Oscillator without complex numbers

Interest-rate parity relationship

Interest-Rate Parity Relationship (IRP) is a formula which relates the time dependence of the exchange rates of two different currencies to the difference of the interest rates in the corresponding countries. If the IRP relationship is violated, then an arbitrage opportunity arises. It is not unusual for some governments and/or central banks, pursuing some particular political or/and economical goals, to interfere with IRP, and manipulate the exchange rates or interest rates or both. Such manipulations inevitably lead to massive flows of currencies in one way or the other. A particularly drastic example of such an operation can be found in the recent history of Poland, where, in the year 1990, the Government decided to freeze, for a longtime (it lasted for about two years), the foreign currency exchange rate on the level of 1 US$ to ca: 10,000 zloty, while keeping the bank interest rates many times higher, even in the order of magnitude, than those in the Western banks. Based on that there is a possible scheme of exploiting these opportunities, consisting of repeated chain of steps: a foreign loan—exchange of currencies—deposit-loan—exchange deposit, etc.

This simple scheme led to many enormous fortunes made by various groups of individuals, of which the best known examples in Poland were the so-called "The Gasiorowski-Bagsik Oscillator" and "the FOZZ-gate". To demonstrate the efficiency of those financial speculations we carried out model calculations assuming that the difference of the interest rates between the rates for deposit rates in Polish banks and those in the West amounted to 70% p.a. throughout the year 1990.

Interest rates 
The interest rates are to be determined each month and at the beginning for the month of January 1990 it is established at 36% per month. To be on the safe side, we propose to consult an offcial document issued by the Polish National Bank. The Decree no. 1989 of the President of the Polish National Bank of the 30th December 1989 orders that since the 1st of January 1990, the interest rates should be 36% per month. We have tracked down all changes of the rates during the year 1990 and they are presented in Table 1. 2 Fig. 1 represents the value of 1 zloty deposited on the 1st of January 1990 and subjected to the rates in Table 1. It is seen from this figure that 1 zloty deposited at the beginning of 1990 increased to 2.23 by the end of that year. This corresponds to an e:ective rate of 134% p.a. In fact, real deposits were at lower rates but the rate 80% p.a. which we assumed for simplicity was not an exaggeration. Incidentally, a deal that Andre Gasiorowski and Boguslaw Bagsik struck with the Polish State Bank PKO BP by the end of 1990, when he deposited 600 billion zloty (equivalent of 60 million US$) for 5 yr, had been made on assumption that current interest rates were on a level of 80% p.a..

"Temperature" of the Gasiorowski - Bagsik Oscillator 
In their article, Prof. Edward Piotrowski and Prof. Skladkowski developed a thermodynamic analogy of financial market games (Black-Scholes Formula for Options Trading). They applied that apparatus to our Gasiorowski-Bagsik Oscillator model assuming the difference of the interest rates to be 30%. Each loop of the Bagsik Oscillator led to riskless profit and everyone who had an understanding what is the meaning of a huge deviation from the IRP, as was the case of Poland, was in a position to exploit it and make a huge profit. Consider Gasiorowski-Bagsik’s deal mentioned above. By the end of 1990 Gasiorowski-Bagsik had deposited an equivalent of 60 million US$ for 5 yr. With the interest rates at a level of 80% p.a. it would lead to the multiplication of the deposited capital to about 50 times. With a bank certificate to the amount equivalent to 3 billion US$ one could play any financial game one pleased. But suppose that the interest rates at that time were not 80% but 40% as Piotrowski and Skladkowski would prefer. In such a case a certificate possible to obtain from the Polish State Bank would amount to not 3 billion US$ but to a figure 10 times lower. How big a loan one could obtain for a state bank certificate amounting to 300 million US$? Whatever be the answer to this question every loop of the "oscillator", i.e.: exchange—deposit in Poland—exchange, would lead to 30% p.a. gain. In fact, the inventors of the "oscillator" revealed their secrets themselves. They also gave it an imaginative name: "B.G. Moneytron" (B&G for Bagsik and Gasiorowski). In their words it consisted of repeated "loan-deposit oscillations within the framework of an international arbitrage". In the same place they boast that this "moneytron" resulted in magnification of the invested capital by 18 000% within 1 yr.

