Theoretical Physics and Finance...?

The above title may seem the start of a good laugh. But it is not. Actually many physicists at the Ph.D. level turn for jobs on financial markets. Why? The pay may seem a good reason. But a more important argument is to work in team atmosphere (even if tough and demanding), fully employing and pulling your abilities to their best. And this means your intelectual, social, personal and physical capacities altogether. Abstract reasoning and conceptual thinking are the kind of abilities one uses in dealing with supersymmetry and quantum cosmology. Well, it is also what it is required when investigating complicated financial products.

But can one use physics in finance, I hear you say? Well, you must!

The financial markets are led by purely mathematics-based products. Physicists are required to develop products and strategies and generally prove and disprove theories. In more simple terms, they need to consider different factors (say, different time zones and different currencies and markets) and maximize the upside of the markets and minimize the risks.

The physicists have to program, develop algorithms, construct differential (price) equations and solve them, then expalin the results in plain english to the traders. Instead of wave functions and phase transitions one has to comtemplate other concepts such as derivatives and options. Neural networks, sthocastic calculus and linear programming are also useful tools, together with Monte-Carlo simulations.

Brilliant, you say, but can a practical example be given, where the use of physics is helpful?

Let us then contemplate the concept of derivative. First of all, a derivative is a security: a general name for stocks and shares. But a derivative is a security whose price is derived from other quantities. Futures and options are special types of derivatives.

A future is an agreement to buy or sell something at a given time in the future for a priced agreed now. No money transfers occur initially although the buyer has to put up some form margin to cover potential losses.

An option is when one has to pay a small amount now for the right (not the obligation) to buy or sell something at a given price at some time in the future. Let us suppose I pay 5 now to buy the option to buy some shares, currently worth 95, at a price of 100 in six months. If in six months the shares are worth 110 I can seel immediatly: for the 5 pounds I invisted I got 10: a profit of 100%! If I had bought the shares for 95 and sold it by 110, the profit would of 16%. If the shares never raise above 100, I lose my initial 5 pounds investment.

Physicists come in this scenario because options and all that are related within partial differential equations. These equations involve also other elements such as volatility parameters and boundary conditions, which specify the the type of derivative (a similar feature happens in quantum cosmology wherey different boundary conditions lead to several wave functions of the universe: Hartle-Hawking's, Vilenin's, etc). In some type of derivatives the equation above mentioned becomes a diffusion equation, which can be solved backwards in time. Attractive comparisons with the Schroedinguer equation and scattering processes in quantum phsyics are evident.

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