BLKSHCLPRC Function

Calculates call prices for European options on stocks, based on the Black-Scholes model.

Category:

Financial

Syntax

BLKSHCLPRC(E, t, S, r, sigma)

Required Arguments

E

is a nonmissing, positive value that specifies the exercise price.

Requirement

Specify E and S in the same units.

t

is a nonmissing value that specifies the time to maturity.

S

is a nonmissing, positive value that specifies the share price.

Requirement

Specify S and E in the same units.

r

is a nonmissing, positive fraction that specifies the risk-free interest rate for period t.

Requirement

Specify a value for r for the same time period as the unit of t.

sigma

is a nonmissing, positive fraction that specifies the volatility of the underlying asset.

Requirement

Specify a value for sigma for the same time period as the unit of t.

Details

The BLKSHCLPRC function calculates the call prices for European options on stocks, based on the Black-Scholes model. The function is based on the following relationship:

\begin{matrix} C A L L = S N (d_{1}) - E N (d_{2}) ε^{- r t} \end{matrix}

Arguments

is a nonmissing, positive value that specifies the share price.

specifies the cumulative normal density function.

is a nonmissing, positive value that specifies the exercise price of the option.

\begin{matrix} d_{1} = & \frac{(\ln (\frac{S}{E}) + (r + \frac{σ^{2}}{2}) t)}{σ \sqrt[]{t}} \\ d_{2} = & d_{1} - σ \sqrt[]{t} \end{matrix}

The following arguments apply to the preceding equation:

specifies the time to expiration.

specifies the risk-free interest rate for period t.

σ

specifies the volatility (the square root of the variance).

σ^{2}

specifies the variance of the rate of return.

For the special case of t=0, the following equation is true:

\begin{matrix} C A L L = \max ((S - E), 0) \end{matrix}

For information about the basics of pricing, see Using Pricing Functions .

Comparisons

The BLKSHCLPRC function calculates the call prices for European options on stocks, based on the Black-Scholes model. The BLKSHPTPRC function calculates the put prices for European options on stocks, based on the Black-Scholes model. These functions return a scalar value.

Example

The following SAS statements produce these results.

SAS Statement	Result
	----+----1----+-—-2--
a=blkshclprc(1000, .5, 950, 4, 2); put a;	831.05008469
b=blkshclprc(850, 2.5, 125, 3, 1); put b;	124.53035232
c=blkshclprc(7500, .9, 950, 3, 2); put c;	719.40891129
d=blkshclprc(5000, -.5, 237, 3, 2); put d;	0

BLKSHCLPRC Function

Syntax

Required Arguments

E

t

S

r

sigma

Details

Comparisons

Example

See Also