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James
NP High Priest

Total Posts: 2024
Joined: May 2004
 
Posted: 2005-04-29 11:38
Just being silly, I'll stop now.

Nonius, I cave on the data set.

To all casual readers: this is my, now tiresome, running joke on good self Johnny and Nonius. They are friends, nothing more, and my posts implying anything else are my juvinallia, and have never been ment to hurt anyone's feelings or reputation.

Sorry, Johnny.

Prior to the publication of the Black-Scholes model in 1973, the quest for a valuation formula that would describe option prices reflected one of the most elusive goals in financial economics. Though much work was done in the 1960s, many of the insights and techniques used to solve the problem were presented or anticipated at the beginning of the twentieth century by Louis Bachelier, an obscure French mathematician. These innovations include the first graphical representation of option pricing, a mathematical description of stock prices utilizing Brownian motion and anticipating the efficient market hypothesis, and the first formal option pricing formula.

Johnny
Founding Member

Total Posts: 4333
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Posted: 2005-04-29 11:39

Cool. Thanks James.

 


Johnny Jupiter Radiation Phynancial phorecasting by the stars for the stars

goldorak


Total Posts: 1091
Joined: Nov 2004
 
Posted: 2005-04-29 11:41
6000 points ? Nonius, if you implemented a stationary model, may I suggest people look for trading strategies on the first 1000 points and require their strategy to work on the next 5000 and have a positive P&L on every sub-sample of 200 points for example.

The simple fact we know there is stationarity in the signal is already a very important information ! We just miss the timeframe of the opportunity to adjust the numbers '1000', '5000' and '200'.

If you are not living on the edge you are taking up too much space.

James
NP High Priest

Total Posts: 2024
Joined: May 2004
 
Posted: 2005-04-29 11:42
I'll edit the posts if you like.

Prior to the publication of the Black-Scholes model in 1973, the quest for a valuation formula that would describe option prices reflected one of the most elusive goals in financial economics. Though much work was done in the 1960s, many of the insights and techniques used to solve the problem were presented or anticipated at the beginning of the twentieth century by Louis Bachelier, an obscure French mathematician. These innovations include the first graphical representation of option pricing, a mathematical description of stock prices utilizing Brownian motion and anticipating the efficient market hypothesis, and the first formal option pricing formula.

Nonius
Founding Member
Nonius Unbound
Total Posts: 12805
Joined: Mar 2004
 
Posted: 2005-04-29 12:07

it is dS=Mu(t)Sdt+SigSdZ

where Mu(t) is the y component of the Hénon Map see ref

with parameters

a 1.4
b 0.3

and with initial x=y=.1

where Sig=
27.18%
=3.5 times the average of about 65000 values of the y component of the henon map

so, while the price is not predictable, the distribution of prices is...constant vol, and predictable (but chaotic) drift.

Initial stock price is 21....and, I took a window way down in the series...


Chiral is Tyler Durden

Johnny
Founding Member

Total Posts: 4333
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Posted: 2005-04-29 12:35

I think I'm going to declare victory (of a sort) on this one. I correctly identified that the process was {time dependent drift, random innovations}. I didn't get the precise form of the Henon map (not surprising as I've never heard of this before) but I did capture the spirit of the drift switching process.

EDIT: I had a look at the Henon map. I know almost nothing about chaotic systems, so I was interested to see that the time series is ergodic. Is this common in chaotic systems?

 


Johnny Jupiter Radiation Phynancial phorecasting by the stars for the stars

JabairuStork
Beat Box King

Total Posts: 970
Joined: May 2004
 
Posted: 2005-04-29 12:36
COME ON, HIT ME!

neural net guy 2:1
james 7:2
opmtrader 5:2
RFMontraz 7:2
johnny 7:2
dgn2 5:1
kubrick 7:2

Sorry, no shorts. Good for 10 USD.

I'll be out today and tomorrow. Someone cover the desk for me.

James
NP High Priest

Total Posts: 2024
Joined: May 2004
 
Posted: 2005-04-29 12:47
errr, I think Johnny deserves better treatment than my equivalent 7:2 odds.

I put the log returns in 34 bins and got a normal distribution, so I should have seen that.

I did isolate the time dependence.

I did not isolate the initial condition sensitivity, but since you took a window deep in a series....

