Friday, August 1 -- Mandelbrot's Multifractal Model of Asset Return
Review
Yesterday: You did serious simulated trading using IB and you learned about and experimented with numerous easy-to-describe trading strategies. These strategies were certainly not built on any nontrivial understanding or model of stock markets.
Our two goals for the rest of this course:
- Describe a framework for a possibly real model of financial markets (the Multifractal Model of Asset Return)
- Describe a powerful computational technique for making inferences about time series (Hidden Markov Models)
Two Quotes
"It is beyond belief that we know so little about how people get rich or poor, about how it is they come to dwell in comfort and health or die in penury and disease. Financial markets are the machines in which much of human welfare is decided; yet we know more about how our car engines work than about how our global financial system functions. We luch from crisis to crisis. So limited is our knowledge that we resort, not to science, but to shamans." -- Mandelbrot, Page 254-255.
" July 31 (Bloomberg) -- The U.S. economy shrank at the end of 2007 and grew less than forecast in this year's second quarter, signaling that the country is in worse shape than investors had anticipated. We're in a recession, Allen Sinai, chief economist at Decision Economics Inc. in New York, said in a Bloomberg Television interview. It's going to widen, it's going to deepen." -- From Bloomberg today
Schedule
- (20 minutes) The Sequence of log Returns Revisited (Day 4 WS 1)
- (30 minutes) The Hurst exponent and Self Similarity (Day 4 WS 2)
- (30 minutes) Fractional Brownian Motion (Day 4 WS 3)
- (10 minutes) Break
- (20 minutes) Fractal Meastures and trading time (Day 4 WS 4)
(30 minutes) Mandelbrot's Multifractal Model of Asset Return (Day 4 WS 5), (see Mandelbrot's paper)
- (10 minutes) Stock trading
- Reading Assignment: Read some of "Rabiner -- A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition"