Well worth a read for those that have the time

http://www.edwardothorp.com/id10.html

http://www.edwardothorp.com/id9.html

I have expressed my views on ability to beat the markets and efficient markets - here is one person that had the edge. He "discovered" Black Scholes, found a way to win at Blackjack and ran several hedge funds

What, exactly did Thorpe have to do with Black-Scholes? I had always thought that the "other guy" was called Merton.

I've not read it in full, but was discouraged by the first sentence:

"We present here a method by which investors can consistently make large profits. We have used this method in the market for the past five years to earn 25% a year."

I couldn't imagine a better indicator that "snake oil follows" - The similarity right down to time-scale has ominous overtones of LTCM... It seems incredible that, if the "system" is viable that it would be shared - unless, of course, the system is extremely flawed; about to collapse - and there's a need to offload positions... though, maybe, I'm being a bit too cynical.

I'm also surprised that you tout "Black Scholes" association in a positive light - given your having pointed me at Taleb... I've finished both his books now - and, by far, the "Black Swan" was the more interesting of the two. I wholeheartedly agree with his (maybe it is mainstream - but I think he explains it reasonably well) idea that Gaussian methods are simply inappropriate for the vast majority of circumstances in which they are applied... though I feel short-changed at where he stopped. Some physical processes, he agrees, do appear to be normally distributed - but we don't get any hint at a strategy to establish which are and which are not. I also think he could have gone further with respect to distributions related to Gaussian - such as log-normal distributions that are now assumed to be a good model for random events such as lightening. I wondered all the time if what we're seeing might not be modelled by the sum of two (or several) normal (or normal related) distributions. There also seems to be a distinct undercurrent throughout the book taking a gybe at "Black Scholes" - while my own intuition is that these 'pure' techniques are dangerous in the hands of those who make real decisions based upon the numbers generated... it is hard not to appreciate their elegance... which I think Taleb tries to achieve. Don't get me wrong, I'm still very sceptical about Black Scholles - even in the absence of a "black swan" - principally because I'm uneasy that it is safe to "take limits" (i.e. to progress from a discrete to a continuous model) where the presence of derivatives as financial instruments might move the prices of the underlying entities. I think that, while the error margin might be small (per step) in a discrete environment - the error might become arbitrarily large as the time-delta tends to zero. I have no formal version of this - it is just a hunch... but, combined with the idea that there might be an orthogonal, say, log-normal distribution that models the probability that reality rejects the basis for the mainstream model... that models a "blow up" in Taleb's terms... maybe this would simultaneously resolve the academic conflict and undermine the usefulness of the model to practitioners?

"I couldn't imagine a better indicator that "snake oil follows" - The similarity right down to time-scale has ominous overtones of LTCM... It seems incredible that, if the "system" is viable that it would be shared - unless, of course, the system is extremely flawed; about to collapse - and there's a need to offload positions... though, maybe, I'm being a bit too cynical."

You need to read it in full. This was a system from a long time ago when markets were less efficient. As he said, returns got less as time moved on

"What, exactly did Thorpe have to do with Black-Scholes? I had always thought that the "other guy" was called Merton."

http://www.wilmottwiki.com/wiki/index.php/Thorp,_Edward

"In the late 1960s Ed Thorp worked with Sheen Kassouf on the pricing of convertibles bonds and together they invented delta hedging and discovered what are now known as the Black-Scholes formulae. Thorp used this work to start a convertible arbitrage hedge fund. "

"I'm also surprised that you tout "Black Scholes" association in a positive light -"

http://www.wilmott.com/blogs/paul/index.cf...oles-and-Merton

Look up volatility smile and 1987 crash

"but I think he explains it reasonably well) idea that Gaussian methods are simply inappropriate for the vast majority of circumstances in which they are applied... though I feel short-changed at where he stopped"

As you say, it is easy to criticise, harder to propose viable solution - there are lots of things you can do with random walk such as random jumps to give you fat tails

"I also think he could have gone further with respect to distributions related to Gaussian - such as log-normal distributions that are now assumed to be a good model for random events such as lightening"

http://www.puc-rio.br/marco.ind/stochast.html

Gaussian is log normal - did you mean something else?

