webcab.lib.finance.options
Class EuropeanGamma

java.lang.Object
  |
  +--webcab.lib.finance.options.EuropeanGamma

All Implemented Interfaces:

Serializable

public class EuropeanGamma

extends Object

implements Serializable

Within this class we consider the evaluation of the Gamma of European options on equities, equity indexes, currencies and futures contracts in accordance with the classical Black-Scholes model.

Recall that the Gamma of an option contract is the rate of change of the rate of change (i.e. the second derivative) of the option price with respect to changes of the underlying asset price.

See Also:

Serialized Form

Constructor Summary

EuropeanGamma()
Creates a new instance.

Method Summary

double	gammaFromThetaDelta(double delta, double theta, double assetPrice, double riskFreeRate, double volatility, double totalValue) We derive the gamma from the delta, theta and some other market variables.
double	optionGamma(double stockPrice, double strike, double riskFreeRate, double volatility, Date evaluatioDate, Date maturityDate, BusinessCalendar businessCalendar) Evaluates the gamma of a European call or put option on a non-dividend paying stock.
double	optionGamma(double stockPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) Evaluates the gamma of a European call or put option on a non-dividend paying stock.
double	optionGammaOnCurrency(double foreignRate, double exchangeRate, double strike, double riskFreeRate, double volatility, Date evaluatioDate, Date maturityDate, BusinessCalendar businessCalendar) Evaluates the gamma of a European call or put option on a currency.
double	optionGammaOnCurrency(double foreignRate, double exchangeRate, double strike, double riskFreeRate, double volatility, double timeToMaturity) Evaluates the gamma of a European call or put option on a currency.
double	optionGammaOnFutures(double futuresPrice, double strike, double riskFreeRate, double volatility, Date evaluatioDate, Date maturityDate, BusinessCalendar businessCalendar) Evaluates the gamma of a European call or put option of a futures contract.
double	optionGammaOnFutures(double futuresPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) Evaluates the gamma of a European call or put option of a futures contract.
double	optionGammaOnIndex(double yield, double indexValue, double strike, double riskFreeRate, double volatility, Date evaluatioDate, Date maturityDate, BusinessCalendar businessCalendar) Evaluates the gamma of a European call or put option on an index.
double	optionGammaOnIndex(double yield, double indexValue, double strike, double riskFreeRate, double volatility, double timeToMaturity) Evaluates the gamma of a European call or put option on an index.
double	optionGammaWithYield(double yield, double stockPrice, double strike, double riskFreeRate, double volatility, Date evaluatioDate, Date maturityDate, BusinessCalendar businessCalendar) Returns the gamma of a European call or put option on a stock which has a continuous yield.
double	optionGammaWithYield(double yield, double stockPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) Returns the gamma of a European call or put option on a stock which has a continuous yield.

Methods inherited from class java.lang.Object

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

Constructor Detail

EuropeanGamma

public EuropeanGamma()

Creates a new instance.

Method Detail

optionGamma

public double optionGamma(double stockPrice,
                          double strike,
                          double riskFreeRate,
                          double volatility,
                          Date evaluatioDate,
                          Date maturityDate,
                          BusinessCalendar businessCalendar)
                   throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option on a non-dividend paying stock.

Parameters:

stockPrice - the price of the underlying security

strike - the strike (or exercise price) of the (call or put) option

riskFreeRate - the continuously compounded risk free interest rate in decimal format (1 percent = 0.01)

volatility - volatility of the futures contract

maturityDate - the date when the option contract matures

businessCalendar - The instance of a BusinessCalendar interface implementation. Specify null to select the London business calendar.

EuropeanGammaDemoException

optionGamma

public double optionGamma(double stockPrice,
                          double strike,
                          double riskFreeRate,
                          double volatility,
                          double timeToMaturity)
                   throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option on a non-dividend paying stock.

Parameters:

stockPrice - the price of the underlying security

strike - the strike (or exercise price) of the (call or put) option

riskFreeRate - the continuously compounded risk free interest rate in decimal format (1 percent = 0.01)

volatility - volatility of the futures contract

timeToMaturity - the time (in years) until the option contract expires

EuropeanGammaDemoException

optionGammaWithYield

public double optionGammaWithYield(double yield,
                                   double stockPrice,
                                   double strike,
                                   double riskFreeRate,
                                   double volatility,
                                   Date evaluatioDate,
                                   Date maturityDate,
                                   BusinessCalendar businessCalendar)
                            throws EuropeanGammaDemoException

Returns the gamma of a European call or put option on a stock which has a continuous yield.

Parameters:

yield - the continuous yield of the underlying stock

stockPrice - the price of the underlying stock or index

strike - value at which the option is exercised

riskFreeRate - the risk free interest rate in decimal format (i.e. 1 percent = 0.01)

volatility - the volatility of the underlying stock

maturityDate - the date when the option contract matures

businessCalendar - The instance of a BusinessCalendar interface implementation. Specify null to select the London business calendar.