Prior to the publication of the Black-Scholes model in 1973, the quest for a valuation formula that would describe option prices reflected one of the most elusive goals in financial economics. Though much work was done in the 1960s, many of the insights and techniques used to solve the problem were presented or anticipated at the beginning of the twentieth century by Louis Bachelier, an obscure French mathematician. These innovations include the first graphical representation of option pricing, a mathematical description of stock prices utilizing Brownian motion and anticipating the efficient market hypothesis, and the first formal option pricing formula.

NIP247


Total Posts: 554
Joined: Feb 2005
 
Posted: 2005-04-29 12:47

So Nonius, could I humbly ask for the mathematical reason as why/if  a simple ta "model" such as mine actually could produce the somewhat significant returns posted or if it was just pure luck in the realisation of the time-series and/or my parameters?

 

 


On your straddle, done on the puts, working the calls...

Nonius
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Posted: 2005-04-29 13:32

well, you bring up a good point that I will list below:

1.  Clearly, it is enough to predict distributions (rather than prices) to make money.  thorp would have a viable strategy for this process, conditioned on knowing the distribution....this is obvious.

2.  I used a two dimensional chaotic system to generate the mean drifts, which suggests that that a machine that expands the dimensions of the "feature space" may make sense in trying to predict certain elements of a distribution.

3.  In some sense, I agree with the evil Taleb that, it is NP hard and perhaps undecidable whether you are right or lucky....that is, I have a distribution that depends on a) a constant parm and b) a time dependent deterministic parm and thus c), if you were trying to calibrate this to any other model, then you would decide about your "correctness" by testing a trading model.....and that, to me, is dangerous, and yet, it seems like the only way.....to me, this is why I am dubious about some of the "trend following" HFs I've met...I would like to give them the NoniusChallenge...In fact, I may do so....

P.S.  If this sounds Reza-ish, kill me slowly with a blunt knife.


Chiral is Tyler Durden

IAmEric
Phorgy Phynance
Banned
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Posted: 2005-04-29 13:34
Too bad. Maybe next time I will put my name down just to reserve some play time for us in NY before the solution gets posted Smiley

Cool puzzle by the way Smiley

Nonius
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Posted: 2005-04-29 13:36

EDIT: I had a look at the Henon map. I now almost nothing about chaotic systems, so I was interested to see that the time series is ergodic. Is this common in chaotic systems?

I do not know if it is true in general, but, a lot of chaotic systems are ergodic....it may be true....basically, a typical situation is you have a system of ODEs that give rise to wildly different limit sets conditioned on the initial conditions.  google strange attractors.

Farmer was my TA....the real Farmer.

 


Chiral is Tyler Durden

Johnny
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Posted: 2005-04-29 13:53

Yes, I know that much and that's why I found it surprising that the series should be ergodic. I was thinking that series prone to wild explosive behaviour would generally not be, but yes, you're right, the strange attractor thing makes sense.

I recreated the Henon map in Excel and found that the drift switches from positive to negative with probability just under half on each time step, i.e. switches approximately every 2 time steps. This behavious is fairly stable over the interval I tested (first 65,000 steps of the series). For my answer this morning I tested for switches on 30, 60, 120 and 240, with positive results for 30 and 60, hence my guess of around 50. I didn't test for switches as rapid as every second step.

btw, what's Farmer like?

 


Johnny Jupiter Radiation Phynancial phorecasting by the stars for the stars

Nonius
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Posted: 2005-04-29 14:00

Johnny, not sure I agree that the sign switches at that rate......I get about 66% of the time it is positive.

I think, though, that in the limit it is the same sign...


Chiral is Tyler Durden

Martingale
NP House Mouse

Total Posts: 2648
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Posted: 2005-04-29 14:06

what did I miss here? I see no data, nothing....well, this does look like the reza chanllenge though


Nonius
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Posted: 2005-04-29 14:09

yes, but there is a difference:

1. I am not a geek.

2. I gave the answer quickly.

3. I am not a geek...oh, I said that...


Chiral is Tyler Durden

Johnny
Founding Member

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Posted: 2005-04-29 14:12

Time

x

y
0 0.1 0.1
1 1.086 0.03
2 -0.62115 0.3258
3 0.785634 -0.18635
4 -0.05046 0.23569
5 1.232126 -0.01514
6 -1.14053 0.369638
7 -0.45148 -0.34216
8 0.372475 -0.13544
9 0.670324 0.111742
10 0.482675 0.201097

These are my first ten values. How does this compare to what you have? Probably I've made a silly mistake somewhere, but this isn't exactly rocket science ... anyway, you can see in mine that the y values switch fairly rapidly between positive and negative.


