NAG CL Interface
s30ccc (opt_binary_aon_price)
1
Purpose
s30ccc computes the price of a binary or digital asset-or-nothing option.
2
Specification
void |
s30ccc (Nag_OrderType order,
Nag_CallPut option,
Integer m,
Integer n,
const double x[],
double s,
const double t[],
double sigma,
double r,
double q,
double p[],
NagError *fail) |
|
The function may be called by the names: s30ccc, nag_specfun_opt_binary_aon_price or nag_binary_aon_price.
3
Description
s30ccc computes the price of a binary or digital asset-or-nothing option which pays the underlying asset itself,
, at expiration if the option is in-the-money (see
Section 2.4 in the
S Chapter 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 , .
4
References
Reiner E and Rubinstein M (1991) Unscrambling the binary code Risk 4
5
Arguments
-
1:
– Nag_OrderType
Input
-
On entry: the
order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by
. See
Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint:
or .
-
2:
– Nag_CallPut
Input
-
On entry: 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.
Constraint:
or .
-
3:
– Integer
Input
-
On entry: the number of strike prices to be used.
Constraint:
.
-
4:
– Integer
Input
-
On entry: the number of times to expiry to be used.
Constraint:
.
-
5:
– const double
Input
-
On entry: must contain
, the th strike price, for .
Constraint:
, where , the safe range parameter, for .
-
6:
– double
Input
-
On entry: , the price of the underlying asset.
Constraint:
, where , the safe range parameter.
-
7:
– const double
Input
-
On entry: must contain
, the th time, in years, to expiry, for .
Constraint:
, where , the safe range parameter, for .
-
8:
– double
Input
-
On entry: , the volatility of the underlying asset. Note that a rate of 15% should be entered as .
Constraint:
.
-
9:
– double
Input
-
On entry: , the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as .
Constraint:
.
-
10:
– double
Input
-
On entry: , the annual continuous yield rate. Note that a rate of 8% should be entered as .
Constraint:
.
-
11:
– double
Output
-
Note: where
appears in this document, it refers to the array element
- when ;
- when .
On exit: contains , the option price evaluated for the strike price at expiry for and .
-
12:
– NagError *
Input/Output
-
The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_INTERNAL_ERROR
-
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
- NE_REAL
-
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: and .
On entry, .
Constraint: .
- NE_REAL_ARRAY
-
On entry, .
Constraint: .
On entry, .
Constraint: and .
7
Accuracy
The accuracy of the output is dependent on the accuracy of the cumulative Normal distribution function,
. This is evaluated using a rational Chebyshev expansion, chosen so that the maximum relative error in the expansion is of the order of the
machine precision (see
s15abc and
s15adc). An accuracy close to
machine precision can generally be expected.
8
Parallelism and Performance
s30ccc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
None.
10
Example
This example computes the price of an asset-or-nothing put with a time to expiry of years, a stock price of and a strike price of . The risk-free interest rate is per year, there is an annual dividend return of and the volatility is per year.
10.1
Program Text
10.2
Program Data
10.3
Program Results