# cum_d1_ (3) - Linux Manuals

## cum_d1_: Black 1976 calculator class.

## NAME

QuantLib::BlackCalculator - Black 1976 calculator class.

## SYNOPSIS

#include <ql/pricingengines/blackcalculator.hpp>

Inherited by **BlackScholesCalculator**.

### Public Member Functions

**BlackCalculator** (const boost::shared_ptr< **StrikedTypePayoff** > &payoff, **Real** forward, **Real** stdDev, **Real** discount=1.0)

**Real** **value** () const

**Real** **deltaForward** () const

virtual **Real** **delta** (**Real** spot) const

**Real** **elasticityForward** () const

virtual **Real** **elasticity** (**Real** spot) const

**Real** **gammaForward** () const

virtual **Real** **gamma** (**Real** spot) const

virtual **Real** **theta** (**Real** spot, **Time** maturity) const

virtual **Real** **thetaPerDay** (**Real** spot, **Time** maturity) const

**Real** **vega** (**Time** maturity) const

**Real** **rho** (**Time** maturity) const

**Real** **dividendRho** (**Time** maturity) const

**Real** **itmCashProbability** () const

**Real** **itmAssetProbability** () const

**Real** **strikeSensitivity** () const

**Real** **alpha** () const

**Real** **beta** () const

### Protected Attributes

**Real** **strike_**

**Real** **forward_**

**Real** **stdDev_**

**Real** **discount_**

**Real** **variance_**

**Real** **D1_**

**Real** **D2_**

**Real** **alpha_**

**Real** **beta_**

**Real** **DalphaDd1_**

**Real** **DbetaDd2_**

**Real** **n_d1_**

**Real** **cum_d1_**

**Real** **n_d2_**

**Real** **cum_d2_**

**Real** **X_**

**Real** **DXDs_**

**Real** **DXDstrike_**

### Friends

## Detailed Description

Black 1976 calculator class.

**Bug**

- When the variance is null, division by zero occur during the calculation of delta, delta forward, gamma, gamma forward, rho, dividend rho, vega, and strike sensitivity.

**Examples: **

## Member Function Documentation

**Real** deltaForward () const

Sensitivity to change in the underlying forward price.

### virtual **Real** delta (**Real** spot) const [virtual]

Sensitivity to change in the underlying spot price.

**Real** elasticityForward () const

Sensitivity in percent to a percent change in the underlying forward price.

### virtual **Real** elasticity (**Real** spot) const [virtual]

Sensitivity in percent to a percent change in the underlying spot price.

**Real** gammaForward () const

Second order derivative with respect to change in the underlying forward price.

### virtual **Real** gamma (**Real** spot) const [virtual]

Second order derivative with respect to change in the underlying spot price.

### virtual **Real** theta (**Real** spot, **Time** maturity) const [virtual]

Sensitivity to time to maturity.

### virtual **Real** thetaPerDay (**Real** spot, **Time** maturity) const [virtual]

Sensitivity to time to maturity per day, assuming 365 day per year.

**Real** vega (**Time** maturity) const

**Real** rho (**Time** maturity) const

Sensitivity to discounting rate.

**Real** dividendRho (**Time** maturity) const

Sensitivity to dividend/growth rate.

**Real** itmCashProbability () const

Probability of being in the money in the bond martingale measure, i.e. N(d2). It is a risk-neutral probability, not the real world one.

**Real** itmAssetProbability () const

Probability of being in the money in the asset martingale measure, i.e. N(d1). It is a risk-neutral probability, not the real world one.

**Real** strikeSensitivity () const

Sensitivity to strike.

## Author

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