## Phynance 101

If you have any questions related to anything I discuss here or anything related to mathematical phynance in general, please feel free to ask in a comment here.

Advertisements

If you have any questions related to anything I discuss here or anything related to mathematical phynance in general, please feel free to ask in a comment here.

Advertisements

Written by Eric

July 24, 2008 at 11:18 am

Subscribe to comments with RSS.

search site archives

- Accrued Interest
- Across the Curve
- Alea
- Calculated Risk
- Central Bank Speeches and Articles
- Digital Lifescapes
- Economic Darwinism
- Financial Armageddon
- Midnight Diaries (εε€θ―»δΉ¦) – China market commentary
- naked capitalism
- Perfectly Reasonable Deviations
- Quantivity
- Techmeme
- Technology Futures
- The Big Picture
- The n-Category Cafe

- February 2013
- January 2013
- October 2012
- August 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- April 2011
- January 2011
- December 2010
- November 2010
- October 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- August 2009
- May 2009
- April 2009
- February 2009
- January 2009
- December 2008
- June 2008
- May 2008
- April 2008
- February 2008
- January 2008
- December 2007
- November 2007
- October 2007
- September 2007
- August 2007
- July 2007

- 3D TV
- Aaron Brown
- ABX
- Anna Schwartz
- Arbitrage Pricing
- Asset Price Inflation
- Azimuth Project
- Balance Sheets
- Bear Stearns
- BNP Paribas
- Broadband
- Cash bonds
- Category Theory
- CCD
- CDO
- CDS
- China
- CLO
- Consumer Spending
- Corporate Leverage
- CPI
- Credit
- Currencies
- David Richards
- Default Rates
- Deflation
- Directed Graphs
- Discount Rate
- Discrete Calculus
- Doyne Farmer
- Economic Darwinism
- Economics
- Electromagnetic Radiation
- Employment
- ETF
- Fair Value Accounting
- Federal Reserve
- Fiber Optics
- Finance
- Fixed Income
- Flight to Quality
- FX Rates
- General Update
- Gold
- Goldman Sachs
- Great Investors
- High Yield
- Housing Market
- Hyman Minsky
- India
- Inflation
- Japan
- Jeremy Grantham
- John Baez
- Knowledge Economy
- LBO
- Leverage
- Leveraged ETF
- LTCM
- M&A
- Mark to Market
- Market Risk
- Markets
- Mathematical Finance
- Matlab
- Maximum Likelihood Estimation
- Modeling
- Monetary Policy
- Mortgages
- Navigation
- Network Theory
- Nuclear Phynance
- Oil
- Pension Funds
- Personal
- Petrodollars
- Private Equity
- Protectionism
- Quantitative Analysis
- Quants
- Ratings Agencies
- Recession
- Resonance
- Retail Investors
- Richter Scales
- Risk Management
- Russia
- SAS
- Savings Glut
- Seabirds
- SFAS 140
- Sovereign Wealth Funds
- Stable Distributions
- Statistics
- Structured Finance
- Tanta
- Uncategorized
- US Treasuries
- VaR
- Visualization
- Wealth Effect
- Wi-Fi

%d bloggers like this:

Hello Mr. Forgy,

I think your site is full of interesting topics! As I have a (albeit only a master’s) degree in physics and I somehow ended up working in the derivatives business, I have been wondering about the following for quite a while; perhaps you can shed some light on it?

Is it possible to arrive directly at the Schrodinger equation in the continuum limit by constructing a complex binomial lattice with a (constant) diffusion sigma = sqrt(i*hbar/m), where i is the complex number, hbar is planck’s constant, and m the particle’s mass?

Cheers, Frido

Frido RolloosDecember 28, 2008 at 3:56 am

Hey! That’s “Dr Forgy”! *just kidding* π

Thanks for your question Frido. Yes, just as you can arrive at Black Scholes via a continuum limit of the binary tree, you can also arrive at Schrodinger via a continuum limit of a complex binary tree. My favorite way to see this is via my paper:

Financial Modeling Using Discrete Stochastic Calculus

https://phorgyphynance.files.wordpress.com/2008/06/discretesc.pdf

In this way, you see it via the fact that the “calculus” itself on a tree converges to the continuum calculus, so anything you build on a tree will converge in the continuum limit. In particular, on a general tree, the discrete calculus results in four commutative relations:

I showed two different continuum limits.

1.) , (leads to exterior calculus)

2.) , (leads to stochastic calculus)

There is a third continuum limit you could take, i.e.

3.) , (leads to Schrodinger)

This is just the “Wick rotation” of 2.)

There are other ways to see quantum stuff from continuum limits. You might enjoy the “Feynman checkerboard” if you haven’t seen it. There, the Dirac equation pops out of a complex random walk. Very neat.

By the way, if you decide to have a look at some of my papers, I’m happy to try to answer any questions you might have.

Cheers and have a happy new year!

phorgyphynanceDecember 28, 2008 at 8:05 am

Mr. Dr. Forgy, thanks for your speedy reply! π

It’s been a while since I’ve done some noncommutative calculus (wrote my thesis on it), but definitely will read your papers on noncommutative geometry & finance. I could be wrong, but as far as I know many theorists in the physics community are not aware that there is a discrete structure approximating, or perhaps underlying, the Schrodinger eqt. and that discrete calculus is an elegant way to derive/show it.

Happy new year to you too, and will most probably ask you more questions in the new year!

Frido RolloosDecember 28, 2008 at 9:37 am

Hey Eric,

You might wanna take a quick look at this paper: Graphical models for correlated defaults. It’s not everyday that you see an algebraic geometer writing a paper on CDOs!

Cheers

-R

Rod CarvalhoJuly 9, 2009 at 1:57 am