NAG Library Routine Document

S30CAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     CALPUT – CHARACTER(1)Input

On entry: determines whether the option is a call or a put.

$\mathbf{CALPUT}=\text{'C'}$

A call. The holder has a right to buy.

$\mathbf{CALPUT}=\text{'P'}$

A put. The holder has a right to sell.

Constraint: $\mathbf{CALPUT}=\text{'C'}$ or $\text{'P'}$.

2:     M – INTEGERInput

On entry: the number of strike prices to be used.

Constraint: $\mathbf{M}\ge 1$.

3:     N – INTEGERInput

On entry: the number of times to expiry to be used.

Constraint: $\mathbf{N}\ge 1$.

4:     X(M) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{X}\left(i\right)$ must contain $X_{\mathit{i}}$, the $\mathit{i}$th strike price, for $\mathit{i}=1,2,\dots ,\mathbf{M}$.

Constraint: $\mathbf{X}\left(\mathit{i}\right)\ge z\text{ and }\mathbf{X}\left(\mathit{i}\right)\le 1/z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter, for $\mathit{i}=1,2,\dots ,\mathbf{M}$.

5:     S – REAL (KIND=nag_wp)Input

On entry: $S$, the price of the underlying asset.

Constraint: $\mathbf{S}\ge z\text{ and }\mathbf{S}\le 1.0/z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter.

6:     K – REAL (KIND=nag_wp)Input

On entry: the amount, $K$, to be paid at expiration if the option is in-the-money, i.e., if $\mathbf{S}>\mathbf{X}\left(\mathit{i}\right)$ when $\mathbf{CALPUT}=\text{'C'}$, or if $\mathbf{S}<\mathbf{X}\left(\mathit{i}\right)$ when $\mathbf{CALPUT}=\text{'P'}$, for $\mathit{i}=1,2,\dots ,m$.

Constraint: $\mathbf{K}\ge 0.0$.

7:     T(N) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{T}\left(i\right)$ must contain $T_{\mathit{i}}$, the $\mathit{i}$th time, in years, to expiry, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

Constraint: $\mathbf{T}\left(\mathit{i}\right)\ge z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

8:     SIGMA – REAL (KIND=nag_wp)Input

On entry: $\sigma$, the volatility of the underlying asset. Note that a rate of 15% should be entered as 0.15.

Constraint: $\mathbf{SIGMA}>0.0$.

9:     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: $\mathbf{R}\ge 0.0$.

10:   Q – REAL (KIND=nag_wp)Input

On entry: $q$, the annual continuous yield rate. Note that a rate of 8% should be entered as 0.08.

Constraint: $\mathbf{Q}\ge 0.0$.

11:   P(LDP,N) – REAL (KIND=nag_wp) arrayOutput

On exit: the leading $\mathbf{M}\times \mathbf{N}$ part of the array P contains the computed option prices.

12:   LDP – INTEGERInput

On entry: the first dimension of the array P as declared in the (sub)program from which S30CAF is called.

Constraint: $\mathbf{LDP}\ge \mathbf{M}$.

13:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry, $\mathbf{CALPUT}\ne \text{'C'}$ or $\text{'P'}$.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{M}\le 0$.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{N}\le 0$.

$\mathbf{IFAIL}=4$

On entry, $\mathbf{X}\left(\mathit{i}\right)<z$ or $\mathbf{X}\left(\mathit{i}\right)>1/z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter.

$\mathbf{IFAIL}=5$

On entry, $\mathbf{S}<z$ or $\mathbf{S}>1.0/z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter.

$\mathbf{IFAIL}=6$

On entry, $\mathbf{K}<0.0$.

$\mathbf{IFAIL}=7$

On entry, $\mathbf{T}\left(\mathit{i}\right)<z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter.

$\mathbf{IFAIL}=8$

On entry, $\mathbf{SIGMA}\le 0.0$.

$\mathbf{IFAIL}=9$

On entry, $\mathbf{R}<0.0$.

$\mathbf{IFAIL}=10$

On entry, $\mathbf{Q}<0.0$.

$\mathbf{IFAIL}=12$

On entry, $\mathbf{LDP}<\mathbf{M}$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (s30cafe.f90)

9.2  Program Data

Program Data (s30cafe.d)

9.3  Program Results

Program Results (s30cafe.r)