Wilmott books

So, as I am a geek with a natural sciences background and have a predisposition for thinking about things too much, I decided to buy this Wilmott book Wilmott introduces Quant to get a sense of what the quant world does and more importantly for me, get an understanding of how it models.

I have two reasons for this:

a) Validate what I am doing as a discretionary trader to identify whether it is a long term and sustainable method of trading.

b) Identify other areas associated with using models in an imperfect world that throw up trading opportunities.

Just out of curiosity, has anybody on these boards had any experience of trying to do something like this or is this so far off piste for most posters on here that they probably wouldn't understand the books content?

Any thoughts welcomed.

I work with a professor friend on developing neural net driven trading systems. He's very into the quant side of the markets.

I can see just from reading the first few chapters, getting some of my (rusty) maths back in shape and digesting some basics from it that there are many opportunities to trade using discretion because:

a) Random walk is used as a basis for modelling, although Wilmott also concurs that he wouldn't swear it to be true. I think it's a bit more predictable in some behavioral attributes.

b) There are an infinite amount of games that can be played in the market and really you are looking for counter-parties to those games that either play the game badly or don't have to worry about running out of money.

I can feel I am only just scratching the surface but it is fascinating, well at least for me.

When you say "Random Walk" are you referring to mean-reversion?

Rhody Trader said:

When you say "Random Walk" are you referring to mean-reversion?

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No, I really mean random walk. It's a model of the price discovery process which basically assume price discovery is random. This process then has a probability distribution which is normally distributed which leads to Mean Reversion behaviour.

That's what I currently understand.

Ummm...Didn't you just say mean reversion behavior.

Basically you have two types of approaches used in systematic processes - and really in trading overall. One is the mean reversion approach which expects moves to reverse back to the thick part of the return distribution. The other is the momentum/trend-following approach which expects moves to continue, reflecting the fact that market returns are not random.

I have two issues with Random Walk. The first is that it's totally unprovable. You cannot prove randomness, you can only disprove it. The second is that folks think that because they connot predict the market it is random, which is not an equivalency which can necessarily be made.

robster970 said:

So, as I am a geek with a natural sciences background and have a predisposition for thinking about things too much, I decided to buy this Wilmott book Wilmott introduces Quant to get a sense of what the quant world does and more importantly for me, get an understanding of how it models.

I have two reasons for this:

a) Validate what I am doing as a discretionary trader to identify whether it is a long term and sustainable method of trading.

b) Identify other areas associated with using models in an imperfect world that throw up trading opportunities.

Just out of curiosity, has anybody on these boards had any experience of trying to do something like this or is this so far off piste for most posters on here that they probably wouldn't understand the books content?

Any thoughts welcomed.

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I would have thought it's aimed at pricing and hedging / financial engineering, rather than discretionary trading. I've looked at his Financial Derivatives for Science Students (or something like that) which you'd probably enjoy.

I was gonna pick that book up but was swayed by a review that said it was sh*te. Might have a go.

LOL John - I think you need to spend $24 to buy the book! Wilmott can explain it better than me.

I agree John - I think this is one of the problem with using Random Walk as your process to model unpredictable nature of price movement. If this was the case, why can I pick out the reversal that usually comes after an opening swing on ES with such regularity? Is it because I can sense where the mean is or is it because I recognise when buyers/sellers are drying up at the top of the opening swing?

Ultimately, PhD's and computational horsepower will probably get you so far but ultimately they are models and not reality.

Joey25 said:

I would have thought it's aimed at pricing and hedging / financial engineering, rather than discretionary trading. I've looked at his Financial Derivatives for Science Students (or something like that) which you'd probably enjoy.

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It's the modelling I am interested in. I might learn something from it that may improve my trading.

scose-no-doubt said:

I was gonna pick that book up but was swayed by a review that said it was sh*te. Might have a go.

