Leonardo Fibonacci Biography

Leonardo Pisano, now better known by his nickname Fibonacci, also sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. He was born in Pisa, Italy around 1170. At the time, Pisa was an important commercial town and had links with many Mediterranean ports. He was the son of Guilielmo Bonacci, a diplomat for the Republic of Pisa. Guilielmo was responsible, beginning around 1192, for directing the Pisan trading colony in Bugia, Algeria where he represented the merchants of the Republic of Pisa. Bugia, later called Bougie and now called Bejaia exported wax candles. The French word for candle, Bougie, is derived from the Algerian port’s name.

Some time after 1192, Guilielmo Bonacci brought Leonardo with him to Bugia. Leonardo received a North African education under the Moors, and was taught their style of mathematics. Guilielmo intended for his son Leonardo to become a merchant and so had arranged for his education in calculational techniques, especially those involving the Hindu-Arabic numerals which had not yet been introduced into Europe. Later, Leonardo was assigned to do business for the Pisan republic and he travelled extensively around the Mediterranean coast. He was sent on trips to Egypt, Syria, Greece, Sicily, and Provence. He took the opportunity offered by his travel abroad to study and learn the mathematical techniques used in these various regions. He would have met with many merchants and thereby discovered their systems of doing arithmetic.

Around 1200, Fibonacci ended his travels and returned to Pisa. On returning home he began to work on his own mathematical texts, and continued to do so for at least the next twenty-five years. His work played an important role in reviving ancient mathematical skills and he also made significant contributions of his own. The five works we know of from this period are: the Liber abbaci (1202, 1228); the Practica geometriae (1220/1221); an undated letter to Theodorus, the imperial philosopher to the court of the Hohenstaufen emperor Frederick II; Flos (1225), a collection of solutions to problems posed in the presence of Frederick II; and the Liber quadratorum (1225), a number-theoretic book concerned with the simultaneous solution of equations quadratic in two or more variables. Fibonacci lived in the days before printing, so his books were hand written and the only way to have a copy of one of his books was to have another hand-written copy made, in light of this we are lucky to have such record as we do of his work.

Frederick II had summoned Fibonacci for an audience when he was in Pisa around 1225. His achievements were clearly recognised during his lifetime, although it was the practical applications rather than the abstract theorems that made him famous to his contemporaries.

After 1228 by decree the Republic of Pisa awarded Fibonacci a yearly stipend for his pro bono advising to the Republic on matters involving accounting and related mathematical matters. Fibonacci died some time after 1240.

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The Secret Of Better Market Timing & Profit Potential

The Fibonacci number sequence and golden ratio is important throughout nature, but traders such as W D Gann made great use of the sequence as a trading tool.

The numbers helped make Gann millions in profits and are useful for any trader to maximize profits.

So what are they and how are they applied to trading?

Let’s find out: Support and resistance levels are important for traders as they help identify entry and exit points when trading.

Fibonacci percentage "retracement" levels based upon the Fibonacci number sequence and golden ratio are used by many savvy traders to improve their entry and exit points.

Fibonacci Numbers and the Golden Ratio
The Fibonacci sequence was printed in the Liber Abaci, written by Leonardo Fibonacci in 1202. It introduced Hindu-Arabic numerals for the first time To Europe, which are at the time was still using roman numerals.

The Fibonacci number sequence came about from the following question:

How many pairs of rabbits can be generated from a single pair, if each month each mature pair produces a new pair, which, from the second month, starts producing?

While the Fibonacci number sequence and golden ratio came about form the above question it produced a number sequence that has importance throughout nature.

After the first few numbers in the sequence, the ratio of any number to the next higher number is approximately .618, and the lower number is 1.618. These two figures are referred to as the golden mean or the golden ratio.

The golden mean and golden ratio
The proportions reflected in these numbers are pleasing to the human senses and appear throughout biology, art, music, and architecture.

