webcab.lib.finance.options
Class EuropeanTheta

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

All Implemented Interfaces:

Serializable

public class EuropeanTheta

extends Object

implements Serializable

Within this class we consider the evaluation of the Theta of a European option on equities, equity indexes, currencies and future contracts in accordance with the classical Black-Scholes model.

Recall that the Theta of an option contract is the rate of change (i.e. the first derivative) of the option with respect to changes in the time to maturity. The Theta is often referred to as the time decay of an option (or portfolio).

See Also:

Serialized Form

Constructor Summary

EuropeanTheta()
Creates a new instance.

Method Summary

double	callTheta(double stockPrice, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) This method calculates the theta per year of a European call option on a non-dividend-paying stock.
double	callTheta(double stockPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) This method calculates the theta per year of a European call option on a non-dividend-paying stock.
double	callThetaOnCurrency(double interest, double exchangeRate, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) Returns the theta of a European call option on a currency.
double	callThetaOnCurrency(double interest, double exchangeRate, double strike, double riskFreeRate, double volatility, double timeToMaturity) Returns the theta of a European call option on a currency.
double	callThetaOnFutures(double futuresPrice, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) Returns the theta of a European call option on a futures contract
double	callThetaOnFutures(double futuresPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) Returns the theta of a European call option on a futures contract
double	callThetaWithYield(double yield, double stockPrice, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) Returns the theta of a European call option on an asset paying a continuous yield (for example an option on a index).
double	callThetaWithYield(double yield, double stockPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) Returns the theta of a European call option on an asset paying a continuous yield (for example an option on a index).
double	putTheta(double stockPrice, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) This method calculates the theta per year of a European put option on a non-dividend paying stock.
double	putTheta(double stockPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) This method calculates the theta per year of a European put option on a non-dividend paying stock.
double	putThetaOnCurrency(double interest, double exchangeRate, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) Returns the theta of a European put option on a currency.
double	putThetaOnCurrency(double interest, double exchangeRate, double strike, double riskFreeRate, double volatility, double timeToMaturity) Returns the theta of a European put option on a currency.
double	putThetaOnFutures(double futuresPrice, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) Returns the theta of a European put option on a futures contract
double	putThetaOnFutures(double futuresPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) Returns the theta of a European put option on a futures contract
double	putThetaWithYield(double yield, double stockPrice, double strike, double riskFreeRate, double volatility, Date evaluationDate, Date maturityDate, BusinessCalendar businessCalendar) Returns the theta of a European put option on an asset paying a continuous yield (for example an option on a index).
double	putThetaWithYield(double yield, double stockPrice, double strike, double riskFreeRate, double volatility, double timeToMaturity) Returns the theta of a European put option on an asset paying a continuous yield (for example an option on a index).
double	thetaFromGammaDelta(double delta, double gamma, double assetPrice, double riskFreeRate, double volatility, double totalValue) We derive the theta from the delta, gamma and some other market variables for a portfolio of derivative all defined on some underlying asset.
double	year2DayThetaConvert(double thetaPerYear) Converts the theta expressed as per year into the equivalent per day reading.

Methods inherited from class java.lang.Object

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

Constructor Detail

EuropeanTheta

public EuropeanTheta()

Creates a new instance.

Method Detail

callTheta

public double callTheta(double stockPrice,
                        double strike,
                        double riskFreeRate,
                        double volatility,
                        Date evaluationDate,
                        Date maturityDate,
                        BusinessCalendar businessCalendar)
                 throws EuropeanThetaDemoException

This method calculates the theta per year of a European call option on a non-dividend-paying stock.

Parameters:

stockPrice - the value of the underlying stock

strike - the strike of the call option

riskFreeRate - the continuously compounded risk free interest rate

volatility - the volatility of the underlying stock price

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

callTheta

public double callTheta(double stockPrice,
                        double strike,
                        double riskFreeRate,
                        double volatility,
                        double timeToMaturity)
                 throws EuropeanThetaDemoException

This method calculates the theta per year of a European call option on a non-dividend-paying stock.