P&S 1.93 Oscillator
Prof. Edward Piotrowski and Prof. Skladkowski (P&S) come up with a sophisticated scheme of making fortunes in the realities of the beginning of the last decade in Poland, which they call "sbO 1.93". The essence of their "oscillator" was to exploit hyperinflation of those years, which, according to their data, amounted to nearly 600% for non-edible goods and to nearly 800% for services. Speculators could then, say at the beginning of the considered period, purchase suffcient amount of goods and/or services, by making due payment deferred till the end of the period, make enormous profits. By repeating such "oscillations" a number of times, one could generate a profit by fivve orders of magnitude ("45 000 times") bigger than the one that could be generated within the framework of the above-described "B.G. Moneytron". P&S suggest that "one could induce directors of state-owned firms to enter such formally legal but tragic in effects contracts". We were discussing in our former article is that an access to the "B.G. Moneytron" was open to everyone who had an understanding of what the interest-rate parity meant and to a substantial loan or credit. No conspiracy (e.g. no "inducement" of directors, etc.) was needed. It is worth to note that the latter could be exploited only in special circumstances of hyperinflation, the arbitrage based on marked deviation from the IRP relationship has been, and still is, used more often all over the world. The case of the recent crisis in Argentina may serve as another good example.

Concluding remarks
Problems of previously closed economies, like those of the former communist countries, are abundant. Incompatibility of financial mechanisms operating there with those normal for free markets made them exposed to easy games, to various forms of arbitrage, which people of these countries had no means of understanding and therefore were unable to oppose effectively. Some of such games were simple enough and to understand them no functional analysis, complex numbers or statistical physics are really needed. We were trying to show that the so-called Gasiorowski-Bagsik Oscillator belonged to the latter category.

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Black-Scholes Formula for Options Trading The original formula for options trading became too limited in its scope of investments and ability to leverage. In 1973, the spirit of the world moved on Fischer Black (deceased), Myron Scholes and Robert Merton, and led them to develop the 1973 "Black-Scholes Model for Options Trading" This complex pricing model revolutionized how options could be used. It expanded the scope of investments to include a multitude of financial instruments, and dramatically increased the user's leveraging ability. In other words, more fractional reserve type debt could be created out of nothing to buy or sell investment assets, which further enhanced the elite's ability to manipulate the markets. The Black-Scholes Model is flexible enough to do almost anything with. When applied to the advances in computer processing and telecommunications, this formula virtually created a multi-trillion dollar investment market out of thin air.

References:

[1] M. Baxter, A. Rennie, Financial Calculus, Cambridge University Press, Cambridge, 1996.
[2] B. Connolly, The Rotten Heart of Europe: The Dirty War for Europe’s Money, Faber & Faber, London, Boston, 1995.
[3] M. Dakowski, J. Przystawa, Via bank i FOZZ, Antyk, Warszawa, 1992 (in Polish).
[4] J. Przystawa, M. Wolf, Physica A 285 (2000) 220–226.
[5] E.W. Piotrowski, J. Skladkowski, Physica A 301 (2001) 441–448.
[6] E.W. Piotrowski, J. Skladkowski, Acta Phys. Pol. B 32 (2001) 597.
[7] http:/info.fuw.edu.pl/donosy/archiwum/
[8] Zarzadzenie Prezesa Narodowego Banku Polskiego nr 1989 z 20 grudnia 1989, Dz.Urz. NBP.89.7.15.
[9] J. Diatlowicki, Polityka 25 (1994).
[10] A. Kwiatkowska, T. Rudomino, Kto sie boi Art. B? Polska Oficyna Wydawnicza BGW, Warszawa, 1997 (in Polish), p. 59.