Calculates call prices for European options on futures, based on the Black model.

Category: | Financial |

is a nonmissing, positive value that specifies exercise price.

Requirement | Specify E and F in the same units. |

is a nonmissing value that specifies time to maturity.

is a nonmissing, positive value that specifies future price.

Requirement | Specify F and E in the same units. |

is a nonmissing, positive fraction that specifies the risk-free interest rate between the present time and t.

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

is a nonmissing, positive fraction that specifies the volatility (the square root of the variance of r).

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

The BLACKCLPRC function
calculates call prices for European options on futures, based on the
Black model. The function is based on the following relationship:

$\begin{array}{c}CALL={\epsilon}^{-rt}(FN\left({d}_{1}\right)-EN\left({d}_{2}\right))\hfill \end{array}$

$\begin{array}{cc}{d}_{1}=\hfill & \frac{(\mathrm{ln}\left(\frac{F}{E}\right)+\left(\frac{{\sigma}^{2}}{2}\right)t)}{\sigma \sqrt[\phantom{\rule{0ex}{0ex}}]{t}}\hfill \\ {d}_{2}=\hfill & {d}_{1}-\sigma \sqrt[\phantom{\rule{0ex}{0ex}}]{t}\hfill \end{array}$

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

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