A few examples of natural shapes based on the Golden Ratio include: Snail shells, galaxies, and hurricanes DNA molecules, sunflowers and many more.

Many traders have found these numbers important in trading as well and such traders as W D Gann for example, used them to amass huge profits.

Retracement Levels
The two Fibonacci percentage retracement levels considered the most important for traders are: 38.2% and 62.8%. Other important retracement percentages are: 75%, 50%, and 33%. Fibonacci Numbers 3 Uses For Traders

1. Fibonacci numbers Define exit numbers
For example, if three or more Fibonacci price levels come together in a tight zone, a stop loss can be placed above the area which denotes important support or resistance.

Setting stops using Fibonacci retracements give important areas that act as support or resistance, allowing traders to set pre defined exit points in a disciplined manner.

2. Fibonacci levels Decide Position Size
Depending on the risk you are prepared to take per trade, Fibonacci numbers can also define the size of position taken. This is because the distance from the stop is different in monetary terms on all trades.

A stop close to resistance and support may warrant a bigger position than one where support or resistance is further away.

3. Fibonacci numbers Define Profit Objectives
With Fibonacci numbers, once a pattern completes against a Fibonacci price area traders can use them for profit objectives. This clear view of where trades may go helps traders to lock in profits at set levels.

The advantage of Fibonacci numbers are: They allow traders to have specific stop loss and profit objectives IN ADVANCE.

One of the keys to trading any market is discipline most traders simply don’t set profit and loss objectives in advance. They therefore let emotions take over, they get greedy or rely on hope and this creates losses over the longer term. Profits are run to long and lost and losses become bigger than they should.

“Run your profits and cut your losses is the way to make longer term capital gains and Fibonacci numbers incorporated in your trading plan will help you do this.

W D Gann was a trader who understood that using Fibonacci numbers could make large profits and used them with stunning success.

Fibonacci numbers combined with the techniques of WD Gann can help any trader achieve long term capital gains. Check out these great profit tools and incorporate them in your trading as they will help you increase your profit potential.
http://www.gann.co.uk

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Fibonacci Model's description 3

Final Results

Then, and based on the model developed to prove the original hypothesis, we came to the following results:

Pair EUR/USD:

Pair USD/CHF:

Pair GBP/USD:

Pair YEN/USD:

If after finishing this job, someone ask me if it is possible to predict the future, mi answer will still be “NO”. I don’t believe that could be, in fact, I don’t believe either we can predict what will happen in the next minutes…

Although this seems the opposite of the objective of this work, I personally want to remark the difference between one thing and the other.

As a technical analyst and according to what was explained above, I maintain technical analysis postulates, and use them with statistics and mathematical tools, to forecast probable target price zones.

And here is the difference: in one hand, you have the certainty, in the other the probability. I personally believe there is no complete certain of what will happen, but using some specific tools, you can determinate probabilities in a defined scenario.

We use mathematic and statistics tools to analyze hundreds of data in order to prove the objective of this work.

That’s why we can affirm than more than 70% of the times, using Fibonacci retracements and ZigZag oscillator, we can determinate the target zones where prices will go, when they show retracements against major trend.

As a conclusion of this work, we propose to you to use Fibonacci tools in intermediate time frames, in order to obtain better results in markets with a defined trend, excluding moments of excessive volatility, but with enough price fluctuation, becoming and excellent tool for short term technical traders.

Finally, I want to invite you all to extend the application of this system to smaller time frames, and to the rest of the currencies in FOREX Market, and also, to other markets, such as futures, options, or any stock market.
http://www.fxstreet.com/education/

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Fibonacci Model's description 2

Step 2

Afterwards, we move the following fields-data to a new table: minor rally number, start price, end price, duration (in hours), and the distance in basic points or pips.


Then, we move the major trend direction to the new table, came up from the application of the Zigzag Oscillator to the major period under study.



After the legs of the ZigZag were found (bullish and bearish rallies), we apply the Fibo’s ratios at any leg (“zig” or “zag”) that coincide with the major trend (In this case, Week), and so, we check if effectively the price retracements will go to the Fibo’s zones, or zones define by this special numbers.

Beginning with the graph example, where it explains the Zig Zag application, we continue the main analysis with the objective of verify graphically the behavior of the Fibo’s ratios in the retracements.

Inside the major trend we isolate in Graph 5, we proceed to apply the ratios of Fibonacci to the bullish rallies A1, A2, and A3.

In case of Rally A1, we take the complete distance from its minimum price at USD 1.0762, to the end at 1.1862 dollars per Eur. Then, we apply the Ratios of Fibonacci trying to see where the prices go after have reached the peak, and started the retracement.



In case of the bullish rally A1 with 110 basic points, and applying the Fibonacci Retracement ratios, we calculate the price for any ratio, trying to find the possible zones where the quotations could stop, so:



Looking at graph 6, and after the price retracement have begun, in opposite direction of the major trend, the price goes to the 23.6% zone. Firstly, the price couldn’t break this zone, and start to reduce the speed, and begun a change direction turning bull. This change is not considerer by the Zig Zag Oscillator, because the slope is lower than 12%.

After the price stops, it moves to the 38.2% zone, where its value is USD 1.1442. According to the results of Zig Zag Oscillator, the quotation stopped in an intermediate zone between 38.2% and 50%.

Secondly, we study the Rally A2. This rally begin after the B2 retracement has finished, at USD 1,1375 per Eur, and finishes on 01-12-2004, with a price value of 1,2900 dollars per Eur (Graph 7).



Besides, we apply again Fibonacci’s retracement ratios, to know the possible quotation behavior,



In this case, we can see a price retracement with a minimum value at 1.2334 dollars per Eur, near to the Fibo’s ratio, 38.2%. After that, the quotation rebound, and continues with the dominant trend.

Finally, and following with the bullish trend on Rally A5, the price goes to 1.2930 and change later the dominant trend, as we can see in graph 5. To confirm a change of the dominant trend, the retracement must be more than a 100% of the last rally, in the present example the price need to break 1,2317.

Continuing with the Statistic Analysis, we calculate the price values of any currency pair under study. In this example of EURUSD, you can see them in the next table:



As you can see in Table 13, the Bullish rally number 4 begins at 1.3836 dollars per Eur and ends at 1.4249. We apply the Fibo’s ratios, and we obtain the corresponding prices. For example, for ratio 23.6% the price is 1.4152 dollars per Eur. In others words, once the quotation rebounds at maximum USD 1.4249 per Eur, should go back to the first target of USD 1.4152.

Step 3

Once the prices targets for any rally were obtained, we proceed to probe the objective success of the system. Previously, we define 3 scenarios, or zones around the price, and test the truthfulness of the retracements go to these values or zones.

Each zone was defined with a percentage of the rally distance (zig or zag). For more information, we refer that we select the complete rally of the leg of the Zig Zag under study, for example: 100 pips, and if the price goes to the zone defined in more or less 7,5% (in this case in more or less 7,5 basic points) of the Fibonacci’s price, so the propose target is accomplished.

The scenarios are:

- 15% Zone: +/- 7.5% of the total rally, above the Fibo’s price.
- 20% Zone: +/- 10% of the total rally, above the Fibo’s price.
- 25% Zone: +/- 12.5% of the total rally, above the Fibo’s price.

Then, using the logical formula, we try to prove if the retracement of the price will go into the define zone.

In case that the final price of the next rally (mean the retracement), go into the Fibo’s define zone, the logical sequence is True, and so, successful. In the other hand, is False, and do not achieve the target.

Step 4

Finally, we proceed to calculate the number of retracements which go to the objective zone inside the dominant trend. In the present example, where we analyze the behavior of the currency pair EURUSD, Diary, we obtain the following results for the 15% zone:



As we see at table 14, we obtain a success of more than 70% of the propose objective. We refer that the retracements go to the Fibo’s price zone, when the minor trend correspond to the major. Meanwhile in case that the minor trends have different direction to the Major ones, the Fibo’s ratios have not got a significant success.

