naginterfaces.library.specfun.opt_​asian_​geom_​greeks

naginterfaces.library.specfun.opt_asian_geom_greeks(calput, x, s, t, sigma, r, b)[source]

opt_asian_geom_greeks computes the Asian geometric continuous average-rate option price together with its sensitivities (Greeks).

For full information please refer to the NAG Library document for s30sb

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s30sbf.html

Parameters
calputstr, length 1

Determines whether the option is a call or a put.

A call; the holder has a right to buy.

A put; the holder has a right to sell.

xfloat, array-like, shape

must contain , the th strike price, for .

sfloat

, the price of the underlying asset.

tfloat, array-like, shape

must contain , the th time, in years, to expiry, for .

sigmafloat

, the volatility of the underlying asset. Note that a rate of 15% should be entered as .

rfloat

, the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as .

bfloat

, the annual cost of carry rate. Note that a rate of 8% should be entered as .

Returns
pfloat, ndarray, shape

contains , the option price evaluated for the strike price at expiry for and .

deltafloat, ndarray, shape

The leading part of the array contains the sensitivity, , of the option price to change in the price of the underlying asset.

gammafloat, ndarray, shape

The leading part of the array contains the sensitivity, , of to change in the price of the underlying asset.

vegafloat, ndarray, shape

, contains the first-order Greek measuring the sensitivity of the option price to change in the volatility of the underlying asset, i.e., , for and .

thetafloat, ndarray, shape

, contains the first-order Greek measuring the sensitivity of the option price to change in time, i.e., , for and , where .

rhofloat, ndarray, shape

, contains the first-order Greek measuring the sensitivity of the option price to change in the annual risk-free interest rate, i.e., , for and .

crhofloat, ndarray, shape

, contains the first-order Greek measuring the sensitivity of the option price to change in the price of the underlying asset, i.e., , for and .

vannafloat, ndarray, shape

, contains the second-order Greek measuring the sensitivity of the first-order Greek to change in the volatility of the asset price, i.e., , for and .

charmfloat, ndarray, shape

, contains the second-order Greek measuring the sensitivity of the first-order Greek to change in the time, i.e., , for and .

speedfloat, ndarray, shape

, contains the third-order Greek measuring the sensitivity of the second-order Greek to change in the price of the underlying asset, i.e., , for and .

colourfloat, ndarray, shape

, contains the third-order Greek measuring the sensitivity of the second-order Greek to change in the time, i.e., , for and .

zommafloat, ndarray, shape

, contains the third-order Greek measuring the sensitivity of the second-order Greek to change in the volatility of the underlying asset, i.e., , for and .

vommafloat, ndarray, shape

, contains the second-order Greek measuring the sensitivity of the first-order Greek to change in the volatility of the underlying asset, i.e., , for and .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: and .

(errno )

On entry, .

Constraint: and .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

opt_asian_geom_greeks computes the price of an Asian geometric continuous average-rate option, together with the Greeks or sensitivities, which are the partial derivatives of the option price with respect to certain of the other input parameters. The annual volatility, , risk-free rate, , and cost of carry, , are constants (see Kemna and Vorst (1990)). For a given strike price, , the price of a call option with underlying price, , and time to expiry, , is

and the corresponding put option price is

where

and

with

is the cumulative Normal distribution function,

The option price is computed for each strike price in a set , , and for each expiry time in a set , .

References

Kemna, A and Vorst, A, 1990, A pricing method for options based on average asset values, Journal of Banking and Finance (14), 113–129