Now we get to the guts of the whole program
- a function that can take all the relevant inputs, and return the theoretical
value of a call or put option.
The Black-Scholes option pricing model
is described in many online sources including wikipedia, and is also
given by Lawrence G. McMillan in his book "Options as a Strategic Investment".
The original Black-Scholes was only
for non-dividend paying stocks. We will be using a version that can
take dividend information if it exists and calculate APPROXIMATE option
values for dividend paying stocks.
If the stock does not pay a dividend
(if you enter 0.00 for the dividend when using the program), the original
Black-Scholes formula is used automatically and option prices calculated
by the program should closely match the actual market.
While the approximate values on options
on dividend paying stocks are usually quite accurate and match the actual
market within a few cents, there are times when the theoretical price
is some distance away from the actual market.
Always double-check the actual market
if you want to trade options on a dividend paying stock, especially
if the dividend is large, there is a long time to expiration, or the
ex-dividend date is very close.
Copy and paste the code below into the
OptionCalcs module, below the words "end function" of the changeexpiration()
function.
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Function optionvalue(ByVal stockprice As Single, ByVal strikeprice
As Single, ByVal timeremain As Single, ByVal interestrate As Single,
ByVal iv As Single, ByVal dividend As Single, ByVal opttype As
String) As Single
'Black-Scholes function with dividend approximation
'avoid one possible divide by zero error
If timeremain <= 0 Then
timeremain = 0.0000001
End If
Dim dividendyield As Single = dividend / stockprice
Dim a, b, c, d1, d2 As Single
a = Math.Log(stockprice / strikeprice)
b = ((interestrate - dividendyield) + 0.5 * iv ^ 2) * timeremain
c = iv * Math.Sqrt(timeremain)
d1 = (a + b) / c
d2 = d1 - iv * Math.Sqrt(timeremain)
If opttype.Contains("Call") Then
Return stockprice * Math.Exp(-dividendyield * timeremain) * NORMSDIST(d1)
- strikeprice * Math.Exp(-interestrate * timeremain) * NORMSDIST(d2)
Else
Return strikeprice * Math.Exp(-interestrate * timeremain) * NORMSDIST(-d2)
- stockprice * Math.Exp(-dividendyield * timeremain) * NORMSDIST(-d1)
End If
End Function
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Save your project.
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