Accessible Approaches to Deriving the Black–Scholes Formula

Summary

The document is a request for beginner-friendly ways to derive the Black–Scholes option pricing formula, aimed at an undergraduate business administration audience. The accepted response recommends consulting a quantitative finance reference that presents multiple derivations, rather than explaining any derivation in the discussion itself.

The methods named include the classic partial differential equation route, a change-of-measure approach, and a binary-tree construction. This range illustrates that the same pricing formula can be reached through different mathematical frameworks, potentially giving learners several ways to build intuition. The response offers no derivation, worked example, or comparison of the assumptions and difficulty of the approaches. Its educational value is therefore mainly as a pointer to a source for further study, and readers would need that source to learn the actual steps or assess which method best suits their background.

Key ideas

• Black–Scholes pricing can be derived through several mathematical approaches.
• The response names PDE, change-of-measure, and binary-tree methods.
• A reference that presents multiple derivations may help beginners compare explanations.
• The discussion itself does not provide the formula’s derivation or assess the methods in detail.

Tags

# Easiest and most accessible derivation of Black-Scholes formula


# Easiest and most accessible derivation of Black-Scholes formula












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!

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

## Answer by SRKX (score 8, accepted)

https://quant.stackexchange.com/a/1440

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.