The
system discussed in the previous post can be easily tested using the
simulation method of its operation. The input record format will be
an Open-High-Low-Close, and I plan to implement the engine of the
system using
C++ compiler together with the R environment. But first I would like to briefly write
down the formulas necessary to program rules of position reversals
and the resulting profits.

The
basic premise of the system, perhaps not very intuitive and difficult
to accept, is to determine the levels of reverse position relative to
the initial quotation, namely Open. Expanding on this thought: if
your position is short, the level set to be reversed at a fixed
distance above the opening price. There will be the potential closure
by Stop Loss and opening a new one by Buy Stop. On the other hand,
taking a long position reversal level is set at a fixed distance
below the opening. There will accordingly be expected Stop Loss and
Sell Stop.

In
essence this means that the user only requires a decision to
determine this distance, denoted hereinafter by the letter "t".
The appropriate level of reversal knows the market. Motivation to use
this kind of strategy, as well as discussions on all the pros and
cons would occupy many pages yet, so we will return to them in the
future. But now I would like to introduce models as soon as possible,
allowing examine its properties in practice.

We'll
start with the simplest problem, which is to write formulas for the
transition between positions. This requires the appropriate symbols.
Long positions will be determined as +1, and short -1. There are
perhaps quite natural signs, which - consistently applied - also will
be useful in implementations and simulations. What is needed is a
variable that stores the current position. I suggest the symbol "s"
as the value of the position at the end of the interval of the
appropriate index. "t" is also necessary here, since this
value will depend on the previous position, and the distance "t"
which determines the level of the reversal.

And
here is the formula for the reversal of the position included in a
conditional expression. The letters O, H, L, C, along with the BID
and ASK indices denote the corresponding quotations within the
interval.

These
formulas allow you to set sequences of positions occupied by a player
on the basis of records OHLC quotes for different cases of the
parameter "t". However, what interests us most is the study
of the effectiveness of the strategy through profit and risk
indicators. To do this, you will need formulas determining gains and
losses as a function of the relevant data and parameters. It will be
presented in the next post.

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