Johnny Jupiter Radiation Phynancial phorecasting by the stars for the stars

Nonius
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Posted: 2005-04-29 14:17

I get the same initial values as well....

Number of Pos 43547
Total Num 65532
Ratio 0.664515


Chiral is Tyler Durden

Martingale
NP House Mouse

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Posted: 2005-04-29 14:18
Big Smile

NIP247


Total Posts: 554
Joined: Feb 2005
 
Posted: 2005-04-29 14:18

>> Nonius >> Thank you for your answer. I think I kind of get your arguments. Reading some Frédéric Laupies under the defintion of "cartésianisme", he points out that "a result without a theory and proof is useless". If I understood you correctly, this is why you are sceptical about trend-following HF's.

On the other side, if there is a mathematical model that perfectly describes a process e.g. the relationship between two assets (as in NOKI SEK vs NOK1V EUR), every trading opportunity/"arbitrage" you might see is probably something that you have missed- As the game evolves, you find less "straight" relationships that offer opportunities and you go on finding more complicated models that try to describe the phenomena you're watching:

In 1995, BS in London could still make profits trading the index-basket against the OMX-future by actually calling a broker in Sweden over the phone and ask them to do the trade even though both the equity-market and the derivatives market were electronic. A few years later, people talk about pairs trading and define mathematical models that should hold given this and this and that. Finally, it gets to the point where Vidyamurthy publishes "Pairs Trading" and all "opportunities" are gone ( I don't imply any causality there :-) )

I think what I'm trying to say is that most people want to hear a good investment/HF story based on cartesian thinking; i.e. a trading model that you can put in nice mathematical formulation and that sounds intuitively right. That's why invetsors keep on throwing money into "long/short" funds and market-"neutral" vehicles.

In a world like that, a guy saying "well we're buying because it has gone up" or "selling because it has gone down" freightens most investors. So they try to sugar-coat the story with quasi-finance speak (like the nonsense: everything is in the price and therefore we buy because it HAS gone up). But ultimately investors are uncomfortable with the lack of theory. And I also think that this is the reason why even a guy like Patrik Brummer, who has incubated a number of  hedge funds directly from start chose to buy a call in Lynx (their TF futures fund) rather than back it from the beginning, watched the performance for 3 years (with only 15mEUR in AUM) before he decided he was comfortable with their type of money management. Today, it has over 400mEUR in management and cannot be compared in sophistaction to the things their sisterfund Nectar is doing, "but it still works"...

(I'm skating on real thin ice and its already spring...)

 


On your straddle, done on the puts, working the calls...

Johnny
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Posted: 2005-04-29 14:29

Nonius: Yes, but that's not what I'm counting. I'm counting how often the drift switches from positive to negative or from negative to positive. As a good ol' fashioned trend-follower, that's what I care about.


Johnny Jupiter Radiation Phynancial phorecasting by the stars for the stars

Nonius
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Posted: 2005-04-29 14:31
I'm confused on that....for me, the relevent metric is the number of ups drifts divided by the total number of observations...am I missing something?

Chiral is Tyler Durden

Johnny
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Posted: 2005-04-29 14:34

Yes. Smiley

If you have a series of 100 increments, half up and half down, then it's easy for a trend follower if all the "ups" come first and then all the "downs" come last, but very difficult if they alternate "up", "down", "up", "down", ...

What is also difficult is if the frequency of switching changes. The model is locked on to one frequency and then ... loses the frequency ... and takes time to lock into the new frequency. Think of your wavelet MRA.

 

 


Johnny Jupiter Radiation Phynancial phorecasting by the stars for the stars

IAmEric
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Posted: 2005-04-29 15:17
I hope dumb questions are allowed Blush

If the drift switches frequently up and down, what justifies the use of the word "drift". Shouldn't the rapid up and down part be shifted to the "vol" term?

Johnny
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Total Posts: 4333
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Posted: 2005-04-29 15:20

If you have a process dS = mu(t).S dt + sigma.S dW(t) then the switching up and down just means that mu changes rapidly as a function of t. An example would be mu(t) = sin(wt). The lower w, the lower the wavelength, the higher the frequency, the more rapidly the drift goes from positive to negative to positive.

In general for a trend-follower it's better to trade low frequency signals and incur lower transaction costs. It's also much easier if the frequency is reasonably stable so that you don't lose track of the signal.

I feel like a fraud talking elementary dsp to an ex-ee ...

HTH.


Johnny Jupiter Radiation Phynancial phorecasting by the stars for the stars
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