Question for Acrary: Financial Mathematics

Discussion in 'Professional Trading' started by granville, Oct 3, 2005.

  1. acrary

    acrary

    A good introductory book is Thinking Strategically - The Competitive Edge in Business, Politics, and Everyday Life by Avinash K. Dixit and Barry J. Nalebuff

    When I was a new trader I thought trading was a tactical game.
    (Buy when x crosses y and sell when y crosses x). I knew I had to trade with the trend, but how to do it and avoid the losing trades was the name of the game. After awhile I noticed similar trades. I could enter and have a feeling the trade was going to workout. I don't believe much in intuition so I went on a search to find out what was going on.

    What I did was draw a sine wave on a piece of paper and mark the days high and low as the extremes of the wave. Then I marked the open and close in relation to the high/low. I noticed after a month of doing this that I had x days of one type and y days of another and z days of yet another, etc. I started dating the sheets and putting them in piles and did it everyday. What I found was a finite number of behaviors present in my market. I went back to the piles and figured the best entry and exit for each behavior I found. Then I tried to estimate which behavior was likely to be present in the market each day. If I suspected behavior 1 was present all I did was follow the best entry/exit and stop placement (if it wasn't that type of day) for the 1 pile. If behavior 2 then follow the 2 pile best strategy.

    The exercise taught me that my entry/exit only had relevance in light of the best strategy for the market I was trading. In essence, the strategy is much more important than anything else I can do. By focusing on the strategy my work is limited to determining what type of day I'm seeing and then working to optimize the entry and exit in light of it. I found it much easier to trade any market by using this approach since I didn't have to determine "are we going up?, down?, trending?, rangebound?, etc. in realtime"

    I've known for awhile that trading is a strategic game and game theory helps focus the mind to think in terms of determining and picking the best strategy for the situation.
     
    #11     Oct 5, 2005
  2. Very interesting, i will definitely check that book out. What you say definitely lines up with my experience. I have a system that i profitably trade. I never override it but i have a pretty good feel for the kinds of days (and situations) that it tends to do well / poorly. I have resisted messing with a good thing so to speak but what you describe sounds like the kind of framework i could use if i want to make my observations systematic.

    Thanks again for the lead on the book and sharing your experience.
     
    #12     Oct 5, 2005
  3. hightech

    hightech

    just how did you estimate the likely behaviour? This seems like a crucial element in the whole scheme.

    Overall, the idea of reducing the number of "behaviours" into finite buckets seems like a pretty good idea.

    thanx,

    hightech
     
    #13     Oct 6, 2005
  4. What is so special about one day? What if each hour the market is in a different "bucket", what about minutely.. yearly? This can happen on potentially infinite timescales. There has been some research on "market heterogeneity" in which they actually separated out roughly how many distinct timescales traders operate on.. check out the following paper.. Volatilities Of Different Time Resolutions: Analyzing the Dynamics Of Market Components



     
    #14     Oct 6, 2005
  5. A few months ago I actually wondered if I knew pretty much everything / all the tools available to someone looking to develop a system. All the books I would pick up at Borders or some other book store were all rehashing of the same topics.

    No sooner had I posed this thought to myself that I stumbled across such topics as volatility based risk control, trading the equity curve, real time optimization ... then not to mention all the posts here on ET. I began picking up a few statistics books and found that yes, I could understand it (with some work:) ) but that properly applying a statistical test or analysis was of paramount importance. I mean, just as in all disciplines, the topics can be simple enough to comprehend, but applying them properly requires real understanding.

    Its fascinating material and the applications of these methods can be very powerful.

    Thanks for all your posts,
    Adam
     
    #15     Oct 6, 2005
  6. newguy1

    newguy1

    i've never met a person on here or wilmott that suggested a fin math degree/understand would improve a daytrader's performance.

    I have a math background, and I had thought about going the masters fin math route prior to picking up a prop job.

    Since we are talking about it, have any of you found fin math useful in daytrading? If so, which markets, and what style of trading?
     
    #16     Oct 7, 2005
  7. thn5625

    thn5625

    I'm in a economics program and all the things acrary mentioned I've been exposed to- but used in other types of applications, industries, fields. My opinion would be to take on a graduate program thats econometrics intensive and take some finance electives. Oh, have a decent calculus/statistical background before you start. Whatever program you choose remember the math and statistics are tools. Its up to you to infer solutions and to use whatever you were taught in grad school in ways the professors have not. Thats why some engineers do well as quants since they are trained from the getgo to use math as tools rather than being an answer in itself.

    Acrary has posted some math that I have found very useful. It has been easier to understand since Ive been exposed to the math already in my grad program(although in nontrading applications) Thanks acrary!

    Programs I would try: financial mathematics, economics (mathematical/econometric based only), mathematics, statistics. Remember, going to these programs are by no means a ticket to success in trading, though, it may help you land a job as a quant.

    I also suggest trading now learning as you go. So far the math has been most useful in risk management/money management.
     
    #17     Oct 14, 2005