The function may be called by the names: s30sac, nag_specfun_opt_asian_geom_price or nag_asian_geom_price.
3Description
s30sac computes the price of an Asian geometric continuous average-rate option for constant volatility, , risk-free rate, , and cost of carry, (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 , .
4References
Kemna A and Vorst A (1990) A pricing method for options based on average asset values Journal of Banking and Finance14 113–129
5Arguments
1: – Nag_OrderTypeInput
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_CallPutInput
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: – IntegerInput
On entry: the number of strike prices to be used.
Constraint:
.
4: – IntegerInput
On entry: the number of times to expiry to be used.
Constraint:
.
5: – const doubleInput
On entry: must contain
, the th strike price, for .
Constraint:
, where , the safe range parameter, for .
6: – doubleInput
On entry: , the price of the underlying asset.
Constraint:
, where , the safe range parameter.
7: – const doubleInput
On entry: must contain
, the th time, in years, to expiry, for .
Constraint:
, where , the safe range parameter, for .
8: – doubleInput
On entry: , the volatility of the underlying asset. Note that a rate of 15% should be entered as .
Constraint:
.
9: – doubleInput
On entry: , the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as .
Constraint:
.
10: – doubleInput
On entry: , the annual cost of carry rate. Note that a rate of 8% should be entered as .
11: – doubleOutput
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).
6Error 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: and .
On entry, .
Constraint: .
NE_REAL_ARRAY
On entry, .
Constraint: .
On entry, .
Constraint: and .
7Accuracy
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 s15abcands15adc). An accuracy close to machine precision can generally be expected.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s30sac 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.
9Further Comments
None.
10Example
This example computes the price of an Asian geometric continuous average-rate put with a time to expiry of months, a stock price of and a strike price of . The risk-free interest rate is per year, the cost of carry is and the volatility is per year.