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1.Presentation 4.Parameters
2.The tool and its use 5. Accuracy
3.Theory - Models 6. Disclamer

Pricer

Discover the best purchase or selling price of a security with "Pricer". Based on the diffusion theory, this tool allows you to estimate the likelihood of an order being met during a given period of time..
1. Presentation

The buying or selling price is determined by several, often conflicting factors :

the willingness to find a buyer/seller;
the desire to pay the lowest price or sell at the highestt;
the ability of a trader to wait for an order to find a taker.

Placing an order between the bid and ask price gives the best chance of finding a taker but can also be the least profitable method.

Placing an order a long way off the bid or ask price will significantly increase your profit potential but it will also be almost impossible to execute a transaction.

While the above scenarios are extreme, the general rule of thumb holds that the earnings potential of a price rises as the probability of finding a taker falls.

Waiting increases the chances of finding a taker, whatever the price.

The ideal price therefore strikes a balance between acceptable risk and the desired profit margin.

How can I determine this price?

Swissquote has developed a tool that takes into account all the relevant factors and calculates the probability of an order being successful.
2. The tool and its use

This flexible tool uses an algorithm based upon several parameters. Users can change the settings to fit their particular requirements.

Variable parameters :

“BUY” and “SELL” modes to calculate the best purchase or sale price.

“Choose the parameter” pull-down menu (“Price” “Probability” or “Time”).

Use the scroll bar to vary the settings of the selected parameter.

An example of each variation is outlined below.

Price verses probability

Select "Price" from the pull-down the menu then set the selling price using the scroll bar and the probability will be automatically updated according to the fixed time periods: (10 mins 30 mins 1hr 2 hrs 5 hrs 1 day 2 days 5 days).



The available price range is calculated so that the probability of finding a taker equals 5% for the longest time period (5 days).

The example above shows a 29.2% probability of finding a taker within an hour, for a buying order of CHF 62.7

Note: The calculation used for the most probable price available through the scroll bar is: “(bid + ask) /2”.

Probability verses Price

When the probability is varied, the fixed time periods will display the corresponding Buy/Sell price.



'"What price has a XX% chance of being achieved within a given time period?" In the example above, there is a 30% chance of the price reaching CHF 59.8 within five hours.
Note: this feature is used to define the test procedures described in paragraph 5.

Time verses price

The third option allows you to view the prices likely to be achieved within your chosen time period..




In the example above, we can see that there is a 60% chance that the price will have reached CHF 61.69 in one day’s time.
3. Theory - Models

Introduced at the beginning of the last century by Bachelier, Stock Exchange modeling has in the last few decades undergone considerable progress. One of the most renowned developments was without doubt the Option Pricing Theory developed by Black and Scholes who were awarded the Nobel Prize in 1997. This theory is based on the assumption that underlying stock price follows a geometric Brownian motion. The following diagram illustrates a computer-generated example of Brownian motion and helps to show that this theory provides a good starting point for further modeling.

A Brownian motion simulation of stock price changes




Our model is based on the same theories and techniques in order to simulate the real world as accurately as possible.

The assumption used for this model can be outlined in the following way:

The probability that an order finds a taker during a given time period, is equal to the probability that during its “motion”, the buying price will hit the target price at least once during the same period.
The solution to this well-known mathematics and physics problem is contained in the theory of Brownian motion.
4. Parameters

The relevant parameters for this problem are as follows:

The desired selling or buying price
The further away the target price is from the bid or ask, the lower the probability of achieving this price will be.

Bid and ask
These are the two reference prices that provide the basis for all subsequent calculations. In "BUY" mode, the tool will use the firmest prices for its default buying prices (bid+ask)/2 whereas in "SELL" mode, the weakest selling prices will be used (bid+ask)/2.

Time periods.
The longer the time period, the greater the probability that the target price will be reached.

Probability or the degree of confidence
Setting the level of probability will enable the tool to determine the corresponding buying or selling price. The lower the probability, the further away the selling or buying price will be from the bid and the ask.
5. Accuracy

We have developed an objective and methodic testing system.

The algorithm developed by Swissquote can be used in two different ways :

When the buying or selling price is set, the algorithm will calculate the probability of an order being fulfilled within the specified time period
When the level of probability for a specified time period is set, the algorithm will calculate the corresponding buying or selling price.

The above functionality is used for our test procedures:

We have comprehensive data on a vast number of securities. In particular the opening price, as well as the highest and lowest price for each trading day. This enables us to deduce the following:

The opening price enables the algorithm to calculate the price that has an XX% chance of being fulfilled before the end of that day's trading. Simply comparing this price with the actual highest and lowest prices of the day will reveal whether the order found a taker. Repeating this process on all data makes it possible to measure the effectiveness of the model, by comparing the frequency of successes YY% (the number of times the price calculated by the algorithm falls between the highest and lowest for the day, divided by the total sum of data), with the projected frequency: XX%.



The results obtained are presented on the following graph :



Looking at the above graph we can see that when the algorithm is used to determine the price that has a 43% chance of being achieved over a given period, the price has a 42.3 times out of one hundred chance of falling between the "high" and "low" for the period.

Calculations are made on all SMI listed securities, over different time periods as well as for different probability levels (XX%), including more than 200,000 comparisons between the projected price provided by the algorithm and the "highs" and "lows" actually recorded for the relevant period.
6. Disclaimer

This model is a Gaussian model and although widely used in finance, is only one approximate model. We therefore recommend that the results obtained be treated with caution. Although tests regarding the accuracy of this model have been conclusive (paragraph 5), we must stress that the indications provided by this tool are purely statistical in nature.

The volume of orders is not taken into account by this model. Naturally, the probability of fulfilling an order reduces in line with the number of securities that you wish to buy or sell.

Consequently, this tool does not under any circumstances constitute an incitement to invest.

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