Thank you very much to all readers for continuing the interest till the end. We want to invite you to see the final part where we offer the investigation results, and the final conclusion. http://www.fxstreet.com/education/

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Fibonacci Range Expansion Trading Zone

The Fibonacci Range Expansion Trading technique is one that I developed back in the early 1990s when I was moving away from lagging indicators like RSI, MACD, moving averages etc. I had no success using those indicators and came to the conclusion that either I didn’t understand them, or that they simply didn’t work. The only thing that I had any success with was trendline breaks, Fibonacci points, and standard pivots with the reading of pure price action. I was taught that in order to be successful in this business of trading, you need a few components.

According to my mentor and senior treasurer, Aldo Pizzoferrato, trading required BMG, or Brains, Money, and Guts. You need the brains to anticipate market momentum and to be a step ahead of the herd. You need capital to advance, and finally, you need the guts to believe in yourself and your systems. Therein lies the problem for most traders. Most traders operate on the simplest level. They have no real trading plan and view charts and price action using gut feel or really just guesswork. Aldo stressed upon me that the most effective approach was acting like a quarterback of a football team. I need to send the signals, by reading the market and finding weakness in the markets’ defenses. He would always say, “Don’t just receive the signals, send the market some feedback.” I had learned that trading is not a spectator sport. In other words, the most effective approach is in the development of systems that generate buy and sell signals. I had to move from “chart artist” to a true technician.

This trading technique that I am about to share with you will help you pick clear and defined points to enter into low-risk and high-reward trades. No longer will you have the excuse of trading with the rear-view mirror. The market will unfold its weakness, and you as a quarterback, will be able to make the audible call.

The Fibonacci Range Expansion Trading Zone Technique

Overview:

Price movements, up and down, very rarely continue uninterrupted. There are always counter trends to the main trend and at some point in time the trend will no longer continue to be your friend. The trend one day has to end.

The Fibonacci range expansion trading zone system attempts to capitalize on counter trends within a trend or even catch trend reversals. With the FRETZ (Fibonacci Range Expansion Trading Zone) we will use three distinct formulas.
1.    The range of yesterday’s daily bar, which is the H-L= x
2.    Pivot point Calculation of the daily range from yesterday.
3.    Fibonacci retracement levels inside the Fibonacci Range Expansion that we will calculate.

Set up:

On the close of the previous daily bar we gather the following information: the high, low and close. Calculating the set up of USD/JPY on the close of June 3, 2010 will obviously be for the trading day of June 4, 2010.

The high was – 92.80
The low was – 92.04
The close was 92.59

We first calculate the daily range which is the high minus the low.
92.80-92.04= .76

Once the true range is calculated we multiply by the Fibonacci Range Expansion ratio of 1.618. Thus .76 x 1 .618 = 1 .2300
We then add and subtract this factor from the close to get the upper and lower Fibonacci range expansion values. The close of the upper Fibonacci expansion value is 92.59 + 1.23 = 93.82. The close of the lower Fibonacci expansion value is 92.59 – 1.23 = 91.36. These levels are what I call a mini market trench. If price breaks above or below the levels the market is telling me there is a potential shift in supply or demand. So these points are like a fence around the price action of yesterday. It is important to note that 85% of the time the markets trade in a range, and these levels will be excellent buy or sell zones. We will now continue to build our FRETZ matrix. We will add pivot points from yesterday’s range onto our charts. This is a standard pivot point formula, and I will add a downloadable calculator in the near future. However, you should know what the formula is:

Base Pivot:

Pivot Formula = High+Low+Close/3= Base Pivot

Resistance 3 = High + 2*(Pivot – Low)
Resistance 2 = Pivot + (R1 – S1)
Resistance 1 = 2 * Pivot – Low

