NAG Library Routine Document

s30saf (opt_asian_geom_price)


s30saf computes the Asian geometric continuous average-rate option price.


Fortran Interface
Subroutine s30saf ( calput, m, n, x, s, t, sigma, r, b, p, ldp, ifail)
Integer, Intent (In):: m, n, ldp
Integer, Intent (Inout):: ifail
Real (Kind=nag_wp), Intent (In):: x(m), s, t(n), sigma, r, b
Real (Kind=nag_wp), Intent (Inout):: p(ldp,n)
Character (1), Intent (In):: calput
C Header Interface
#include <nagmk26.h>
void  s30saf_ (const char *calput, const Integer *m, const Integer *n, const double x[], const double *s, const double t[], const double *sigma, const double *r, const double *b, double p[], const Integer *ldp, Integer *ifail, const Charlen length_calput)


s30saf computes the price of an Asian geometric continuous average-rate option for constant volatility, σ, risk-free rate, r, and cost of carry, b (see Kemna and Vorst (1990)). For a given strike price, X, the price of a call option with underlying price, S, and time to expiry, T, is
Pcall = S e b--r T Φ d- 1 - X e-rT Φ d- 2 ,  
and the corresponding put option price is
Pput = X e-rT Φ -d-2 - S e b--r T Φ - d-1 ,  
d-1 = lnS/X + b- + σ-2 / 2 T σ- T  
d-2 = d-1 - σ- T ,  
σ- = σ 3 ,  b- = 1 2 r- σ2 6 .  
Φ is the cumulative Normal distribution function,
Φx = 1 2π - x exp -y2/2 dy .  
The option price Pij=PX=Xi,T=Tj is computed for each strike price in a set Xi, i=1,2,,m, and for each expiry time in a set Tj, j=1,2,,n.


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


1:     calput – 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: calput='C' or 'P'.
2:     m – IntegerInput
On entry: the number of strike prices to be used.
Constraint: m1.
3:     n – IntegerInput
On entry: the number of times to expiry to be used.
Constraint: n1.
4:     xm – Real (Kind=nag_wp) arrayInput
On entry: xi must contain Xi, the ith strike price, for i=1,2,,m.
Constraint: xiz ​ and ​ xi 1 / z , where z = x02amf , the safe range parameter, for i=1,2,,m.
5:     s – Real (Kind=nag_wp)Input
On entry: S, the price of the underlying asset.
Constraint: sz ​ and ​s1.0/z, where z=x02amf, the safe range parameter.
6:     tn – Real (Kind=nag_wp) arrayInput
On entry: ti must contain Ti, the ith time, in years, to expiry, for i=1,2,,n.
Constraint: tiz, where z = x02amf , the safe range parameter, for i=1,2,,n.
7:     sigma – Real (Kind=nag_wp)Input
On entry: σ, the volatility of the underlying asset. Note that a rate of 15% should be entered as 0.15.
Constraint: sigma>0.0.
8:     r – Real (Kind=nag_wp)Input
On entry: r, the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as 0.05.
Constraint: r0.0.
9:     b – Real (Kind=nag_wp)Input
On entry: b, the annual cost of carry rate. Note that a rate of 8% should be entered as 0.08.
10:   pldpn – Real (Kind=nag_wp) arrayOutput
On exit: pij contains Pij, the option price evaluated for the strike price xi at expiry tj for i=1,2,,m and j=1,2,,n.
11:   ldp – IntegerInput
On entry: the first dimension of the array p as declared in the (sub)program from which s30saf is called.
Constraint: ldpm.
12:   ifail – IntegerInput/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this argument, the recommended value is 0. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

Error Indicators and Warnings

If on entry ifail=0 or -1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, calput=value was an illegal value.
On entry, m=value.
Constraint: m1.
On entry, n=value.
Constraint: n1.
On entry, xvalue=value.
Constraint: xivalue and xivalue.
On entry, s=value.
Constraint: svalue and svalue.
On entry, tvalue=value.
Constraint: tivalue.
On entry, sigma=value.
Constraint: sigma>0.0.
On entry, r=value.
Constraint: r0.0.
On entry, ldp=value and m=value.
Constraint: ldpm.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.


The accuracy of the output is dependent on the accuracy of the cumulative Normal distribution function, Φ. 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.

Parallelism and Performance

s30saf 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 routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

Further Comments



This example computes the price of an Asian geometric continuous average-rate put with a time to expiry of 3 months, a stock price of 80 and a strike price of 85. The risk-free interest rate is 5% per year, the cost of carry is 8% and the volatility is 20% per year.

Program Text

Program Text (s30safe.f90)

Program Data

Program Data (s30safe.d)

Program Results

Program Results (s30safe.r)