via Big Picture - How Subprime Really Works  - hysterical - really.

So - I an effort to get back in the game with my maths, I have ordered a series of books and I am planning on weekly study time. Here is my basic list:

Calculus:

• Functions and limits

• Differentiation and integration

• Taylor series

• Complex numbers

• Functions of several variables

• Gamma and beta function

• Numerical integration

Differential Equations:

• First order equations

• Second and higher order equations

• Partial Differential Equations

• Diffusion equation

• Black-Scholes equation

Linear Algebra:

• Matrices and Vectors

• Systems of linear equations

• Eigenvalues and eigenvectors

• Vector spaces

Elementary Probability Theory:

• Discrete and continuous distributions

• Simple moments (mean and variance)

• Higher moments (skew and kurtosis)

• Important distributions

• Correlation

• Central Limit Theorem

Basic Stochastic Calculus:

• Random walks/SDE

• Brownian motion and Itô’s lemma

• Basic Monte Carlo

This is taken from the Wilmott’s Maths Primer. I have been considering taking the Wilmott/ 7City CQF. I am obviously interested in continued automated trading efforts. I am relatively strong with the probability/ statistics driven work - I have done the most professionally there. I am also obviously interested in the business of trading, including more and more derivative products. I have been able to work with quants in the past to implement automated systems. The way I figure it - the more I can work directly with quants, the closer I am to doing more and more of quantitatively minded fully automated real time trading.

I will let you know how it goes - my continued maths studies.

-Chris-

So - I posted earlier about the Fed’s shocker cut this week. It turned out to be an amazingly volatile week for the global markets- 1 day in the US - the Dow had a ~600 point swing (that is around the 3rd biggest % swing day ever for the Dow). The Hang Seng was down ~10% one day, up 5%/ 6% on other days. The Stoxx 50 had similar volatility - just huge global markets volatility.
Also Societe Generale Reports EU4.9 Billion Trading Loss.because of a rogue, evil, bad, no-goodnik trader. Shocking in and of itself. This morning I was reading John Mauldin’s weekly markets newsletter. He points over to a Financial Times article “Markets ask if the Fed was duped?”. Essentially - the idea is that - SocGen accounted for some 10% of the market action as it unwound its evil, bad, wrong way trade… thus driving down the global markets.

It is not supposed to be the Fed’s remit to manage the stock market - so there is plenty of criticism of the Fed for seemingly reacting to big down futures prices and downtrending global markets. Via Big Picture or Seeking Alpha - you can see the same article titled “Fed’s Folly: Fooled by Flawed Futures”. It says basically the same stuff - why is the fed reacting to the futures pit? Too bad we did not know Soc Gen was unwinding a mega fraud position. As I put said the other day - so much for the decoupling in global markets.

John Mauldin goes on to say he thinks the Fed believes the bond insurers are in more trouble than most think, etc, etc. Perhaps the Fed move will have helped us or not -either way - it is all amazing stuff. Dram of a global scale.

-Chris

I just can’t help but comment on the markets. Today was really an amazing day in the global markets. I went to bed last night and saw the Hang Seng was down some … 7% or 8% - that is steep. I woke up, flipped on the TV for the kids - it was on .. CBS news and they were talking about the ‘destroyed markets in Asia this morning’. Amazing - Asian markets getting crushed - all off by 5-10%. European markets - Stoxx 50, the FTSE - all look like death as well. This was an abnormally bad morning for the world.

As I got to the office - there were several folks on their Bloomberg terms watching the US futures off by some large numbers - the DOW futures were down some 500+ points. There was more chatter than usual - more folks than usual obsessively watching the markets - complaining about trades they made that they were now pissed about, etc.

Then - surprise fed move - cut .75 basis points. Futures flicker and wave, stoxx 50 recovers, markets open. My basic prediction was gap down, trend up day for the US markets - which proved to be the case.

Anyhow - 2 points:

1. The US economy is not in the best of shape. (The rates game has a funny way of devaluing our currency doesn’t it!?!?!)
2. The global markets are really, really, really coupled.

The comments from ‘the market gurus’ of the media and world were of course amusing. “NO big deal” to “the end of the world”.

Anyhow - I just had to comment on the day - it was impressive.

-Chris

PS - Here are a few links - the stuff I read daily regarding the markets:

• Seeking Alpha
• VIX and More
• The Big Picture
• The Money Blogs (warning - some crap here, but also some goodies)
• Of course Bloomberg, Reuters, CNBC

Newsgator RSS aggregator comes in handy

(I had this stupid post 75% typed, and my IE crashed… Microsoft, Vista and friends have been GETTING ON MY NERVES!) 

So… I had a recent post about variance swaps. I have been thinking a fair bit about the ideas of volatility - it is after all what options are all about. It is just interesting to me how darn versitile options are. It is possible to put together really novel views of risk depending on your options strategy. Strategies focused on volatility are what I am currently working through mentally. 

How to profit from volatility
Here is a good post on volatility strategies using vanilla options. Essentially - you can put together combinations of options that allow you to “focus in on” and profit based on the volatility characteristics/ changes. They mention the concept of volatility of volatility which reminds me of some work I did in the past with a guy named Lester Ingber - really, really bright guy. 

Volatility of Volatility
Lester’s article on Volatility of Volatility. This is interesting inasmuch as it is another layer of derivation on top of volatility. The idea that volatility itself has volatility is just another example of the complex mechanics that make up the financial world we are part of. We did work in this space looking at ways to achieve “adaptation” of trading system parameters based on volatility - and on volatility of volatility. Lester’s work is excellent - I also suggest reading his CMI work here and his work on Adaptive Simulated Annealing (the work I originally found him for) is also excellent. 

Dispersion Trading 
I have also been working over dispersion trading ideas - here is a good article from IVolatility.com (Good site, I used to get IV info from these guys for implementing an ETF trading strategy based on options and opening range breakout). 

Volatility Arbitrage
Daily options report has a good set of posts on volatility arb’ing. The most recent post is pointing to potential arb opportunities between the VIX and VXN - or the S&P market and NASDAQ market. The article mentions “mean reversion of volatility” - which brings me back to a few years ago… 

Toby Crabel and Mean Reversion
Toby Crabel is a relatively famous trader that popularized (to the best of my understanding) a particular trade patter for stocks and futures based on HV ratios. Essentially - you take a short range return/ longer range return and you get a ratio. This basically says things to you like; “today the volatility is relatively low” or “yesterday the volatility was relatively high”. The idea is based on the concept that “volatility is mean reverting“. This means that when volatility is relatively high, it is more likely it will be relatively low next. Often volatility arbing strategies depend on this concept. I worked through most of the “crabel-isms” a few years back while working on automated trading strategies based on some of Crabel’s ideas. 

All of this volatility stuff does bring me back to past experiences. The difference is that in the past we were looking at this information for different reasons. Currently, I am trying to understand all the more the detailed bits and pieces that would allow you to make trades that allow you to trade a view on volatility… interesting stuff!!! 

-Chris 

 

In working on a current trader interface - I am dealing with more derivs traders. Along with other things - we will be dealing in Variance Swaps. I have good product knowledge in some areas - and in some areas - I am still learning (finance is a big world). In any case - I am always trying to understand the “business incentive” for using a particular product. In trying to understand this for variance swaps - I found this article that gave me just the angle I was looking for: The Art of the Variance Swap. Here are  a few more refs; Volatility Swaps (technical), @ Wikipedia.

 -Chris