This is for any other physicists who are attempting to learn the field of mathematical finance. I found a pretty cool book which might ease the transition. To be clear, it is in no way a substitute for a good introductory text (eg Concepts and Practice), but it might ease the transition. The book is called ``Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates'' by Baaquie.

To motivate why Quantum Mechanics MAY be useful for finance, consider that the Black-Scholes equation is basically the heat/diffusion equation, just like Schroedinger's equation. The analogy is a bit simpler if you exchange S<->x---so the spot price is like the position. (This also leads to the interesting relationship that

[S, dS/dt] = \sigma^2. )

The difference, of course, is that the Black-Scholes eq. has a first derivative wrt to time, which means that the Hamiltonian is non-unitary. In the language of QM, this just means that the forward evolution (in time) isn't really related to the backwards evolution (in time). This accounts for the lack of an i in the above relationship. Presumably, the path integral approach is much more natural, but I haven't read that chapter yet. And, the author spends a few chapters on applying quantum field theory to interest rate models.

At the end of the day, I don't know how useful this stuff is. (Interest rates are not constant, so being able to model them---to optimize hedges and such---seems important, at least.) The point is, the hardest part (for me) of learning a new field (aside from the jargon) is developing an intuition about how things work. But if I can parse all of finance in terms of things I already know, I can cut out a bit of pain from the process. To be sure, I don't ever expect to USE path integrals to price options.

Anyway, I'm interested to see if there are any other physics people around, who may have heard of/read this book, or any of the several papers on the subject you can find by googling ``Quantum Finance''.