Support 1 = 2 * Pivot – High
Support 2 = Pivot – (R1 – S1)
Support 3 = Low – 2*(High – Pivot)
———————————————————————–

The third and final part of the Fibonacci expansion trading zone matrix is using your Fibonacci retracement tool. I would suggest changing the .786 level to .8200. I have found that the 82% works a bit better in foreign exchange trading. I know it’s not much of a difference, but I am always striving for perfection. Here is a rule when applying the retracement levels: If the close of yesterday (the bar we’re using) was a down close mark (less than the open), start from the lower level first and then retrace upwards to the upper Fibonacci expansion level. Conversely, if the close on yesterday’s bar was at an up close mark (close greater than the open), start from the upper expansion level first and then retrace down to the lower level. This idea keeps in line with my Fibonacci Strike System.

Now That we have all of these levels plotted, our matrix is set. We will use these levels as support and resistance. The closer the pivots and the Fibonacci Levels are to each other, the stronger the level will be. It’s important to note that if the market “zooms” through these levels, a shift has occurred in supply or demand. If you are on the wrong side, escape quickly (First Rule Of Trading is to preserve capital!) I use a simple trend line as a trigger to enter long or short and the Fibonacci and pivot levels as my resistance and support.
See Chart below for an explanation of trade that occurred in USD/JPY on June 4th 2010.

The chart above shows the full matrix constructed with the Upper Expansion level at 93.81 and the Lower Expansion Level at 91.36 (91.29 in this chart.) Also, note in trading the market that I pulled the lower expansion level down 7 pips as a warning. If USD/JPY broke all those tight levels that converged at 91.30-40 area, the move in my mind should be more violent.

I also just extended the trend line in this chart to extend out to infinity (it’s the red segment above).
Just to be clear, the light blue lines are the Pivot Support at Resistance Levels, and the purple lines are the Fibonacci Retracement levels calculated inside the range of the upper and lower expansion.
I added an advanced technique that I mentioned at one time or another: a Gann 45 degree angle of death from what was the closest Root Point low. A root point for me is the lowest low (or highest high). It’s the genesis of the up move (or down move.) I may confuse some here but study the chart. I picked the pivot low from where USD/JPY recovered and rallied up to 92.88 (this will now be the Root Point for the decline down to 91.42)

When I add this Gann line, I create what I call Nella Bocca di Lupo – the price has entered in the “mouth of the wolf.”

It’s in this area where the support line and the Gann line create the upper and lower resistance. A vortex that once the support is broken should trade lower to the internal Fibonacci levels. I will then gauge price action to determine how strong the move appears.

So how did I trade the USD/JPY?

The market price came up to the Fibonacci Retracement level at 92.88. There was a pivot R1 at 92.91 and the Gann line at approximately at 92.93. I sold the 92.83 level with a tight stop loss at 93.04 (markets tend to push one last time through a R1, so I need a little bit of cover) My first thought was that a 1:2 ratio was worth the risk, and I knew if the price could break the recent support at 92.66 Nella Bocca Di Lupo was in play! I should at least get a chance to scoop USD/JPY at 92.56 or better at 92.27 the lower Fibonacci levels. So the plan was to see if price could break the recent support and once it did how will it react? Will it get dull and stall or will it zoom through the Fibonacci Support of 92. 56? It zoomed through at that point I moved my stop Loss down to 10 pips above the entry price. I now need the Fibonacci level at 92.27 to break, and the S1 at 92.15 to go as well. I want you all to see how the market gave several opportunities to get involved in this short. Look how it retraced back up and slightly above the trigger line (old support line at 92.66) and failed. It then zoomed down through 92.27 and the S1 level at 92.15. It stopped dead cold at the 91.92 level. The market then rallied up to the S1 level at 92.15 (giving another opportunity for a short with a Stop Loss above the Fibonacci Level of 92.27) This is surgical accuracy, as a matter of fact its laser surgical Accuracy! Once the Market touched the 91.92 level, I moved my stop profit down to 92.37 just above the Fibonacci level, I was then planning on taking 1/3 my position off at the 91.72 S2 level. The market hit the S2 and 1/3 was taken off. I then moved my stop profit for 2/3 to the 92.15 level (the S1.)

