# Bonus Lesson 13: The Binomial Method is Rubbish

Thanks for bearing with me through a dozen lessons. As a reward for your patience and tolerance I am going to give you a bonus lesson! And this bonus lesson is probably the easiest one for quants to implement immediately. The lesson is ... dump the binomial method!

I really like the binomial method. But only as a teaching aid. It is the easiest way to explain

1. hedging to eliminate risk

2. no arbitrage

3. risk neutrality.

I use it in the CQF to explain these important, and sometimes difficult to grasp, concepts.[1] But once the CQFers have understood these concepts they are instructed never to use the binomial model again, on pain of having their CQFs withdrawn!

Ok, I exaggerate a little. The binomial model was the first of what are now known as finite-difference methods. It dates back to 1911 and was the creation of Lewis Fry Richardson, all-round mathematician, sociologist, and poet.

A lot of great work has been done on the development of these numerical methods in the last century. The binomial model is finite differences with one hand tied behind its back, hopping on one leg, while blindfolded. So when I refer to the 'binomial method here what I am really criticizing is people s tendency to stick with the simplest, most naive finite-difference method, without venturing into more sophisticated territory, and without reading up on the more recent numerical-methods literature.

Why is the binomial method so ubiquitous? Again, habit is partly to blame. But also all those finance professors who know bugger all about numerical methods but who can just about draw a tree structure, they are the ones responsible. Once an academic writes his lecture notes then he is never going to change them. It s too much effort. And so generations of students are led to believe that the binomial method is state of the art when it is actually prehistoric.

# Summary

Question 1: What are the advantages of diversification among products, or even among mathematical models? Answer 1: No advantage to your pay whatsoever!

Question 2: If you add risk and curvature what do you get? Answer 2: Value!

Question 3: If you increase volatility what happens to the value of an option?

Answer 3: It depends on the option!

Question 4: If you use ten different volatility models to value an option and they all give you very similar values what can you say about volatility risk?

Answer 4: You may have a lot more than you think!

Question 5: One apple costs 50p, how much will 100 apples cost you?

How did you do in the quiz at the start? If you are new to quant finance you may have got some of the answers correct. If you have just come out of a Masters in Financial Engineering then you probably got most of them wrong. But if you're a quant or risk manager who likes to think for himself and is not happy with the classical 'results' of quantitative finance, then maybe you even got all of them right!

QF is interesting and challenging, not because the mathematics is complicated, it isn't, but because putting maths and trading and market imperfections and human nature together and trying to model all this, knowing all the while that it is probably futile, now that's fun!

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• [1] It's also instructive to also take a quick look at the trinomial version, because then you see immediately how difficult it is to hedge in practice.

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