naginterfaces.library.specfun.opt_​binary_​con_​greeks

naginterfaces.library.specfun.opt_binary_con_greeks(calput, x, s, k, t, sigma, r, q)[source]

opt_binary_con_greeks computes the price of a binary or digital cash-or-nothing option together with its sensitivities (Greeks).

For full information please refer to the NAG Library document for s30cb

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s30cbf.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.

kfloat

The amount, , to be paid at expiration if the option is in-the-money, i.e., if when , or if when , for .

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 .

qfloat

, the annual continuous yield 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 annual cost of carry rate, i.e., , for and , where .

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: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

opt_binary_con_greeks computes the price of a binary or digital cash-or-nothing 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. This option pays a fixed amount, , at expiration if the option is in-the-money (see the S Introduction). For a strike price, , underlying asset price, , and time to expiry, , the payoff is, therefore, , if for a call or for a put. Nothing is paid out when this condition is not met.

The price of a call with volatility, , risk-free interest rate, , and annualised dividend yield, , is

and for a put,

where is the cumulative Normal distribution function,

and

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

References

Reiner, E and Rubinstein, M, 1991, Unscrambling the binary code, Risk (4)