The market came down within 7 pips of the S3 level (91.39ish) I scooped another 1/3 of the short at 91.51 and moved my stop profit down to S2 at 91.72 where the market decided to take me out. So, you see how important it is to send signals to the market, be that Quarter Back, and yes at times you will get sacked, but it’s all in the name of trading. After All…Profitable Trading Is Not A Spectator Sport!

http://theforexsignals.com

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Fibonacci Model's description

Firstly, I whish to remark that the different Technical tools named in this work, were used to make diagnostics about the probable price behavior, find the triggers (sell price and buy price), and to calculate the stop loss, and the price target, every day since more than a year.

Well now, to develop this work as objective as possible, and get rid of all subjective coming from trader criteria, in order to apply the concepts developed above, we use a simple Microsoft Excel model, where we try to find, in historical data the accomplish of this system objectives.

The population defined for each currency pair under study, could be seen in the following tables:

EURUSD:


CHFUSD:


GBPUSD:


YENUSD:

Step 1

Using Metatrader trading platform, V 4.00, we are able to see the currencies prices in real time. This system allows us to see the different quotation charts of all majors currencies in Forex and besides, the quotation of NYSE most important stocks, and gold.

This application not only let us see real time quotation, but also keeps historical record of each pair in it’s different time frames.

We proceed to isolate a significant number of records (sessions) in a continuous time serie: date (and hour, in the case of 4 hours sessions) maximum price of the session (HIGH), minimum price (LOW), opening price (OPEN) and close price (CLOSE or LAST PRICE).
o LAST PRICE).

Ex.: EUR/USD, Dialy



Then we proceed to apply the Zigzag oscillator in the chart, in order to identify the bullish or bearish rallies, their end and duration for each studied session. In the case of bullish rallies, we take the minimum price of the session (low) as start, and the maximum (high) as the end. This last one, becomes the next bearish rally beginning.

To explain the graph analysis, we choose a random set of time for EURUSD quotation, and applied the ZigZag oscillator.

In the following chart of a week session (Chart 4) you can see a bullish rally that starts on 09/03/2003 with a minimum price at 1.0762, that ends on 12/30/2004 at 1.3665 USD dollars against Euro.

Chart 4


To this bullish rally of 2903 basic points, we apply the ZIGZAG oscillator (red line) showing 3 trend lines:
The first one bullish till 1.2930 day 02/19/2004, second bearish until 1.1759 day 04/26/04 to finally return the bullish trend with it’s third leg.

After isolating the major trend, in this particular case for week sessions, we start analyzing the currency behavior inside it. That’s why we apply the ZigZag oscillator to a 1 day chart (next inferior time frame) in order to find out through charts the minor trends or sub trends, and it’s corrections.

Then we proceed to isolate the first week dominant trend (Chart 5) starting at 1.0762 ending day 02/18/2004 at 1.2930 in the maximum of the session. When we apply the ZigZag oscillator, we found out 5 sub trend lines: 3 bullish (A1, A3 and A5), and 2 bearish (B2 and B4).

Chart 5


According to what we say before, we can see that A1, A3, and A5 are minor bullish trends that correspond with the major one, while B2 and B4 are just price corrections.

Continuing with the model development, we put together the tables for each currency under study, where we list every price rally, showing it trend: Bullish or Bearish and the start and end price. In the particular case of EURUSD, daily session we came out with the following results.

