Archive for the 'random' Category

Games and Decisions | take #02

February 12, 2011
  • Understanding incentives in online news distribution ? How about “social sharing” incentives ?  Consider the “like” game on Facebook and derive equilibrium conditions.

daily snapshot | 04 august 2010

August 4, 2010
  • Pricing / validating prices of new options using regression analysis ? Black-Scholes pricing essentially represents non-linear relationship between option price and price determinants (time to maturity, spot price, strike price, risk free rate, volatility + quantiles of normal distribution) 
  • The question is using option market trade data to create nonlinear model of this dependency – predict future prices using regression , calculate BS prices and compare values with actual traded prices.
  • Computational Complexity and Information Asymmetry in Financial Products
  • Thirty Books Everyone Should Read Before They’re Thirty – interesting selection
  • Use and abuse of dummy variable regression – differences between regression trees and single regression with dummies ? The danger of perfect collinearity with large number of boolean dummy variables.

Paul Wilmott et al : the math of financial derivatives | 45 min redux

July 30, 2010
  • A classical piece (1995) – focus on continuous side of financial math (SDEs etc.)
  • Basic intro – options, real world data, interest rates, continuous compounding, present value
  • Random walk nature of financial time series – discrete vs continuous walk – SDE representation
  • We base derivative strategies around time series / stochastic process statistics rather than estimation
  • Enter Ito’s lemma – description based on Taylor series expansion : ignore stochastic nature of function, get Taylor expansion of function value change due to delta-change in single function parameter, get differential of sde-representation of function, big-O analysis and series approximation, get approximated value back to Taylor expansion and voila ! – we have the relation of small change in function of random variable to the small change in the variable itself
  • Consequence of Ito’ lemma – we can relate change in dependent variable (which we can’t observe directly) to the change in observed dependent variable (statistically – these two variables should be perfectly correlated)
  • Obvious application : determining change in option price based on change in stock price (in general – this can be abstracted to any similar problem)
  • We can generalize Ito’s lemma by introducing time-dependency of function (that is – multivariate dependency)
  • Finally – we can derive probability distributions of variables and use standard probability toolkit to relate value range of variables with appropriate probabilities

statistics review : marginal regression | take #0

July 29, 2010

Popular concept often used in high-dimensional statistics is the notion of marginal regression – which essentially means regression on marginal variables. By marginal variable we assume any variable that is obtained by performing arithmetic operations on row/column data in original dataset.

Bagel’s Park blues

July 29, 2010

Among the narrow streets of Belgrade’s downtown, just across the Terazije tunnel – a small treasure is hidden. If you’re in the mood for pesto chicken bagels, fresh orange juice and a bit of espresso – it’s the best way to start your morning routine. Free wifi, large tables and just a bit of street schizophrenia – it’s just about the spot for the tech people to bootstrap their ideas.