It would be interesting to compare two sciences of physics and finance. While one deals with the money the other deals with the physical universe. Both are important branches of studies so drawing a parallel between them will be interesting to many lovers of sciences.

Most of the theories in physics have models explaining a certain phenomenon. Whether it is electricity, magnetism, thermodynamics, gravitation each field has a subsets of models to explain various observations. For e.g. the Doppler Effect model in waves theory explains the plain variation of sound frequencies by a single set of equations. The Kirchhoff’s law explains the law of flow of electric current in a closed circuit of electricity is a model based on some set of equations. The financial theory in recent times has become model based where the price of options comes from Black S Merton models. There are a set of inputs required in the model to describe and price the option. Similar to the physics models where one need to put in several parameters values to find an ideal solution.

Uncertainty is common to both finance and quantum physics. Quantum physics has a ground in uncertainty and that everything we see is in a random state of motion. Everything is arbitrary and does not has well-defined laws that can predict the outcome. Heisenberg’s uncertainty principle states that the place and momentum of the electron cannot be determined simultaneously with exact precisions so where will be the electron located after sometime in the future cannot be determined exactly. Similar case happens in stock markets where an investor cannot be certain as where would be the index after sometime with exactness. There is always a degree of uncertainty associated with the market movements and thus closely resembles the Heisenberg’s principle. Interest rates are the most dynamic measure of all that keeps on changing with the time and shows volatility so predicting where it will go the next moment requires a rocket scientist who can by all his knowledge can come out with a shrewd model that can predict the interest rates sometimes if not all the times. This uncertainty is a very important concept that happens everyday in the financial world. The speculators, hedging traders and the arbitrage traders all face this uncertainty and the risk of the market movement that could loss or gain them financially.

The geometric Brownian motion describes the path of the particle suspended in a liquid. A physician first observed this random motion of a pollen grain suspended in a liquid to follow a random path termed as the Brownian motion. Einstein described these Brownian motion mathematically in his paper, giving a set of equations that could describe the path followed by the suspended particle. His equation explains that the path of the particle is jointly described by a constant displacement term and a volatility term. It is the set of these equations that explains today the path of interest rates, the path of stock market index or the volatility path.

In their famous paper Black S and Merton describes the path followed by the stock prices follows Brownian motion equations which laid the foundation for the famous Black S Merton model that is widely used today by traders all over the world to values options. Black did use the law of equilibrium of physics to lay the basic idea behind the Black S equation. The joint portfolio of a long stock and a short call option would yield the same constant risk free rate over a short period. So the joint position would always be restored to the same risk free return. Various interest rate models like the lee model, Ross model or the White Hull models are mathematically given by the same set of Brownian motion equation difference is only that they are different in their displacement terms and volatility terms to describe the interest rates movements. The displacement coefficient can depend on time, a constant or a zero.The volatility coefficient is also sometimes depends on time or on the volatility itself. Thus when it comes to determining an uncertain quantity in the future there comes into play Brownian motion equations.

Uncertainty plays a big role in valuation models used today for valuing securities like equity and bonds. There are a thousand of different scenarios of future are possible when forecasting the interest rates, earnings or the discount factors in the valuation exercise. Similar observations happens when calculating the path taken by electron. An electron can take a very large number of paths when moving from one place to another. Richard Feynman gave an approximate number for the path that the electron can take through his sum over histories methods. Similarly the earnings of the company can follow several paths. Monte Carlo simulation can see different scenarios of path and a final value calculated by taking a mean of values calculated from values observed in several different paths. The forecasted values could be misleading and could be totally different, in a similar fashion the electron place could be misleading and incorrect. So if price of a security cannot be determined precisely and exactly, the present state of the electrons cannot be used to predict the future place by the quantum theory precisely.

If there is uncertainty then some models and theories do come close to predicting the next outcome. Take such as the theory of photoelectric effect which has a single equation given by Einstein. Theory is simple and elegant and beautifully explains the observed phenomenon with high degree of precision experimentally. The bond valuation includes discounting the future cash flows which are certain to occur and through proper discount rates one can come close to exact present value of the bond in the market. Sometimes theories do come close in explaining the real world. If a physicist wants to explain the falling of a ball under gravity he would use equations of motion to describe the path of the body. The frequency of light in a heat radiation is given by energy divided by the Planck’s constant. Similar scenarios happens when a credit analyst wants to find the credit spread of a bond he would simply multiply the loss given default for the bond and the Probability of default for the bond.

Phenomenon of heat equilibrium states that the heat flow between two surfaces takes place until the temperatures of both the surfaces attains the same temperature and is in thermal equilibrium. Once the thermal equilibrium or two surfaces have equal temperatures the flow of heat stops. Arbitrage is the trading of incorrectly priced securities in different markets so if security is over-priced in one market trader sells in that market and buys in the market where it is under-priced until the price levels are same in both the markets. So flow of security takes place from the market where it is under-priced to the market where it is over-priced. See how temperature and price are analogous in explaining the two different phenomena’s in same way. So money is flowing from one market to another market in the same way that the heat is flowing from one surface to another surface till the state of equilibrium of prices or temperatures reaches.

The quantitative theory of money states that measure of money in the economy determines inflation. So if money supply increases then there is inflation and if the money supply decreases then there is lower inflation. It could be compared with the heating of a body so that if the temperature of the body increases the heat radiates in large proportions to the fourth power of temperature and if it lowers then the heat radiated lowers proportionally. The inflation measures the amount of excess money in the economy in a similar way the temperature of the body measures the amount of excess heat in the body.

Thus overall the theories of finance and physics could be seen in a similar way except that they are taking place in two different worlds. Various theories have models that have a few set of parameters. There is uncertainty in some theories then there is some certainty in other theories in explaining the observed phenomenon. Laws of electricity, magnetism, gravitation and heat are applicable in finance also but not in same way as in physics. The same sets of explanations characterize what happens in both the worlds in the end they are different sciences. While physics deals with the study of nature and observed phenomenon then finance deals with the study of markets and its instruments.Nevertheless some parallels can still be drawn that should not sound meaningless.