Table 8


As you can see on table 8 the Number 2 rally, starts on day 05/18/1995 at 1.3380 dollars per Euro, and ends the day 05/26/1995, with a maximum price of 1.4235. This rally last 7 days, or 168 hours and represents 855 basic points.http://www.fxstreet.com/education/

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Fibonacci application in the Objective Market

Definition of the sample

Once chosen the objective market, the study was focused in 4 (four) currency pairs, in the Forex International Market. 

In order to make it as objective as possible, the study was based in those pairs with higher volume trade in the Forex market, because they accumulate the 85% of the daily transactions.

• Pair EUR (Euro)/USD (United States Dollars)
  Since it’s apparition in December 1999, the Eur, soon replace the German Mark, and becomes the second currency in the world, getting day by day more importance. The strength of EUR is based on the power of the European Economic Community, no matter how many political factors may affect it.
• Pair GBP (Great Britain Pound)/USD
  It was the reference currency till Second War, and most of the transaction involving it. Took place in London, the biggest international market regardless his small volume during American market sessions.
• Pair USD/JPY (Japanese Yen)
  This is the third currency trade in the world, making market liquid 24 hours a day. Notice that oriental economy moves according to Japan, and so, Yen is very sensitive to oriental agricultural production, technological factors, salaries and NIKKEI.
• Pair USD/CHF (Helvetic Confederation Franc)
  This is the other European currency not included in Eur or G-7, but at the same time, it seems favour related to politic uncertainly of the European Community. Practically, we can say that Swiss Franc moves almost the same way that EUR in relation with the USD.

Sample: scope

This work was developed based in the following time frames, because they represent a prominent quantity of subjacent quotation time, and allows reducing “noise”, in short time:

• Daily sessions: 24 hours of transactions or quotations. We use it to deeply analyze the trend in Medium Term (weeks) and Long Term (months).
• 4 (four) hours sessions, that gives us more detail of temporality, due to in a 24 hours day trading there are moments with higher transaction volume, like the opening or close of the biggest world financial centers (Tokyo, London, Frankfurt and New York).

Anyway, we invite the readers to extend this analysis to sessions with more or less duration, where you can find similar results.

Field work

Once introduced Leonardo Pisano and his invaluable contribution to science, we will stop at his more important ratios, specifically in the target zones created because of them.

Based on what we can see in financial markets, there are retracements or backward movements in a certain percentage. According to Fibonacci, in a strong tendency, a minimum retracement generally address in its first impulse to the zone of 23.6% of the rally; and in case this zone is broken, the quotation usually goes to the zone near the 38.2%, then to the 50 % zone, and in a weaker tendency, the maximum retracement could reach the 61.8%; but if this point is broken, the quotation will continue to a point not consider by Leonardo Pisano, but very important to remark, because of the results given in our diary work, the 76,4 % to finally reach the 100 %.

Once the quotation runs over the 100 % retracement, and confirms that point, we can suppose that the dominant tendency has changed, and price will look for other objectives, that according to Fibonacci, will be at first place the 161.8%, then the 261.8% and finally the 423.6%.

In Table 2, you can see Fibonacci ratios, coming from the division of each number of the numerical sequence he developed by the one before it.



Now we propose combine the price Fibonacci retracements with the Zigzag Oscillator, in a major defined trend, to corroborate the accomplishing of the target quotations.

The popularity and use of Zigzag oscillator are based in three main characteristics: is a good “noise” filtering; it represents the main trend clearly, and is a simple indicator for the market price final interpretation.

However, this oscillator has as main disadvantage his natural dynamic: the last line of its draw marking trend could be tricky and needs confirmation.

It works simply presenting the major movement by connecting picks (high prices) and depressions (low prices) with straight lines.

The inclination parameter of the slope in the specific quotation specifies the percentage that this price has to move to draw a new line or Zigzag line.

Its formula is:

ZZO= 100 * (CL-BASE)/BASE
Where base is the initial price (maximum or minimum) or the Zigzag leg
CL or Last Closing of the before session

This oscillator filters the changes in the subjacent chart, smaller than the quantity specified in the inclination parameter of the scope. It only shows significant changes. The minimum price movements are fixed as percentages, and could be based in close price, or in maximum/minimum ranges.

