Physics and Finance
By Melvin J. Howard
Belal E. Baaquie put out a book by Cambridge
University Press called Quantum Finance. This book applies the mathematics and
concepts of quantum mechanics and quantum field theory to the modelling of
interest rates and the theory of options. Particular emphasis is placed on path
integrals and Hamiltonians.
Financial mathematics is dominated by stochastic
calculus. The present book offers a formulation that is completely independent
of that approach. As such many results emerge from the ideas developed by the
author. This work will be of interest to physicists and mathematicians working
in the field of finance, to quantitative analysts in banks and finance firms
and to practitioners in the field of fixed income securities and foreign
exchange. The book can also be used as a graduate text for courses in financial
physics and financial mathematics. Applies the formalism of quantum mechanics
and quantum field theory to finance. Contains a detailed discussion on the
empirical aspects of the forward rate curve and comparison of the field theory
model with market data. Addresses many problems in finance that cannot be
solved using other approaches.
Remember the Black-Scholes model their options theory.
It goes something like this options are known to be divided into two types, the
first type is called a call option and the second type is called a put option
and these options are offered to stock holders in order to hedge their
positions against risky fluctuations of the stock price. It is important to
mention that due to fluctuations of the stock price, options can be found
sometimes deep in the money, at the money and out of the money. A deep in the
money option is described when the option's holder has a positive expected
payoff, at the money option is when the option's holder has a zero expected
payoff and an out of the money option is when the payoff is negative. It is
also possible that hedging leaves society worse off than it would be if
unhedged since it can make markets more volatile than they otherwise would be.
The rescue of LTCM by a consortium of banks after its near failure in September
1998 indicates that there were real fears that the liquidation of its positions
would threaten the entire financial system. Derivatives flourish in an
environment when the ability to pay is optimistic, where the creditworthiness
of the chain of issuers is not in doubt. Like in a bull market now flip to a
bear market and everything starts to unravel.
Much of the early success of LTCM was a result of the
credibility of Merton and Scholes, which attracted heavyweight investors,
lenders and trading partners to the firm, and their ideas, which provided
potentially profitable trading opportunities. But for all the brilliance of
their theory, it was based on 'expected volatility', which implicitly assumes
that history repeats itself, that the future movements of asset prices will
mirror their past movements. Unexpected events in the real world such the case,
of Russia's debt default was not calculated. That’s life soon as you think
you’ve got it figured out it changes on you.
Indeed, all models that are being used for risk
control and to buy assets on the basis of historical movements and small
increments using extraordinary leverage must be challenged. Now that Academia
and Finance have got together each working on a better theory for financial
engineering. Who knows which ones to pick the problem is you don’t know if you
are winning or losing until it’s too late hence LTCM. Financial science is just
as complex as theoretical physics, based on the fact that "energy is not
continuous but comes in small and discrete units," as one definition puts
it. "The movement of these particles is inherently random. It is
physically impossible to know both the position and the momentum of a particle
at the same time...[and] the atomic world is nothing like the world we live
in." Just like today's financial markets, in other words – a random,
unknowable and unreal world of atom-sized yields.
Quantum Finance – the science of making money appear
out of nowhere – is too complex for all but the very brightest to grasp. Yet it
underpins the entire financial universe today. The very fabric of money,
mortgages and markets has come to rely on concepts not even the sales desks can
follow. And Quantum Finance in its higher forms remains unregulated of course,
which is just as it should be. For by the time the SEC and FSA get round to
hiring the PhDs they need to make sense of the mess, the smart money will have
already moved on, selling out as their Lear Jets get cleared for take-off. What
about the dumb money, you may wonder? Well, if you can't spot the patsy, then
it must be you.