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The Mathematics of Financial Derivatives: A Student Introduction: Amazon.co.uk: Paul Wilmott, Sam Howison, Jeff Dewynne: 9780521497893: Books

This is the one. All you need is some knowledge of ordinary differential equations. Has pseudo-code for the numerical parts.

robster970 said:

No, I really mean random walk. It's a model of the price discovery process which basically assume price discovery is random. This process then has a probability distribution which is normally distributed which leads to Mean Reversion behaviour.

That's what I currently understand.

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A random walk itself does not lead to mean reversion. You could choose to model a random walk specifically with mean reversion. Is that what it's doing? Tossing a coin and adding 1 for heads and -1 for tails will give you a random walk. The mean might be zero, but if you get 10 heads in a row, and you're on +10, there's no reason at all why it would revert back to 0.

I don't think many doubt the randomness in the markets. I think it's just that they doubt it is 50-50.

In terms of how useful these models are...well I'd say they could be very useful if done correctly. But that most of what I've read in this field uses unrealistic models that are a sort of hangover from Black-Scholes pricing, which has done it's job for option pricing nicely, but is not necessarily going to help a great deal for your average intraday trader on the ES or currencies. I quite like some of the ideas in the behavioural finance area, but I haven't seen a truly convincing model for it yet.

What I've never understood about the whole mean reversion thing is that to my understanding it applies to returns so why is a mean reversion in price expected after a move down? Also, what kind of sample are you using to look at the returns? A year? 10 years? Where's your starting point? Are massive fat tail occurrences like 09 to be included?

Shakone said:

A random walk itself does not lead to mean reversion. You could choose to model a random walk specifically with mean reversion. Is that what it's doing? Tossing a coin and adding 1 for heads and -1 for tails will give you a random walk. The mean might be zero, but if you get 10 heads in a row, and you're on +10, there's no reason at all why it would revert back to 0.

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So let's take you coin toss. We know coin tossing for a single event has a 50% probability of occurrence (0.5^1).

So 10 consecutive tosses would be 0.5^10 would be 0.00097 ( a little less than 0.1% probability of occurrence).

The probability distribution of N number of occurrences is Normally distributed. It is this probability distribution which gives it the mean reverting characteristic.

It will over a large enough sample tend back to 0 even if it did go to +10 unless it is a biased coin.

I'm not being pedantic here and it is probably down to my poor understanding but doesn't a Random Walk process for price discovery naturally possess a Probability Distribution Function which is Normally Distributed because of it's adherence to the Central Limit Theorem.

Shakone said:

In terms of how useful these models are...well I'd say they could be very useful if done correctly. But that most of what I've read in this field uses unrealistic models that are a sort of hangover from Black-Scholes pricing, which has done it's job for option pricing nicely, but is not necessarily going to help a great deal for your average intraday trader on the ES or currencies. I quite like some of the ideas in the behavioural finance area, but I haven't seen a truly convincing model for it yet.

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I can see the lack of realism just from reading Wilmott and I concur with you. I also read something from Andrew Lo about the Adaptive Market Hypothesis which sounded interesting too.

scose-no-doubt said:

What I've never understood about the whole mean reversion thing is that to my understanding it applies to returns so why is a mean reversion in price expected after a move down?

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Because it's an auction and perfect auctions demonstrate normally distributed price. After a low, there are no more sellers interested in selling at that price and buyers force price back up through laws of supply/demand.

robster970 said:

So let's take you coin toss. We know coin tossing for a single event has a 50% probability of occurrence (0.5^1).

So 10 consecutive tosses would be 0.5^10 would be 0.00097 ( a little less than 0.1% probability of occurrence).

The probability distribution of N number of occurrences is Normally distributed. It is this probability distribution which gives it the mean reverting characteristic.

It will over a large enough sample tend back to 0 even if it did go to +10 unless it is a biased coin.

I'm not being pedantic here and it is probably down to my poor understanding but doesn't a Random Walk process for price discovery naturally possess a Probability Distribution Function which is Normally Distributed because of it's adherence to the Central Limit Theorem.



I can see the lack of realism just from reading Wilmott and I concur with you. I also read something from Andrew Lo about the Adaptive Market Hypothesis which sounded interesting too.

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No I don't consider that mean reverting. Mean-reverting implies there is something within the process that pushes its path back towards the mean.

