NAG Toolbox: nag_specfun_opt_binary_con_price (s30ca)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{calput}$ – string (length ≥ 1)

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:     $\mathrm{x}\left(\mathbf{m}\right)$ – double array

$\mathbf{x}\left(i\right)$ 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 $z=\mathbf{x02am}\left(\right)$, the safe range parameter, for $\mathit{i}=1,2,\dots ,\mathbf{m}$.

3:     $\mathrm{s}$ – double scalar

$S$, the price of the underlying asset.

Constraint: $\mathbf{s}\ge z\text{ and }\mathbf{s}\le 1.0/z$, where $z=\mathbf{x02am}\left(\right)$, the safe range parameter.

4:     $\mathrm{k}$ – double scalar

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: $\mathbf{k}\ge 0.0$.

5:     $\mathrm{t}\left(\mathbf{n}\right)$ – double array

$\mathbf{t}\left(i\right)$ 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 $z=\mathbf{x02am}\left(\right)$, the safe range parameter, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

6:     $\mathrm{sigma}$ – double scalar

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

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

7:     $\mathrm{r}$ – double scalar

$r$, the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as 0.05.

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

8:     $\mathrm{q}$ – double scalar

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

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

Optional Input Parameters

1:     $\mathrm{m}$ – int64int32nag_int scalar

Default: the dimension of the array x.

The number of strike prices to be used.

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

2:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the dimension of the array t.

The number of times to expiry to be used.

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

Output Parameters

1:     $\mathrm{p}\left(\mathit{ldp},\mathbf{n}\right)$ – double array

$\mathit{ldp}=\mathbf{m}$.

$\mathbf{p}\left(i,j\right)$ contains $P_{ij}$, the option price evaluated for the strike price ${\mathbf{x}}_i$ at expiry ${\mathbf{t}}_j$ for $i=1,2,\dots ,\mathbf{m}$ and $j=1,2,\dots ,\mathbf{n}$.

2:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry, $\mathbf{calput}=\_$ was an illegal value.

   $\mathbf{ifail}=2$

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

   $\mathbf{ifail}=3$

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

   $\mathbf{ifail}=4$

Constraint: $\mathbf{x}\left(i\right)\ge \_$ and $\mathbf{x}\left(i\right)\le \_$.

   $\mathbf{ifail}=5$

Constraint: $\mathbf{s}\ge \_$ and $\mathbf{s}\le \_$.

   $\mathbf{ifail}=6$

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

   $\mathbf{ifail}=7$

Constraint: $\mathbf{t}\left(i\right)\ge \_$.

   $\mathbf{ifail}=8$

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

   $\mathbf{ifail}=9$

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

   $\mathbf{ifail}=10$

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

   $\mathbf{ifail}=12$

Constraint: $\mathit{ldp}\ge \mathbf{m}$.

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: s30ca_example

function s30ca_example


fprintf('s30ca example results\n\n');

put = 'P';
s = 100.0;
k = 10.0;
sigma = 0.35;
r = 0.06;
q = 0.0;
x = [80.0];
t = [0.75];
[p, ifail] = s30ca( ...
                    put, x, s, k, t, sigma, r, q);


fprintf('\nBinary (Digital): Cash-or-Nothing\n European Put :\n');
fprintf('  Spot       =   %9.4f\n', s);
fprintf('  Payout     =   %9.4f\n', k);
fprintf('  Volatility =   %9.4f\n', sigma);
fprintf('  Rate       =   %9.4f\n', r);
fprintf('  Dividend   =   %9.4f\n\n', q);

fprintf('   Strike    Expiry   Option Price\n');
for i=1:1
  for j=1:1
    fprintf('%9.4f %9.4f %9.4f\n', x(i), t(j), p(i,j));
  end
end

s30ca example results


Binary (Digital): Cash-or-Nothing
 European Put :
  Spot       =    100.0000
  Payout     =     10.0000
  Volatility =      0.3500
  Rate       =      0.0600
  Dividend   =      0.0000

   Strike    Expiry   Option Price
  80.0000    0.7500    2.2155