfCarry = interestRate - dividend, which the derivative also acts on.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - The interest rate

costOfCarry - the cost of carry

isCall - true for call, false for put

Returns:

the rho

carryRho

public static double carryRho(double spot,
                              double strike,
                              double timeToExpiry,
                              double lognormalVol,
                              double interestRate,
                              double costOfCarry,
                              boolean isCall)

Computes the carry rho.

This is the derivative of the option value with respect to the cost of carry . Note that costOfCarry = interestRate - dividend, which the derivative also acts on.

Parameters:

spot - the spot value of the underlying

strike - the strike

timeToExpiry - the time to expiry

lognormalVol - the log-normal volatility

interestRate - The interest rate

costOfCarry - The cost of carry

isCall - true for call, false for put

Returns:

the carry rho