I gave 10 for simplicity, but it doesn't really matter. They don't have to be consecutive. Consider the same game, that starts at +10, rather than 0. You add one for each coin toss that's heads, subtract for tails. What is the mean, given that you've started at 10? It's 10, right? Now a game that begins at 0, but which gets to +10 at some point (110 heads, 100 tails if you like )will not revert back towards 0. Why would it? It's just as likely from there to go up as go down. There's nothing pushing it back down towards 0.

Plot a bunch of these random walks, and the majority will be around 0, but there will be some that just trended up a long way, and some that just trended down. The sum of them will give you a mean of about 0 (as it should), but no individual path is mean-reverting in that.

Shakone said:

Now a game that begins at 0, but which gets to +10 at some point (110 heads, 100 tails if you like )will not revert back towards 0. Why would it? It's just as likely from there to go up as go down. There's nothing pushing it back down towards 0.

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I have to disagree with you Shake. It tends to it's starting point for this example.

So when it started at 10 - it will revert to 10.

When it started at 0 - it will revert to 0.

The 'pushing' is to do with how the probability distribution lies for the random walk process. I don't think we're going to agree on this dude

Be useful if Martinghoul could answer this not from the PoV of being right or wrong but purely to stop me feeling like I have sh1t muddled up.

Here's a more eloquent description lifted from the internet. Obviously I am not vouching completely for it's correctness, what with it being the internet:

"A mathematical description of this generic concept: "Reversion to the Mean" is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far. In other words, an extreme event is likely to be followed by a less extreme event. Although this phenomenon appears to violate the definition of independent events, it simply reflects the fact that the probability function P(x) of any random variable x, by definition, is nonnegative over every interval and integrates to one over the interval . Thus, as you move away from the mean, the proportion of the distribution that lies closer to the mean than you do increases continuously"

http://www.learner.org/courses/mathilluminated/units/7/textbook/06.php

robster970 said:

I have to disagree with you Shake. It tends to it's starting point for this example.

So when it started at 10 - it will revert to 10.

When it started at 0 - it will revert to 0.

The 'pushing' is to do with how the probability distribution lies for the random walk process. I don't think we're going to agree on this dude

Be useful if Martinghoul could answer this not from the PoV of being right or wrong but purely to stop me feeling like I have sh1t muddled up.

Here's a more eloquent description lifted from the internet. Obviously I am not vouching completely for it's correctness, what with it being the internet:

"A mathematical description of this generic concept: "Reversion to the Mean" is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far. In other words, an extreme event is likely to be followed by a less extreme event. Although this phenomenon appears to violate the definition of independent events, it simply reflects the fact that the probability function P(x) of any random variable x, by definition, is nonnegative over every interval and integrates to one over the interval . Thus, as you move away from the mean, the proportion of the distribution that lies closer to the mean than you do increases continuously"

Mathematics Illuminated | Unit 7 | 7.6 Central Limit Theorem

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You're missing the distinction between a path, and the sum of paths averaged. If you simulate paths with a particular mean, The sum of paths divided by number of paths will converge to the mean that's why it's the mean. A particular path can do whatever it likes, it's not mean reverting.

Example, the mean height of the population might be 5ft 10 at age 18. That doesn't mean that when you grow to 6ft 4 approaching that age, that you start shrinking towards the mean. If anything you're more likely to grow some more. The individual (path) is not mean-reverting. Probably not the best example but hopefully you get what I mean.

If you are at +10, the probability of going up is the same as going down> To use your quote "the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far."This quote is saying that if you are far above 0, then there should be a higher probability of it moving down than up. But you know it's 50-50 here, so it's not mean-reverting according to your quote.

It doesn't really matter in the big scheme of things, it's just a term after all. But as you agreed, if you're at +10, from then on the mean is +10, if you're at +50, the mean would be +50. Many of the paths that start at 0, will reach +10, +50 and so on. They don't mean revert to 0.

Shake - I am talking about a single path here. I'm just doing family stuff and will try and draw something up later to explain my madness.