Parameters:

stockPrice - the value of the underlying stock

strike - the strike of the call option

riskFreeRate - the continuously compounded risk free interest rate

timeToMaturity - the length of time until the option expires

volatility - the volatility of the underlying stock price

EuropeanThetaDemoException

putTheta

public double putTheta(double stockPrice,
                       double strike,
                       double riskFreeRate,
                       double volatility,
                       Date evaluationDate,
                       Date maturityDate,
                       BusinessCalendar businessCalendar)
                throws EuropeanThetaDemoException

This method calculates the theta per year of a European put option on a non-dividend paying stock.

Parameters:

stockPrice - the value of the underlying stock

strike - the strike of the put option

riskFreeRate - the continuously compounded risk free interest rate

volatility - the volatility of the underlying stock price

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

putTheta

public double putTheta(double stockPrice,
                       double strike,
                       double riskFreeRate,
                       double volatility,
                       double timeToMaturity)
                throws EuropeanThetaDemoException

This method calculates the theta per year of a European put option on a non-dividend paying stock.

Parameters:

stockPrice - the value of the underlying stock

strike - the strike of the put option

riskFreeRate - the continuously compounded risk free interest rate

timeToMaturity - the length of time until the option expires

volatility - the volatility of the underlying stock price

EuropeanThetaDemoException

year2DayThetaConvert

public double year2DayThetaConvert(double thetaPerYear)
                            throws EuropeanThetaDemoException

Converts the theta expressed as per year into the equivalent per day reading. Note that the trading year contains 252 trading days.

Parameters:

thetaPerYear - this is the theta per year of an asset

EuropeanThetaDemoException

callThetaWithYield

public double callThetaWithYield(double yield,
                                 double stockPrice,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 Date evaluationDate,
                                 Date maturityDate,
                                 BusinessCalendar businessCalendar)
                          throws EuropeanThetaDemoException

Returns the theta of a European call option on an asset paying a continuous yield (for example an option on a index).

Parameters:

yield - the continuous yield of the underlying asset

stockPrice - the value of the underlying stock price

strike - the strike of the call option

riskFreeRate - the continuously compounded risk free interest rate

volatility - the volatility of the underlying stock price

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

callThetaWithYield

public double callThetaWithYield(double yield,
                                 double stockPrice,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 double timeToMaturity)
                          throws EuropeanThetaDemoException

Returns the theta of a European call option on an asset paying a continuous yield (for example an option on a index).

Parameters:

yield - the continuous yield of the underlying asset

stockPrice - the value of the underlying stock price

strike - the strike of the call option

riskFreeRate - the continuously compounded risk free interest rate

volatility - the volatility of the underlying stock price

timeToMaturity - the length of time until the option expires

EuropeanThetaDemoException

putThetaWithYield

public double putThetaWithYield(double yield,
                                double stockPrice,
                                double strike,
                                double riskFreeRate,
                                double volatility,
                                Date evaluationDate,
                                Date maturityDate,
                                BusinessCalendar businessCalendar)
                         throws EuropeanThetaDemoException

Returns the theta of a European put option on an asset paying a continuous yield (for example an option on a index).

Parameters:

yield - the continuous yield of the underlying asset

stockPrice - the value of the underlying stock price

strike - the strike of the call option

riskFreeRate - the continuously compounded risk free interest rate

volatility - the volatility of the underlying stock price

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

putThetaWithYield

public double putThetaWithYield(double yield,
                                double stockPrice,
                                double strike,
                                double riskFreeRate,
                                double volatility,
                                double timeToMaturity)
                         throws EuropeanThetaDemoException

Returns the theta of a European put option on an asset paying a continuous yield (for example an option on a index).

Parameters:

yield - the continuous yield of the underlying asset

stockPrice - the value of the underlying stock price

strike - the strike of the call option

riskFreeRate - the continuously compounded risk free interest rate

timeToMaturity - the length of time until the option expires

volatility - the volatility of the underlying stock price

EuropeanThetaDemoException

callThetaOnCurrency

public double callThetaOnCurrency(double interest,
                                  double exchangeRate,
                                  double strike,
                                  double riskFreeRate,
                                  double volatility,
                                  Date evaluationDate,
                                  Date maturityDate,
                                  BusinessCalendar businessCalendar)
                           throws EuropeanThetaDemoException

Returns the theta of a European call option on a currency.