"principally because I'm uneasy that it is safe to "take limits" (i.e. to progress from a discrete to a continuous model) where the presence of derivatives as financial instruments might move the prices of the underlying entities"

Monte Carlo (one way of valuing CDO) is not continuous.

I'll add it to my reading list... though I remain highly sceptical about it.



Which surprises me that an entirely different bunch are credited with the discovery. The idea that a gambler might have actually done most of the groundwork seems intuitively plausible to me... since such a perspective safely allows one to ignore feedback effects... the model does not affect the probabilities of future 'random' events.



I've read about it - and it made sense when I read it - though I couldn't explain it at a dinner party any more... but, when someone else does, it sounds remarkably familiar.



My intuition is that "random jumps" are a horrible hack and a dead-end.



Gaussian is "normal" - whereas "log normal" is where the logarithm is Gaussian.



I'm familiar with the Monte Carlo method... but I reject that it can be used to evaluate the model I suggested.

This might be too adventurous (my mathematically trained friends go spare when I say things like this - and my non-mathematically trained friends find the mathematics too complex)... the real problem of course, is that I can only clearly express a small portion of what I want to describe sufficiently formally for the mathematicians - yet the non-mathematicians don't see how my idea differs from orthodoxy.

Say we have a Normal distribution for return on an investment (adjusted for the risk free rate of money) - and that, for a single investment, if the area to the right of 0 is larger than the area to the left then we've got a buy signal (for a single unit) - to the left, a sell. This is very clean and elegant, but it assumes only one market participant and only one model... and that investment is risk neutral.

Now, if you can, switch domains - and think of sound... and think of this neat graph as analogous of a sine wave. Imagine a 'perfect' instrument that makes a clean sound - which, in the frequency domain, say, closely approximates the normal distribution graph. Next imagine that this is not the only noise - imagine that other notes are being played from independent sources simultaneously - all over the world. Some will be so distant as to be irrelevant - but some, close by, may either re-enforce the expected frequency ranges - or, others might shift the frequency - for example - by playing a harmonic.

Next, if we return from that vague and abstract distraction, and think about the normal distribution, it seems unlikely that a single normal distribution accurately reflects the likely risks. There are likely millions of normal or normal-related probability distributions driven by alternative models... maybe models we have not yet perceived - maybe so complex that they defy any model. Without feedback, approximations are useful - with feedback, the errors grow over time - and, if the model is not updated frequently (and intelligently) the errors (noise), will quickly come to drown out the signal (behaviour matching the original model.) While a simple Gaussian (related) model might permit a short-term predictive advantage - that advantage necessarily diminishes over time. If one were to extend the model with multiple Gaussian (related) distributions - then the predictive power would increase - but so would the potential profits from applying the model - since more of the risks would be accounted. The most lucrative models are necessarily the most flawed... where time will be the ultimate judge.

I think the bottom line is this: there is no free lunch. The best one can hope to do is to identify demographic groups whom you can exploit for a period - until you either loose interest - or where you don't care if they retaliate in whatever way would be most devastating.

"My intuition is that "random jumps" are a horrible hack and a dead-end."

Agreed

"Gaussian is "normal" - whereas "log normal" is where the logarithm is Gaussian."

http://en.wikipedia.org/wiki/Black%E2%80%93Scholes


The price of the underlying instrument St follows a geometric Brownian motion with constant drift μ and volatility σ, and the price changes are log-normally distributed:

Are we talking about different things?

I was mainly being pedantic - in insisting that Gausian is not equivalent to log-normal... though, obviously, closely related.

