s30aaf computes the price of a European call (or put) option for constant volatility,
, and risk-free interest rate,
, with a possible dividend yield,
, using the Black–Scholes–Merton formula (see
Black and Scholes (1973) and
Merton (1973)). For a given strike price,
, the price of a European call with underlying price,
, and time to expiry,
, is
and the corresponding European put price is
and where
denotes the cumulative Normal distribution function,
and
-
1:
– Character(1)
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 .
-
2:
– Integer
Input
-
On entry: the number of strike prices to be used.
Constraint:
.
-
3:
– Integer
Input
-
On entry: the number of times to expiry to be used.
Constraint:
.
-
4:
– Real (Kind=nag_wp) array
Input
-
On entry: must contain
, the th strike price, for .
Constraint:
, where , the safe range parameter, for .
-
5:
– Real (Kind=nag_wp)
Input
-
On entry: , the price of the underlying asset.
Constraint:
, where , the safe range parameter.
-
6:
– Real (Kind=nag_wp) array
Input
-
On entry: must contain
, the th time, in years, to expiry, for .
Constraint:
, where , the safe range parameter, for .
-
7:
– Real (Kind=nag_wp)
Input
-
On entry: , the volatility of the underlying asset. Note that a rate of 15% should be entered as .
Constraint:
.
-
8:
– Real (Kind=nag_wp)
Input
-
On entry: , the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as .
Constraint:
.
-
9:
– Real (Kind=nag_wp)
Input
-
On entry: , the annual continuous yield rate. Note that a rate of 8% should be entered as .
Constraint:
.
-
10:
– Real (Kind=nag_wp) array
Output
-
On exit: contains , the option price evaluated for the strike price at expiry for and .
-
11:
– Integer
Input
-
On entry: the first dimension of the array
p as declared in the (sub)program from which
s30aaf is called.
Constraint:
.
-
12:
– Integer
Input/Output
-
On entry:
ifail must be set to
,
. If you are unfamiliar with this argument you should refer to
Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this argument, the recommended value is
.
When the value is used it is essential to test the value of ifail on exit.
On exit:
unless the routine detects an error or a warning has been flagged (see
Section 6).
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
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
s15abf and
s15adf). An accuracy close to
machine precision can generally be expected.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
None.
This example computes the prices for six European call options using two expiry times and three strike prices as input. The times to expiry are taken as and years respectively. The stock price is , with strike prices, , and . The risk-free interest rate is per year and the volatility is per year.