Black-Scholes visits Ghana Stock Exchange

A seemingly innocent problem in Physics ended up on the corridors of traders in Wall Street. Rightly so, it was Louis Bachelier who in 1900 first applied stochastic integration to problems in Finance. He preceded Einstein in finding a solution to processes driven by a Brownian motion. What a happy birth. It was Ito, the Japanese who gave one of the closed-form solutions widely used today. Consequently Black and Scholes and Merton established the formula used by traders on every part of the globe to price financial instruments since 1973. Popularly known as the Black-Scholes model (call it BS model) has even travelled as far to Ghana.

It is even used to price things such as the cost of shea butter (from the Northern part of Ghana) or cassava-dough (agbelimor from the traders in my village in Atikpui). It is used to price commodities such as cocoa, gold and coffee. Its area of influence is unbounded. It is used to price Electricity, foreign exchange and very recently Ghana's oil find would all be valuated using BS model. But its use comes with a cost.

Recently after the financial crush of 2008-2009, the Quants and their methods were held responsible. BS model was attacked for imposing unrealistic conditions on the market. Short selling is another culprit who caused the crush. Obviously it is regulated on some Exchanges around the world. Mortgage and credit-card use were not left out of the blame. Perhaps the loudest is Dr David Li's Gaussian copula formula for modelling risk. Ironically this formula was developed in 2000. Then maybe the crush started gradually thereafter. It was particularly selected for criticism because Banks based their collaterized debt obligation form of diversification on Li's model.

To the average Ghanaian, markets are Makola, Kantamanto, Kejetia, Ho Asigame, Bawku Cattle market. From historical times we hear Timbuktu used to be a flourishing market, just as the Ghana Empire was known for its trading activities. They might have never used BS model but they were flourishing markets. In Ghana, we hear often of Foreign Exchange Bureaux.

Today's modern market involves a computer freak sitting in front of a computer using automated trading systems such as Integrated FX, XETRA, CATS to do business with several people across the globe. This is the market. This market can even be located in the village of Atikpui. For now a business executive sitting in Ghana Stock Exchange in front of a digital computer connected to the internet could be trading. Of course the flow of electricity in Ghana is not continuous. So the market in Ghana may not be continuous. The BS model gets weak here. But we have stand-by generators.

Perhaps Electricity Company of Ghana is even trustworthy. If you are looking for a discontinuous movement of the flow of electricity, visit Abuja. This is perhaps the most modern and beautiful city in West Africa with friendly people, but trust me, you can always predict, with the same certainty that you can predict daybreak and nightfall that electricity would never flow constantly.

Now, this piece was meant to be a short one so I shall continue the next time with Part 2. I shall attempt to simulate stock price changes on Ghana Stock Exchange with the BS model. For now I can hear music behind my window. Guess what, they are dancing to a dance form that sounds like my surname, clapping their hands to music that I can faintly recollect: akodja yefere no se kyeya, akodja yefere no se kyeya…. yefere no se kyeya, yefere no se kyeya……

Credit: Paul A. Agbodza
(From Atikpui, Ghana)
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