For example, the Zigzag established in a 10% respect to the OHCL (Open-High-Close-Last) candles, will draw a line that will only change direction if the changes between maximum and minimum exceed the 10%. This means any smaller variation will be ignored.

Then, after we defined the system used to calculate the bullish or bearish rallies objectives, through Zigzag Oscillator, we start the empiric confirmation of the information for each pair under study, main subject of the next session.http://www.fxstreet.com/education/

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Fibonacci's applications

The verification of the Fibonacci Sequence in many real phenomenon’s, makes lots of people decide to study the relationship between these mathematics of nature and the behavior of the financial markets. 

May be this is the most curious and captivating, so it has be proved that the Fibonacci Sequence appears in nature, forming physical structures and defining the process of chance of this dynamics structures. Many authors have mentioned this concept in theirs books.

At the end of XIX Century, a botanist calls A. H. Church, had discovered, studying the sunflower the presence of Fibonacci. His seeds are arranged around the middle in 89 curves, turning 55 of these in one direction and the others 34 to the opposite direction.

From here, the botanists have found Fibonacci numbers in different pieces of Nature. For example, the margarita forms spiral model similar of the sunflower in the middle of his flower. There are also many varieties of flowers where the numbers of petals are Fibo numbers.

A mathematician from Arizona University, Alan Newell, and his pupil Patrick Shipman have been studying recently the cactus to determinate the reason why this numeric pattern is universal. These researchers analyzed the form of this plant, his skin size, and another biomechanics that surge in his growth. When their introduced all of the data in the computer, found by surprise, that the more stable configuration followed the forms based of the Fibonacci Sequence.

We can find other applications, for example the spiral that many trees developed in their branches; the number of little branches in a big one, and the follow of the same vertical is a Fibonacci number, if we use to calculated one of the to branches.

The Fibonacci numbers appear also, in the human body. The men have five appendixes (two arms, two legs, and a head); each arm and each leg are divide in three parts, ending each of them in five appendixes (five fingers), divide each of them in three little phalanx, except two of them which have just two. In the same way, the head has three outstanding characteristics (two ears and a nose), and three inlaid characteristics (two eyes and a mouth). In the end, the human body has five physical senses: sight, ear, sense of smell, taste, and touch.

”The human body presents the golden number or phi”. Leonardo Da Vinci, in his famous picture, the Vitrubio man, illustrated the Luca Pacioli book “Divine Proportion” edited in 1509. This book, describes witch must be the proportion of artistic creations. He proposes that a human figure where each part of the body must respect a specific proportion to be harmonic. This perfect man, for Pacioli, is based on the following mathematical calculation: the high of the men, (side of the square) divided the distance between the navel and the extreme of the extended hand (circle radio), represents the divine number.



Also, many animals body have a trunk and five appendixes, (head and four legs); birds have 5 projections too: a head two legs, two wings.

Fibonacci is also present in music: see for example the piano. The division of the keyboard in scales of eight white keys and five black ones; the black keys are distributed all along the keyboard in groups of three and two. A complete keyboard has eleven scales, and could have one more key, meaning 89.
The chords that allow us to identify any tone are formed by the first, third, fifth and eight note of the scale.

Since professors Church and Hambridge, the interest on Fibonacci numbers by many researchers end in the creation in 1963 of the Fibonacci Society in California, formed by mathematics, witch main objective is exchange ideas and stimulate research on Fibonacci’s relationship with nature.

It has been proved that the Fibonacci sequence is highly connected with the progressive development of dynamical structures, an as society is a dynamical system, human history could be running according to this Nature Law, based on the proportion 3-5 or 0,618; if we add to this concept, the idea that financial markets are the reflect of mass behavior, we can conclude that Fibonacci sequence could be applicable to those markets.
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