However, in spite of that pedantry, I was utterly vague myself... I hadn't been specifically thinking about price-changes in black-scholles... and now, I'm afraid, I'm going to get even more vague.

When I consider social systems, the one thing that seems to come-up over-and-over again is the difference between additive and multiplicative quantities. Examples include:

* the classic stand-off between trade-unions and management - where the former think additively in terms of cumulative wages - and the latter think geometrically in terms of return on capital.
* the extensive legislation regarding APR - because the public are deemed incapable of grasping continuous compounding.
* The common error of estimating emotionally that a 10% gain followed by a 10% loss is equivalent to no gain.
* The frequent mistake made by children when initially introduced to fractions that (x+a)/(y+a) is somehow equivalent to x/y - because both the numerator and denominator has increased.
* Arguments that technology progresses exponentially - when, in fact, progress is linear (or worse) though measured with an exponential metric.

The public today are mainly ignorant of logarithms - even the elder generation seem to have forgotten the point and can only mechanically employ logs to avoid using a calculator... without grasping their structural implication to the world around them. I'd argue that while everyone says that they understand multiplication, I think we only "understand" it academically - I think our subjective response is almost always additive... and that this may have a genetic basis. I think this is important because when we are presented with series data (either explicitly in the context of analytical endeavour or implicitly in the context of our everyday experiences) it is far from clear if effects are multiplicative or additive... or, as will be the case in most circumstances, part and part. I also think that we can go a step further - and think in terms of higher orders - linear/polynomial; exponential; double exponential - etc.

If we jump back towards probability, it seems obvious to me that higher order terms will not typically be exposed by empirical analysis... and the relative dominance of the high and low order terms will, likely, change over time. The problem is, of course, that these higher order terms really are important... or, at least, can't be safely ignored. If we assume ordinary price-moves to be log-normal (as for BS) then maybe we need to consider extraordinary price moves (defaults, say) as being, perhaps, log-log normal.

I hope that anyone reading the above can do so first while wearing a woolly non-mathematician hat... as my ramblings (while, I think, pointing towards my intuitions) are far from rigorous, formal, prescriptive or comprehensive. Please bring all your intuition along for the ride - and, maybe, you'll wonder what I wondered.

"I was mainly being pedantic - in insisting that Gausian is not equivalent to log-normal... though, obviously, closely related.

However, in spite of that pedantry, I was utterly vague myself... I hadn't been specifically thinking about price-changes in black-scholles... and now, I'm afraid, I'm going to get even more vague."

OK - I was talking about the derivation of Black Scholes (there are over 10 ways) and the underlying lognormal random walk.
For the CQF coursework we did some option stuff including stochastic volatility (an alternative to poisson process jumps) and valuing different types of options (European, Asian, lookback etc).

Wilmott's book is worth a read

http://www.amazon.co.uk/Paul-Wilmott-Quant...6395&sr=8-2

At £99, it would have to be more than just "a read"

I have, however, read John Hull's book (the one recommended to me below Willmott's) which I found interesting - if a bit of a steep learning curve in early 2007. I'd probably learn more if I re-read the book I already have. Black Scholes is introduced by Hull, though - as I remember it - he only walks the reader through one derivation. Hull also covers option pricing - though (as I remember) this is restricted to American/European... I don't even know what an Asian/Lookback option is.

I've been extremely interested in everything related to derivatives since I first encountered them... but I am wary that I don't spend too much time chasing one specific detail... I suspect that rather than the mechanical minutia of the calculations, the problems are rather with the base assumptions. For example, I find the "efficient market" hypothesis extraordinarily dubious at best... it doesn't gel with the empiric evidence. For example, I am far more willing to believe that prices are influenced to a greater extent by corrupt/stupid behaviour than by an objective analysis of industry or commerce; supply or demand. Let's face it - the dumb people massively outnumber those who think... and this can only be exacerbated when participants are rewarded not by their ultimate success - but based upon estimates arising from how closely their choices correlate with the herd over the short term.