EuropeanGammaDemoException

optionGammaWithYield

public double optionGammaWithYield(double yield,
                                   double stockPrice,
                                   double strike,
                                   double riskFreeRate,
                                   double volatility,
                                   double timeToMaturity)
                            throws EuropeanGammaDemoException

Returns the gamma of a European call or put option on a stock which has a continuous yield.

Parameters:

yield - the continuous yield of the underlying stock

stockPrice - the price of the underlying stock or index

strike - value at which the option is exercised

riskFreeRate - the risk free interest rate in decimal format (i.e. 1 percent = 0.01)

volatility - the volatility of the underlying stock

timeToMaturity - time period until the option expires

EuropeanGammaDemoException

optionGammaOnIndex

public double optionGammaOnIndex(double yield,
                                 double indexValue,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 Date evaluatioDate,
                                 Date maturityDate,
                                 BusinessCalendar businessCalendar)
                          throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option on an index.

Parameters:

yield - the average continuous yield of the constituents of the index

indexValue - the value of index

strike - value at which the option is exercised

riskFreeRate - the risk free interest rate

volatility - the volatility of the underlying stock

maturityDate - the date when the option contract matures

businessCalendar - The instance of a BusinessCalendar interface implementation. Specify null to select the London business calendar.

EuropeanGammaDemoException

optionGammaOnIndex

public double optionGammaOnIndex(double yield,
                                 double indexValue,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 double timeToMaturity)
                          throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option on an index.

Parameters:

yield - the average continuous yield of the constituents of the index

indexValue - the value of index

strike - value at which the option is exercised

riskFreeRate - the risk free interest rate

volatility - the volatility of the underlying stock

timeToMaturity - time period until the option expires

EuropeanGammaDemoException

optionGammaOnCurrency

public double optionGammaOnCurrency(double foreignRate,
                                    double exchangeRate,
                                    double strike,
                                    double riskFreeRate,
                                    double volatility,
                                    Date evaluatioDate,
                                    Date maturityDate,
                                    BusinessCalendar businessCalendar)
                             throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option on a currency.

Parameters:

foreignRate - the continuously compounded risk free interest rate in the foreign currency

exchangeRate - the present exchange rate

strike - the exchange rate at which the option can be exercised

riskFreeRate - the risk free interest rate in the base currency

volatility - the volatility of the exchange rate

maturityDate - the date when the option contract matures

businessCalendar - The instance of a BusinessCalendar interface implementation. Specify null to select the London business calendar.

EuropeanGammaDemoException

optionGammaOnCurrency

public double optionGammaOnCurrency(double foreignRate,
                                    double exchangeRate,
                                    double strike,
                                    double riskFreeRate,
                                    double volatility,
                                    double timeToMaturity)
                             throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option on a currency.

Parameters:

foreignRate - the continuously compounded risk free interest rate in the foreign currency

exchangeRate - the present exchange rate

strike - the exchange rate at which the option can be exercised

riskFreeRate - the risk free interest rate in the base currency

volatility - the volatility of the exchange rate

timeToMaturity - the time until the option expires

EuropeanGammaDemoException

optionGammaOnFutures

public double optionGammaOnFutures(double futuresPrice,
                                   double strike,
                                   double riskFreeRate,
                                   double volatility,
                                   Date evaluatioDate,
                                   Date maturityDate,
                                   BusinessCalendar businessCalendar)
                            throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option of a futures contract.

Parameters:

futuresPrice - the futures price at time zero

strike - the value of the futures contract at which option can be exercised

riskFreeRate - the risk free interest rate

volatility - volatility of the futures contract

maturityDate - the date when the option contract matures

businessCalendar - The instance of a BusinessCalendar interface implementation. Specify null to select the London business calendar.

EuropeanGammaDemoException

optionGammaOnFutures

public double optionGammaOnFutures(double futuresPrice,
                                   double strike,
                                   double riskFreeRate,
                                   double volatility,
                                   double timeToMaturity)
                            throws EuropeanGammaDemoException

Evaluates the gamma of a European call or put option of a futures contract.

Parameters:

futuresPrice - the futures price at time zero

strike - the value of the futures contract at which option can be exercised

riskFreeRate - the risk free interest rate

volatility - volatility of the futures contract

timeToMaturity - the time period until the option contract expires

EuropeanGammaDemoException

gammaFromThetaDelta

public double gammaFromThetaDelta(double delta,
                                  double theta,
                                  double assetPrice,
                                  double riskFreeRate,
                                  double volatility,
                                  double totalValue)
                           throws EuropeanGammaDemoException

We derive the gamma from the delta, theta and some other market variables. Note that for a delta neutral portfolio of derivatives on an underlying asset this expression relates the gamma and theta functions.

Parameters:

theta - the theta of the portfolio

totalValue - the value of the whole portfolio

assetPrice - the underlying asset price

volatility - the volatility of the underlying asset price

riskFreeRate - the continuously compounded risk free interest rate

EuropeanGammaDemoException