Parameters:

interest - the continuously compounded risk free interest rate on the foreign currency

exchangeRate - the exchange rate

strike - the exchange rate at which the currency option is exercised at

riskFreeRate - the continuously compounded risk free interest rate in the base currency

volatility - the volatility of the exchange rate

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

callThetaOnCurrency

public double callThetaOnCurrency(double interest,
                                  double exchangeRate,
                                  double strike,
                                  double riskFreeRate,
                                  double volatility,
                                  double timeToMaturity)
                           throws EuropeanThetaDemoException

Returns the theta of a European call option on a currency.

Parameters:

interest - the continuously compounded risk free interest rate on the foreign currency

exchangeRate - the exchange rate

strike - the exchange rate at which the currency option is exercised at

riskFreeRate - the continuously compounded risk free interest rate in the base currency

timeToMaturity - the time until the option expires

volatility - the volatility of the exchange rate

EuropeanThetaDemoException

putThetaOnCurrency

public double putThetaOnCurrency(double interest,
                                 double exchangeRate,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 Date evaluationDate,
                                 Date maturityDate,
                                 BusinessCalendar businessCalendar)
                          throws EuropeanThetaDemoException

Returns the theta of a European put option on a currency.

Parameters:

interest - the continuously compounded risk free interest rate on the foreign currency

exchangeRate - the exchange rate

strike - the exchange rate at which the currency option is exercised at

riskFreeRate - the continuously compounded risk free interest rate in the base currency

volatility - the volatility of the exchange rate

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

putThetaOnCurrency

public double putThetaOnCurrency(double interest,
                                 double exchangeRate,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 double timeToMaturity)
                          throws EuropeanThetaDemoException

Returns the theta of a European put option on a currency.

Parameters:

interest - the continuously compounded risk free interest rate on the foreign currency

exchangeRate - the exchange rate

strike - the exchange rate at which the currency option is exercised at

riskFreeRate - the continuously compounded risk free interest rate in the base currency

timeToMaturity - the time until the option expires

volatility - the volatility of the exchange rate

EuropeanThetaDemoException

callThetaOnFutures

public double callThetaOnFutures(double futuresPrice,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 Date evaluationDate,
                                 Date maturityDate,
                                 BusinessCalendar businessCalendar)
                          throws EuropeanThetaDemoException

Returns the theta of a European call option on 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

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

callThetaOnFutures

public double callThetaOnFutures(double futuresPrice,
                                 double strike,
                                 double riskFreeRate,
                                 double volatility,
                                 double timeToMaturity)
                          throws EuropeanThetaDemoException

Returns the theta of a European call option on 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 to maturity of the option (in years)

EuropeanThetaDemoException

putThetaOnFutures

public double putThetaOnFutures(double futuresPrice,
                                double strike,
                                double riskFreeRate,
                                double volatility,
                                Date evaluationDate,
                                Date maturityDate,
                                BusinessCalendar businessCalendar)
                         throws EuropeanThetaDemoException

Returns the theta of a European put option on 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

evaluationDate - the date when the theta of the option contract is evaluated

maturityDate - the date when the option contract matures

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

EuropeanThetaDemoException

putThetaOnFutures

public double putThetaOnFutures(double futuresPrice,
                                double strike,
                                double riskFreeRate,
                                double volatility,
                                double timeToMaturity)
                         throws EuropeanThetaDemoException

Returns the theta of a European put option on 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 to maturity of the option (in years)

EuropeanThetaDemoException

thetaFromGammaDelta

public double thetaFromGammaDelta(double delta,
                                  double gamma,
                                  double assetPrice,
                                  double riskFreeRate,
                                  double volatility,
                                  double totalValue)
                           throws EuropeanThetaDemoException

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

Parameters:

delta - the delta with respect to the underlying asset of the portfolio

gamma - the gamma with respect to the underlying asset of the portfolio

assetPrice - the underlying assets price

volatility - the volatility of the underlying assets price

riskFreeRate - the continuously compounded risk free interest rate

totalValue - the value of the whole portfolio

EuropeanThetaDemoException