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Untersuchte Arbeit:
Seite: 75, Zeilen: 13-20
Quelle: Brealey Myers 1981
Seite(n): 439, Zeilen: 29 ff.
The exact Black and Scholes (1973) formula is expressed below:
c = Present Value of a call option = SN (d1) – Xe-rft N(d2)
where:
d1 = [log (S/X) + rf t + σ2t/2] * 1/σ√t
d2 = [log (S/X) + rf t - σ2t/2] * 1/σ√t
N(d)...cumulative normal probability density function

N(d) is the probability that a normally distributed random variable will be less than or equal to d.

Black and Scholes show that there is only one call price formula that meets that requirement. This unpleasant-looking formula is:


Present value of call option = PN(d1) — EXe-rftN(d2)

where

N(d) = cumulative normal probability density function15

EX = exercise price of option

t = time to exercise date


15 That is, N(d) is the probability that a normally distributed random variable will be less than or equal to d.

[page 430]

P = price of stock now

σ2 = variance per period of (continuously compounded) rate of return on the stock

rf = (continuously compounded) risk-free rate of interest

Anmerkungen

UNFERTIG

[Anm. evtl. so oder so ähnlich sinnvoll?]

The source is given, but only in a footnote text for the one sentence in the main text that follows this fragment.

The comparison shows that passages like the listed ones cannot be found in Black and Scholes (1973):

  • "is the probability that a normally distributed random variable"
  • "will be less than or equal to".
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