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I am preparing a QuantFinance lecture and I am looking for the easiest and most accessible derivation of the Black-Scholes formula (NB: the actual formula, not the differential equation).

My favorite at the moment is
Intuitive Proof of Black-Scholes Formula Based on Arbitrage and Properties of Lognormal Distribution by Alexei Krouglov
which uses the truncated or partial lognormal distribution.

I would love to see derivations which are even easier - Thank you!

The course is for beginners. It is business administration, so the math level is undergraduate.

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It would be useful to known the kind of attendance you'll be facing. Beginners? Mathematicians? Young / older... – SRKX Jul 13 '11 at 12:18
Then, a binomial tree first with 3 steps example and then generalized to infinite steps model. The result gives BS and explains actually well what Phi(d1) and Phi(d2) are... – SRKX Jul 13 '11 at 18:57
Neil Chriss wrote an excellent book describing the options pricing formula. It's no longer in print and quite expensive on the secondary market, but worth a look at your local library – Ram Ahluwalia Jul 14 '11 at 3:50
@Quant Guy: Yeah, the title is "BS and beyond" - I am proud owner of one copy :-) – vonjd Jul 14 '11 at 5:26
@vonjd - yep that's the one! – Ram Ahluwalia Jul 15 '11 at 5:03
up vote 8 down vote accepted

You should look at Paul Willmott's Frequently Asked Questions In Quantitative Finance. He offers 12 (I think) ways of deriving BS and I think you'll find what you look for there.

The cool thing is that you really have many different approaches; one is the classic PDE, one is done using change of measure, one is done using binary trees, and so on....

Really worth it. And the book is very useful to introduce complicated topics to beginners.

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