compute the Vega of a European-style option with given payoff

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Finance[BlackScholesVega] - compute the Vega of a European-style option with given payoff

	Calling Sequence
	BlackScholesVega(, K, T, sigma, r, d, optiontype) BlackScholesVega(, P, T, sigma, r, d)

Parameters

	-	algebraic expression; initial (current) value of the underlying asset
K	-	algebraic expression; strike price
T	-	algebraic expression; time to maturity
sigma	-	algebraic expression; volatility
r	-	algebraic expression; continuously compounded risk-free rate
d	-	algebraic expression; continuously compounded dividend yield
P	-	operator or procedure; payoff function
optiontype	-	call or put; option type

Description

•	The Vega of an option or a portfolio of options is the sensitivity of the option or portfolio to changes in the volatility of the underlying asset.

•	The BlackScholesVega command computes the Vega of a European-style option with the specified payoff function.

•	The parameter is the initial (current) value of the underlying asset. The parameter T is the time to maturity in years.

•

The parameter K specifies the strike price if this is a vanilla put or call option. Any payoff function can be specified using the second calling sequence. In this case the parameter P must be given in the form of an operator, which accepts one parameter (spot price at maturity) and returns the corresponding payoff.

•	The sigma, r, and d parameters are the volatility, the risk-free rate, and the dividend yield of the underlying asset. These parameters can be given in either the algebraic form or the operator form. The parameter d is optional. By default, the dividend yield is taken to be 0.

Compatibility

•	The Finance[BlackScholesVega] command was introduced in Maple 15.

•	For more information on Maple 15 changes, see Updates in Maple 15.

Examples

(1)

(2)

First you compute the Vega of a European call option with strike price 100, which matures in 1 year. This will define the Vega as a function of the risk-free rate, the dividend yield, and the volatility.

38.32995298*exp(-0.1999999999e-3/sigma^2)*exp(-.1249999999*sigma^2)-0.1000000000e-9*exp(-0.1999999999e-3/sigma^2)*exp(-.1249999999*sigma^2)/sigma^2

(3)

In this example you will use numeric values for the risk-free rate, the dividend yield, and the volatility.

(4)

You can also use the generic method in which the option is defined through its payoff function.

38.32995295*exp(-0.1999999999e-3/sigma^2)*exp(-.1249999999*sigma^2)-0.1000000000e-9*exp(-0.1999999999e-3/sigma^2)*exp(-.1249999999*sigma^2)/sigma^2

(5)

(6)

(7)

Here are similar examples for the European put option.

0.5000000000e-8*exp(-0.1317414389e-1/sigma^2)*exp(-.1249999999*sigma^2)/sigma^2+41.98835974*exp(-0.1317414389e-1/sigma^2)*exp(-.1249999999*sigma^2)

(8)

(9)

41.98835976*exp(-0.1317414390e-1/sigma^2)*exp(-.1250000000*sigma^2)-0.4000000000e-8*exp(-0.1317414390e-1/sigma^2)*exp(-.1250000000*sigma^2)/sigma^2

(10)

(11)

In this example, you will compute the Vega of a strangle.

S := 0.6000000000e-8*exp(-0.7857629440e-2/sigma^2)*exp(-.1249999999*sigma^2)/sigma^2+36.36298620*exp(-0.7857629440e-2/sigma^2)*exp(-.1249999999*sigma^2)-0.1000000000e-8*exp(-0.2835811589e-2/sigma^2)*exp(-.1249999999*sigma^2)/sigma^2+40.20079382*exp(-0.2835811589e-2/sigma^2)*exp(-.1249999999*sigma^2)

(12)

C := 40.20079384*exp(-0.2835811588e-2/sigma^2)*exp(-.1249999999*sigma^2)

(13)

P := 4.558482700*exp(-0.7857629432e-2/sigma^2)*exp(-.1249999999*sigma^2)/sigma^2+18.18149311*exp(-0.7857629432e-2/sigma^2)*exp(-.1249999999*sigma^2)-4.558482700*exp(-0.7857629431e-2/sigma^2)*exp(-.1249999999*sigma^2)/sigma^2+18.18149311*exp(-0.7857629431e-2/sigma^2)*exp(-.1249999999*sigma^2)

(14)

Check that is sufficiently close to .

	See Also
	Finance[AmericanOption], Finance[BermudanOption], Finance[BlackScholesDelta], Finance[BlackScholesGamma], Finance[BlackScholesPrice], Finance[BlackScholesRho], Finance[BlackScholesTheta], Finance[EuropeanOption], Finance[ImpliedVolatility], Finance[LatticePrice]