De-Mystifying "Rocket Science"
Feb 21, 2005
In the mid-eighties most finance practitioners with liberal arts or just MBA background on Wall Street mistakenly thought that the science of – or rather, the physics of - rocketry is perhaps the most difficult branch of science. Hence they started calling the physicists who migrated from the academia to Wall Street “rocket scientist”. These days they are simply called “quants”. Also, “quants” is a more generalized term for all physicists, mathematicians and computer scientists who have made their way into the field of finance and who are generally concerned with model building aspects of asset prices and derivative products.
But the phrase is certainly pertinent now as it was then, because a lot of what goes on in the area of quantitative finance is premised upon not only the physics of rocketry but quantum mechanics as well. Incidentally, quantitative finance is just another term for financial engineering or the science of manufacturing, analyzing and reverse engineering financial products made up of assets like stocks, bonds, currencies, etc. and their derivatives.
Take the famous equation of a parabola given by ax2 + bx + c = 0 where is any variable quantity and a, b and c are constants. This is the equation that we have all studied in our high school algebra and those of us who have studied physics or mechanical engineering in our graduate degrees have encountered this equation in a variety of different form for projectile motion. One such variation was d = ut² + bt + c where d is the distance and t is the time taken by an object. This equation with the constants is also an equation of a parabola. This equation can be called an equation of rocket science as it forms the fundamental equation upon which the motions of rockets and satellites are based.
But what does an equation of parabolic motion got to do with finance? Well, nothing and everything. The one of the best examples of this can be found in the area of market risk management. When fixed income or interest sensitive cash flows, such as those of swaps, bonds, FRAs, etc. are mapped on to risk factors in calculating the diversified value at risk (VaR) of a portfolio an equation exactly like the above - the equation of a parabola - is used to find out how much of the given cash flow to map onto a particular risk factor vertex. In that case x, the variable quantity, is the amount of cash flow.
Another example of a parabolic equation is the famous heat transfer equation in physics. The simplest form of a heat transfer equation is of the form ∂H / ∂t = ∂²H / ∂t². If you carefully look at this equation you will realize that this equation can also be reduced to a simple equation of a parabola as sated above, with a certain constants and the variable quantity is simply . This equation is actually called a partial differential equation, but is nevertheless a parabolic equation. The option pricing equation in quantitative finance is exactly similar to this equation. The only change is a change in variables and the boundary conditions. There are scores of equations in financial economics, most notably in the areas of option pricing and volatility modelling which are parabolic in nature. They are all essentially of the form of ax² + bx + c = 0 If we adjust the variables in certain manner most equations in financial economics can be transformed into heat transfer equation.
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