[REBOL] FINANCE CALCULATIONS: BLACK-SCHOLES EQUATION

From: lcdr::licholai::msc::navy::mil at: 3-Dec-2001 15:38

Hello,

For anyone interested in calculating theoretical option prices using REBOL.
Below is a script for evaluating the Black-Scholes equation.  The script
should be fairly easy to use and understand, any comments or suggestions are
welcome.

	Matt

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REBOL [
	Title: "Black Scholes Option Price"
	Date: 11-Nov-2001
	Author: "Matt Licholai"
	Email: [M--S--Licholai--ieee--org]
	File: %black-scholes.r
	Rights: "(C)Matt Licholai 2001 "
	Version: 0.1.1
	History: [0.1 [{Initial version using parens and multiple assignment
                   lines for clarity}]
		0.1.1 [{Changed assignments of constants to use set block
                syntax sugar}]
	]
	Purpose: {Provide a Rebol function for computing the Black-Scholes
(1973) formula
		for determining an European style Option Price.}
	Comment: {Written for clarity and following Espen Gaarder Haug's
              Black-Scholes notation. See
              http://home.online.no/~espehaug/SayBlackScholes.html
              for other interesting versions.}
	Usage: { black-scholes/put $42.0 $40.0 .5 .1 .2
	  to compute the put price of an option where the strike is $40
	  the current underlying is at $42 there are 6 months till
        expiration, the risk free interest rate is 10% per annum
        and the volatility of the underlying is 20% per annum.}
	Language: 'English
]

cum-normal-dist: func [
	{Calculate the cumulative normal distribution using a fifth order
polynomial approximation.}
	x [number!]
	/local
	K L a a1 a2 a3 a4 a5 w1 w
][
	L: abs x

	set [a a1 a2 a3 a4 a5] [0.2316419 0.31938153 (- 0.356563782)
1.781477937 (- 1.821255978) 1.330274429]

	K: 1 / (1 + (a * L))

	w1: (K * a1) + (a2 * (K ** 2)) + (a3 * (K ** 3)) + (a4 * (K ** 4)) +
(a5 * (K ** 5))
	w: 1 - ((w1 / square-root (2 * pi)) * exp (- (L * L) / 2))

	if negative? x [return 1 - w]
	return w
]

black-scholes: func [
	{Calculate the Black Scholes (1973) stock option pricing formula}
	s [money!] "actual stock price"
	x [money!] "strike price"
	t [number!] "years to maturity"
	r [number!] "risk free interest rate"
	v [number!] "volatility"
	/call "call option (default)"
	/put "put option"
	/local
	d1 d2
][
	d1: (log-e (s / x) + ((r + ((v ** 2) / 2)) * T)) / ( v * square-root
t)
	d2: d1 - ( v * square-root t)

	either (not put) [
		(s * cum-normal-dist d1) - ((x * exp (- r * t)) *
cum-normal-dist d2)
	][
		((x * exp (- r * t)) * cum-normal-dist negate d2) - (s *
cum-normal-dist - d1)
	]
]

-- Binary/unsupported file stripped by Listar --
-- Type: application/octet-stream
-- File: black-scholes.r

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